Optimal Parametric Feedback Excitation of Nonlinear Oscillators
Braun, David J.
2016-01-01
An optimal parametric feedback excitation principle is sought, found, and investigated. The principle is shown to provide an adaptive resonance condition that enables unprecedentedly robust movement generation in a large class of oscillatory dynamical systems. Experimental demonstration of the theory is provided by a nonlinear electronic circuit that realizes self-adaptive parametric excitation without model information, signal processing, and control computation. The observed behavior dramatically differs from the one achievable using classical parametric modulation, which is fundamentally limited by uncertainties in model information and nonlinear effects inevitably present in real world applications.
Tuneable, non-degenerated, nonlinear, parametrically-excited amplifier
Dolev, Amit; Bucher, Izhak
2016-01-01
The proposed parametric amplifier scheme can be tuned to amplify a wide range of input frequencies by altering the parametric excitation with no need to physically modify the oscillator. Parametric amplifiers had been studied extensively, although most of the work focused on amplifiers that are parametrically excited at a frequency twice the amplifier's natural frequency. These amplifiers are confined to amplifying predetermined frequencies. The proposed parametric amplifier's bandwidth is indeed tuneable to nearly any input frequency, not bound to be an integer multiple of a natural frequency. In order to tune the stiffness and induce a variable frequency parametric excitation, a digitally controlled electromechanical element must be incorporated in the realization. We introduce a novel parametric amplifier with nonlinearity, Duffing type hardening, that bounds the otherwise unlimited amplitude. Moreover, we present a multi degree of freedom system in which a utilization of the proposed method enables the projection of low frequency vector forces on any eigenvector and corresponding natural frequency of the system, and thus to transform external excitations to a frequency band where signal levels are considerably higher. Using the method of multiple scales, analytical expressions for the responses have been retrieved and verified numerically. Parametric studies of the amplifiers' gain, sensitivities and spatial projection of the excitation on the system eigenvectors were carried out analytically. The results demonstrate the advantage of the proposed approach over existing schemes. Practical applications envisaged for the proposed method will be outlined.
Bifurcations of a parametrically excited oscillator with strong nonlinearity
Institute of Scientific and Technical Information of China (English)
唐驾时; 符文彬; 李克安
2002-01-01
A parametrically excited oscillator with strong nonlinearity, including van der Poi and Duffing types, is studied for static bifurcations. The applicable range of the modified Lindstedt-Poincaré method is extended to 1/2 subharmonic resonance systems. The bifurcation equation of a strongly nonlinear oscillator, which is transformed into a small parameter system, is determined by the multiple scales method. On the basis of the singularity theory, the transition set and the bifurcation diagram in various regions of the parameter plane are analysed.
Nonlinear Dynamical Analysis for the Cable Excited with Parametric and Forced Excitation
Directory of Open Access Journals (Sweden)
C. Z. Qian
2014-01-01
Full Text Available Considering the deck vibration effect on the cable in cable-stayed bridge, using nonlinear structure dynamics theory, the nonlinear dynamical equation for the stayed cable excited with deck vibration is proposed. Research shows that the vertical vibration of the deck has a combined parametric and forced excitation effect on the cable when the angle of the cable is taken into consideration. Using multiscale method, the 1/2 principle parametric resonance is studied and the bifurcation equation is obtained. Despite the parameters analysis, the bifurcation characters of the dynamical system are studied. At last, by means of numerical method and software MATHMATIC, the effect rules of system parameters to the dynamical behavior of the system are studied, and some useful conclusions are obtained.
NONLINEAR FARADAY WAVES IN A PARAMETRICALLY EXCITED CIRCULAR CYLINDRICAL CONTAINER
Institute of Scientific and Technical Information of China (English)
菅永军; 鄂学全; 柏威
2003-01-01
In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode bysolving potential equations of water waves in a rigid circular cylinder, which is subject to avertical oscillation. It is assumed that the fluid in the circular cylindrical vessel is inviscid ,incompressible and the motion is irrotational, a nonlinear amplitude equation with cubicand vertically excited terms of the vessel was derived by expansion of two-time scales withoutconsidering the effect of surface tension. It is shown by numerical computation that differentfree surface standing wave patterns will be formed in different excited frequencies andamplitudes. The contours of free surface waves are agreed well with the experimental resultswhich were carried out several years ago.
Energy Technology Data Exchange (ETDEWEB)
Zhang Wei [College of Mechanical Engineering, Beijing University of Technology, Beijing 100022 (China)] e-mail: sandyzhang0@yahoo.com
2005-11-01
This paper presents an analysis of the chaotic motion and its control for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. A new method of controlling chaotic motion for the nonlinear nonplanar oscillations of the cantilever beam, refereed as to the force control approach, is proposed for the first time. The governing nonlinear equations of nonplanar motion under combined parametric and external excitations are obtained. The Galerkin procedure is applied to the governing equation to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations for the in-plane and out-of-plane modes. The work is focused on the case of 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance-primary resonance for the out-of-plane mode. The method of multiple scales is used to transform the parametrically and externally excited system to the averaged equations which have a constant perturbation force. Based on the averaged equations obtained here, numerical simulation is utilized to discover the periodic and chaotic motions for the nonlinear nonplanar oscillations of the cantilever beam. The numerical results indicate that the transverse excitation in the z direction at the free end can control the chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam. The methodology of controlling chaotic motion by using the transverse excitation is proposed. The transverse excitation in the z direction at the free end may be thought about to be an open-loop control. For the problem investigated in this paper, this approach is an effective methodology of controlling chaotic motion to a period n motion or a static state for the nonlinear nonplanar oscillations of the cantilever beam.
Parametrically Excited Nonlinear Two-Degree-of-Freedom Systems with Repeated Natural Frequencies
Directory of Open Access Journals (Sweden)
A. H. Nayfeh
1995-01-01
Full Text Available The method of normal forms is used to study the nonlinear response of two-degree-of-freedom systems with repeated natural frequencies and cubic nonlinearity to a principal parametric excitation. The linear part of the system has a nonsemisimple one-to-one resonance. The character of the stability and various types of bifurcation including the formation of a homoclinic orbit are analyzed. The results are applied to the flutter of a simply supported panel in a supersonic airstream.
Non-linear stochastic optimal control of acceleration parametrically excited systems
Wang, Yong; Jin, Xiaoling; Huang, Zhilong
2016-02-01
Acceleration parametrical excitations have not been taken into account due to the lack of physical significance in macroscopic structures. The explosive development of microtechnology and nanotechnology, however, motivates the investigation of the acceleration parametrically excited systems. The adsorption and desorption effects dramatically change the mass of nano-sized structures, which significantly reduces the precision of nanoscale sensors or can be reasonably utilised to detect molecular mass. This manuscript proposes a non-linear stochastic optimal control strategy for stochastic systems with acceleration parametric excitation based on stochastic averaging of energy envelope and stochastic dynamic programming principle. System acceleration is approximately expressed as a function of system displacement in a short time range under the conditions of light damping and weak excitations, and the acceleration parametrically excited system is shown to be equivalent to a constructed system with an additional displacement parametric excitation term. Then, the controlled system is converted into a partially averaged Itô equation with respect to the total system energy through stochastic averaging of energy envelope, and the optimal control strategy for the averaged system is derived from solving the associated dynamic programming equation. Numerical results for a controlled Duffing oscillator indicate the efficacy of the proposed control strategy.
Directory of Open Access Journals (Sweden)
Paulo S. Varoto
2006-01-01
Full Text Available Flexible structures are frequently subjected to multiple inputs when in the field environment. The accurate determination of the system dynamic response to multiple inputs depends on how much information is available from the excitation sources that act on the system under study. Detailed information include, but are not restricted to appropriate characterization of the excitation sources in terms of their variation in time and in space for the case of distributed loads. Another important aspect related to the excitation sources is how inputs of different nature contribute to the measured dynamic response. A particular and important driving mechanism that can occur in practical situations is the parametric resonance. Another important input that occurs frequently in practice is related to acoustic pressure distributions that is a distributed type of loading. In this paper, detailed theoretical and experimental investigations on the dynamic response of a flexible cantilever beam carrying a tip mass to simultaneously applied external acoustic and parametric excitation signals have been performed. A mathematical model for transverse nonlinear vibration is obtained by employing Lagrange’s equations where important nonlinear effects such as the beam’s curvature and quadratic viscous damping are accounted for in the equation of motion. The beam is driven by two excitation sources, a sinusoidal motion applied to the beam’s fixed end and parallel to its longitudinal axis and a distributed sinusoidal acoustic load applied orthogonally to the beam’s longitudinal axis. The major goal here is to investigate theoretically as well as experimentally the dynamic behavior of the beam-lumped mass system under the action of these two excitation sources. Results from an extensive experimental work show how these two excitation sources interacts for various testing conditions. These experimental results are validated through numerically simulated results
Wang, Yi-Ze; Wang, Yue-Sheng; Ke, Liao-Liang
2016-09-01
In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.
DEFF Research Database (Denmark)
Sorokin, Vladislav; Thomsen, Jon Juel
2015-01-01
Parametrically excited systems appear in many fields of science and technology, intrinsically or imposed purposefully; e.g. spatially periodic structures represent an important class of such systems [4]. When the parametric excitation can be considered weak, classical asymptotic methods like...... the method of averaging [2] or multiple scales [6] can be applied. However, with many practically important applications this simplification is inadequate, e.g. with spatially periodic structures it restricts the possibility to affect their effective dynamic properties by a structural parameter modulation...... of considerable magnitude. Approximate methods based on Floquet theory [4] for analyzing problems involving parametric excitation, e.g. the classical Hill’s method of infinite determinants [3,4], can be employed also in cases of strong excitation; however, with Floquet theory being applicable only for linear...
Chacón, R.; García-Hoz, A. Martínez; Martínez, J. A.
2017-05-01
We study the effectiveness of locally controlling the impulse transmitted by parametric periodic excitations at inducing and suppressing chaos in starlike networks of driven damped pendula, leading to asynchronous chaotic states and equilibria, respectively. We found that the inducing (suppressor) effect of increasing (decreasing) the impulse transmitted by the parametric excitations acting on particular nodes depends strongly on their number and degree of connectivity as well as the coupling strength. Additionally, we provide a theoretical analysis explaining the basic physical mechanisms of the emergence and suppression of chaos as well as the main features of the chaos-control scenario. Our findings constitute proof of the impulse-induced control of chaos in a simple model of complex networks, thus opening the way to its application to real-world networks.
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability...
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability o...
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.
Institute of Scientific and Technical Information of China (English)
侯之超; 祖武争
2004-01-01
Nonlinear dynamic analysis is performed on moving belts subjected to geometric nonlinearity and initial tension fluctuation.To incorporate more accurately the damping mechanism of belt material, linear viscoelastic models are adopted in a unified form of differential operators.To circumvent high-order differential vibration equation of time-varying coefficients and with gyroscopic and nonlinear terms, where analytical solution is almost impossible, a systematic approach is presented by reforming the motion equation and directly using the method of multiple scales.To exemplify the procedure, the solutions at principal resonance are obtained and their stability conditions are derived for employing a Kelvin-Voigt model to reflect the property of the belt material.The solutions and stability conditions successfully reduce to those for using Kelvin model and elastic model, which validate the present approaches.Numerical simulations highlight the effects of tension fluctuations and translating speeds on the stability of the belt vibration.
Parametrically Driven Nonlinear Oscillators with an Impurity
Institute of Scientific and Technical Information of China (English)
张卓; 唐翌
2002-01-01
By virtue of the method of multiple scales, we study a chain of parametrically driven nonlinear oscillators with a mass impurity. An equation is presented to describe the nonlinear wave of small amplitude in the chain.In our derivation, the equation is applicable to any eigenmode of coupled pendulum. Our result shows that a nonpropagation soliton emerges as the lowest or highest eigenmode of coupled pendulum is excited, and the impurity tends to pin the nonpropagation soliton excitation.
Institute of Scientific and Technical Information of China (English)
Su Min-Bang; Rong Hai-Wu
2011-01-01
The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over "fast" variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the case without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value,or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.
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...
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...
Frequency detuning effects for parametrically and directly excited elastic structures
DEFF Research Database (Denmark)
Neumeyer, Stefan; van Gastel, M. H. M.; Sorokin, Vladislav
2015-01-01
numerical integration and experiments showing good agreement. For frequency detuned superthreshold parametric excitation some of the theoretical frequency-amplitude solution branches appear to merge. For some ranges of parametric excitation frequency a drop in experimental steady-state vibration amplitude...... was found, indicating performance degradation whereas for other frequency ranges, frequency detuning may yield an increased steady-state vibration amplitude. This makes frequency detuning a feature which can purposefully be avoided or utilized, dependent on the application.......This study investigates the frequency detuning effects of parametric and direct excitation for near-resonant nonlinear structural vibrations. Specifically, the detuning effects of a two-to-one frequency ratio between the parametric and direct excitation, and of a drift in natural frequency...
Modeling of autoresonant control of a parametrically excited screen machine
Abolfazl Zahedi, S.; Babitsky, Vladimir
2016-10-01
Modelling of nonlinear dynamic response of a screen machine described by the nonlinear coupled differential equations and excited by the system of autoresonant control is presented. The displacement signal of the screen is fed to the screen excitation directly by means of positive feedback. Negative feedback is used to fix the level of screen amplitude response within the expected range. The screen is anticipated to vibrate with a parametric resonance and the excitation, stabilization and control response of the system are studied in the stable mode. Autoresonant control is thoroughly investigated and output tracking is reported. The control developed provides the possibility of self-tuning and self-adaptation mechanisms that allow the screen machine to maintain a parametric resonant mode of oscillation under a wide range of uncertainty of mass and viscosity.
On the unlimited gain of a nonlinear parametric amplifier
DEFF Research Database (Denmark)
Sorokin, Vladislav
2014-01-01
The present paper is concerned with analysis of the response of a nonlinear parametric amplifier in abroad range of system parameters, particularly beyond resonance. Such analysis is of particular interestfor micro- and nanosystems, since many small-scale parametric amplifiers exhibit a distinctly...... nonlinearbehavior when amplitude of their response is sufficiently large. The modified method of direct separa-tion of motions is employed to study the considered system. As the result it is obtained that steady-stateamplitude of the nonlinear parametric amplifier response can reach large values in the case...... of arbitrarilysmall amplitude of external excitation, so that the amplifier gain tends to infinity. Very large amplifiergain can be achieved in a broad range of system parameters, in particular when the amplitude of para-metric excitation is comparatively small. The obtained results clearly demonstrate that very...
Rotary bistable and Parametrically Excited Vibration Energy Harvesting
Kurmann, L.; Jia, Y.; Hoffmann, D.; Manoli, Y.; Woias, P.
2016-11-01
Parametric resonance is a type of nonlinear vibration phenomenon [1], [2] induced from the periodic modulation of at least one of the system parameters and has the potential to exhibit interesting higher order nonlinear behaviour [3]. Parametrically excited vibration energy harvesters have been previously shown to enhance both the power amplitude [4] and the frequency bandwidth [5] when compared to the conventional direct resonant approach. However, to practically activate the more profitable regions of parametric resonance, additional design mechanisms [6], [7] are required to overcome a critical initiation threshold amplitude. One route is to establish an autoparametric system where external direct excitation is internally coupled to parametric excitation [8]. For a coupled two degrees of freedom (DoF) oscillatory system, principal autoparametric resonance can be achieved when the natural frequency of the first DoF f1 is twice that of the second DoF f2 and the external excitation is in the vicinity of f1. This paper looks at combining rotary and translatory motion and use autoparametric resonance phenomena.
Nonlinear dynamic response of stay cables under axial harmonic excitation
Institute of Scientific and Technical Information of China (English)
Xu XIE; He ZHAN; Zhi-cheng ZHANG
2008-01-01
This paper proposes a new numerical simulation method for analyzing the parametric vibration of stay cables based on the theory of nonlinear dynamic response of structures under the asynchronous support excitation.The effects of important parameters related to parametric vibration of cables,I.e., characteristics of structure,excitation frequency,excitation amplitude,damping effect of the air and the viscous damping coefficient of the cables,were investigated by using the proposed method for the cables with significant length difference as examples.The analysis results show that nonlinear finite element method is a powerful technique in analyzing the parametric vibration of cables,the behavior of parametric vibration of the two cables with different Irvine parameters has similar properties,the amplitudes of parametric vibration of cables are related to the frequency and amplitude of harmonic support excitations and the effect of distributed viscous damping on parametric vibration of the cables is very small.
Bifurcations in dynamical systems with parametric excitation
Fatimah, Siti
2002-01-01
This thesis is a collection of studies on coupled nonconservative oscillator systems which contain an oscillator with parametric excitation. The emphasis this study will, on the one hand, be on the bifurcations of the simple solutions such as fixed points and periodic orbits, and on the other hand o
New Logic Circuit with DC Parametric Excitation
Sugahara, Masanori; Kaneda, Hisayoshi
1982-12-01
It is shown that dc parametric excitation is possible in a circuit named JUDO, which is composed of two resistively-connected Josephson junctions. Simulation study proves that the circuit has large gain and properties suitable for the construction of small, high-speed logic circuits.
Measurement of velocity field in parametrically excited solitary waves
Gordillo, Leonardo
2014-01-01
Paramerically excited solitary waves emerge as localized structures in high-aspect-ratio free surfaces subject to vertical vibrations. Herein, we provide the first experimental characterization of the hydrodynamics of thess waves using Particle Image Velocimetry. We show that the underlying velocity field of parametrically excited solitary waves is mainly composed by an oscillatory velocity field. Our results confirm the accuracy of Hamiltonian models with added dissipation in describing this field. Remarkably, our measurements also uncover the onset of a streaming velocity field which is shown to be as important as other crucial nonlinear terms in the current theory. The observed streaming pattern is particularly interesting due to the presence of oscillatory meniscii.
PARAMETRIC EXCITATION IN A SELF-EXCITED THREE-DEGREES OF FREEDOM PROBLEM
Directory of Open Access Journals (Sweden)
SITI FATIMAH
2012-05-01
Full Text Available The efect of parametric excitation in self-excited has been investigated in two-degrees of freedom problems. The possibility of suppressing self-excited vibrationsby using parametric excitation and the dynamic behavior of those kind systems were discussed. In the this paper, we consider a system in three-degrees of freedom problem which by using a linear transformation the system becomes an Autoparametric. The system consists of a central mass and two external masses where those masses are conectedby springs with the same constant stiffness. The flow-generated self-excited force is actingon the external masses, it is represented by Rayleigh force. The variable stiffness isperiodically varying in time, represents a parametric excitation. It turns out that forcertain parameter ranges full vibration cancellation is possible. The analysis of linearcase of system shows that there are two conditions in order to obtain an interval ofthe parametric excitation. Using the averaging method the fully non-linear system is investigated producing as non-trivial solutions unstable periodic solutions. The behaviorof this unstable solution is studied in the full system.
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel
2016-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system, a...
Macromechanical parametric amplification with a base-excited doubly clamped beam
DEFF Research Database (Denmark)
Neumeyer, Stefan; Thomsen, Jon Juel
2013-01-01
of steady-state vibration amplitude of the directly and parametrically excited system, to vibration amplitude of the directly excited only system. The nonlinear effect of midplane stretching is compared to the effects of nonlinear inertia and curvature. An approximate analytical expression for the vibration......Parametric amplification is realized by adding parametric excitation to externally driven near-resonant oscillations. The effect of specific cubic nonlinearities on the parametrically amplified steady-state vibrations and gain is investigated theoretically. Here, gain is defined as the ratio...... amplitude is derived. For a given small level of transverse displacement for both the cantilever and doubly clamped beam, the effect of midplane stretching is dominant compared to those caused by nonlinear inertia and curvature. It was found that the beam slenderness ratio can be used as an effective design...
Institute of Scientific and Technical Information of China (English)
时培明; 李纪召; 刘彬; 韩东颖
2012-01-01
Considering the effects caused by the coexisting of two different periodic parametric excitations in rotating machinery driving system, the dynamical equation of a nonlinear torsional vibration system was established based on Lagrange equation. The model contains quasi-periodic parametrically excited stiffness and friction damping. The amplitude-frequency characteristic equation and bifurcation response equation were obtained by solving the torsional vibration system using multi-scale method. On this basis, the periodic bursting of the nonlinear torsional vibration system was studied when large difference gap exists between the frequencies of the two periodic parametrical excitations. The influences of fast-varying parametrical excitation and slow-varying parametrical excitation on the periodic bursting of the torsional vibration system were analyzed. The parameter regions of periodic bursting were obtained with the help of numerical simulation. The mutual transition between quiescent state and spiking state of the system occurs in this region. When the amplitude of the fast-varying excitation reduces, the area of spiking state extends and the time of bursting prolongs. The bursting type and trajectory of the system can be changed by regulating the amplitude of slow-varying parametric excitation.%摘要:考虑旋转机械中两种频率不同的周期参数激励同时存在对其传动系统的影响,基于拉格朗日方程,建立一类含准周期参激刚度和摩擦阻尼的非线性扭振系统的动力学方程.运用多尺度法对该扭振系统进行求解,得到系统在1/2亚谐波主参数共振下的幅频特性方程和分岔响应方程.在此基础上,研究了当两种周期参激的频率相差较大时非线性扭振系统的周期簇发现象,分析了快变参激和慢变参激对扭振系统的周期簇发的影响.通过数值仿真,给出了产生周期簇发的参数取值区域.在该区域内系统发生静息态与激发态的相互转
A Dynamic Branch-Switching Method for Parametrically Excited Systems
Directory of Open Access Journals (Sweden)
A.Y.T. Leung
1999-01-01
Full Text Available The branch-switching algorithm in static is applied to steady state dynamic problems. The governing ordinary differential equations are transformed to nonlinear algebraic equations by means of harmonic balance method using multiple frequency components. The frequency components of the (irrational nonlinearity of oscillator are obtained by Fast Fourier Transform and Toeplitz Jacobian method (FFT/TJM. All singularities, folds, flips, period doubling and period bubbling, are computed accurately in an analytical manner. Coexisting solutions can be predicted without using initial condition search. The consistence of both stability criteria in time and frequency domains is discussed. A highly nonlinear parametrically excited system is given as example. All connected solution paths are predicted.
Parametrically excited internal wave breathers and kinks in liquids
Institute of Scientific and Technical Information of China (English)
陈伟中; 魏荣爵; 王本仁
1996-01-01
In parametrically excited Faraday experiment the non-propagating solitons-breathers, kinksand breather pairs-have been observed at the interface of two insoluble liquids with different densities.Phenomena observed at the interface are similar to those on the surface, except that the eigenfrequencies are remarkably red-shifted, and the wave forms are flatter and less stable due to the presence of the upper liquid. A nonlinear Schrodinger equation with damping and drive terms has been derived to explain the new observations. Both experiment and theory show that the free surface wave is a special case of the interface wave.
Dynamics of a Parametrically Excited System with Two Forcing Terms
Directory of Open Access Journals (Sweden)
Anastasia Sofroniou
2014-09-01
Full Text Available Motivated by the dynamics of a trimaran, an investigation of the dynamic behaviour of a double forcing parametrically excited system is carried out. Initially, we provide an outline of the stability regions, both numerically and analytically, for the undamped linear, extended version of the Mathieu equation. This paper then examines the anticipated form of response of our proposed nonlinear damped double forcing system, where periodic and quasiperiodic routes to chaos are graphically demonstrated and compared with the case of the single vertically-driven pendulum.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....
Synchronization of chaos in non-identical parametrically excited systems
Energy Technology Data Exchange (ETDEWEB)
Idowu, B.A. [Department of Physics, Lagos State University, Ojo (Nigeria)], E-mail: babaidowu@yahoo.com; Vincent, U.E. [Department of Physics, Olabisi Onabanjo University, P.M.B 2002, Ago-Iwoye (Nigeria)], E-mail: ue_vincent@yahoo.com; Njah, A.N. [Department of Physics, University of Agriculture, Abeokuta (Nigeria)
2009-03-15
In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The active control technique is employed to design control functions based on Lyapunov stability theory and Routh-Hurwitz criteria so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendulum and Duffing oscillator. Numerical simulations are implemented to verify the results.
Global synchronization of two parametrically excited systems using active control
Energy Technology Data Exchange (ETDEWEB)
Lei Youming [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)] e-mail: leiyouming@nwpu.edu.cn; Xu Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)] e-mail: weixu@nwpu.edu.cn; Shen Jianwei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); Fang Tong [Department of Engineering Mechanics, Northwestern Polytechnical University, Xi' an 710072 (China)
2006-04-01
In this paper, we apply an active control technique to synchronize a kind of two parametrically excited chaotic systems. Based on Lyapunov stability theory and Routh-Hurwitz criteria, some generic sufficient conditions for global asymptotic synchronization are obtained. Illustrative examples on synchronization of two Duffing systems subject to a harmonic parametric excitation and that of two parametrically excited chaotic pendulums are considered here. Numerical simulations show the validity and feasibility of the proposed method.
Parametric excitation of whistler waves by HF heater
Kuo, S. P.; Lee, M. C.
1989-01-01
Possible generation of whistler waves by Tromso HF heater is investigated. It is shown that the HF heater wave can parametrically decay into a whistler wave and a Langmuir wave. Since whistler waves may have a broad range of frequency, the simultaneously excited Langmuir waves can have a much broader frequency bandwidth than those excited by the parametric decay instability.
Parametric excitation of plasma oscillations in Josephson Junctions
DEFF Research Database (Denmark)
Pedersen, Niels Falsig; Samuelsen, Mogens Rugholm; Særmark, Knud
1973-01-01
A theory is presented for parametric excitation of plasma oscillations in a Josephson junction biased in the zero voltage mode. A threshold curve for the onset of the parametric excitation is deduced via the stability properties of a Mathieu differential equation obtained by a self...
Nonlinear spin-wave excitations at low magnetic bias fields
Woltersdorf, Georg
We investigate experimentally and theoretically the nonlinear magnetization dynamics in magnetic films at low magnetic bias fields. Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. In the experiments we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common Suhl instability model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behavior in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. For these modes, we also find pronounced frequency locking effects that may be used for synchronization purposes in magnonic devices. By using this effect, effective spin-wave sources based on parametric spin-wave excitation may be realized. Our results also show that it is not required to invoke a wave vector-dependent damping parameter in the interpretation of nonlinear magnetic resonance experiments performed at low bias fields.
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
Neumeyer, S.; Sorokin, V. S.; Thomsen, J. J.
2017-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing-Mathieu equation with appended quadratic nonlinearity is considered as the model system, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic nonlinearities may generate additional amplitude-frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi-stability in the amplitude-phase characteristics are predicted, supporting previously reported experimental observations.
Finite strain effects in piezoelectric energy harvesters under direct and parametric excitations
Mam, Koliann; Peigney, Michaël; Siegert, Dominique
2017-02-01
This paper addresses the dynamic behavior of piezoelectric cantilevers under base excitations. Such devices are frequently used for applications in energy harvesting. An Euler-Bernoulli model that accounts for large-deflection effects and piezoelectric nonlinearities is proposed. Closed-form expressions of the frequency response are derived, both for direct excitation (i.e. with a base acceleration transverse to the axis of the cantilever) and parametric excitation (i.e. with a base acceleration along the axis of the cantilever). Experimental results are reported and used for assessing the validity of the proposed model. Building on the model presented, some critical issues related to energy-harvesting are investigated, such as the influence of nonlinearities on the optimal load resistance, the limits of validity of linear models, and hysteresis effects in the electrical power. The efficiency of direct and parametric excitation is also compared in detail.
Bifurcations and sensitivity in parametric nonlinear programming
Lundberg, Bruce N.; Poore, Aubrey B.
1990-01-01
The parametric nonlinear programming problem is that of determining the behavior of solution(s) as a parameter or vector of parameters alpha belonging to R(sup r) varies over a region of interest for the problem: Minimize over x the set f(x, alpha):h(x, alpha) = 0, g(x, alpha) is greater than or equal to 0, where f:R(sup (n+r)) approaches R, h:R(sup (n+r)) approaches R(sup q) and g:R(sup (n+r)) approaches R(sup p) are assumed to be at least twice continuously differentiable. Some of these parameters may be fixed but not known precisely and others may be varied to enhance the performance of the system. In both cases a fundamentally important problem in the investigation of global sensitivity of the system is to determine the stability boundaries of the regions in parameter space which define regions of qualitatively similar solutions. The objective is to explain how numerical continuation and bifurcation techniques can be used to investigate the parametric nonlinear programming problem in a global sense. Thus, first the problem is converted to a closed system of parameterized nonlinear equations whose solution set contains all local minimizers of the original problem. This system, which will be represented as F(z,alpha) = O, will include all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points of the problem. The local existence and uniqueness of a solution path (z(alpha), alpha) of this system as well as the solution type persist as long as a singularity in the Jacobian D(sub z)F(z,alpha) is not encountered. Thus the nonsingularity of this Jacobian is characterized in terms of conditions on the problem itself. Then, a class of efficient predictor-corrector continuation procedures for tracing solution paths of the system F(z,alpha) = O which are tailored specifically to the parametric programming problem are described. Finally, these procedures and the obtained information are illustrated
Study of Linear and Nonlinear Wave Excitation
Chu, Feng; Berumen, Jorge; Hood, Ryan; Mattingly, Sean; Skiff, Frederick
2013-10-01
We report an experimental study of externally excited low-frequency waves in a cylindrical, magnetized, singly-ionized Argon inductively-coupled gas discharge plasma that is weakly collisional. Wave excitation in the drift wave frequency range is accomplished by low-percentage amplitude modulation of the RF plasma source. Laser-induced fluorescence is adopted to study ion-density fluctuations in phase space. The laser is chopped to separate LIF from collisional fluorescence. A single negatively-biased Langmuir probe is used to detect ion-density fluctuations in the plasma. A ring array of Langmuir probes is also used to analyze the spatial and spectral structure of the excited waves. We apply coherent detection with respect to the wave frequency to obtain the ion distribution function associated with externally generated waves. Higher-order spectra are computed to evaluate the nonlinear coupling between fluctuations at various frequencies produced by the externally generated waves. Parametric decay of the waves is observed. This work is supported by U.S. DOE Grant No. DE-FG02-99ER54543.
Parametric Symmetry Breaking in a Nonlinear Resonator
Leuch, Anina; Papariello, Luca; Zilberberg, Oded; Degen, Christian L.; Chitra, R.; Eichler, Alexander
2016-11-01
Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far-from-equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work unveils that the double hysteresis is a manifestation of an out-of-equilibrium symmetry breaking between parametric phase states. Such a fundamental phenomenon, in the most ubiquitous building block of nature, paves the way for the investigation of new dynamical phases of matter in parametrically driven many-body systems and motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
Non-parametric system identification from non-linear stochastic response
DEFF Research Database (Denmark)
Rüdinger, Finn; Krenk, Steen
2001-01-01
An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable p...
Recursive design of nonlinear H∞ excitation controller
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This work is concerned with the problem of L2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinear H∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.
Coupled parametric processes in binary nonlinear photonic structures
Saygin, M Yu
2016-01-01
We study parametric interactions in a new type of nonlinear photonic structures, which is realized in the vicinity of a pair of nonlinear crystals. In this kind of structure, which we call binary, multiple nonlinear optical processes can be implemented simultaneously, owing to multiple phase-matching conditions, fulfilled separately in the constituent crystals. The coupling between the nonlinear processes by means of modes sharing similar frequency is attained by the spatially-broadband nature of the parametric fields. We investigate the spatial properties of the fields generated in the binary structure constructed from periodically poled crystals for the two examples: 1) single parametric down-conversion, and 2) coupled parametric down-conversion and up-conversion processes. The efficacy of the fields' generation in these examples is analyzed through comparison with the cases of traditional single periodically poled crystal and aperiodic photonic structure, respectively. It has been shown that the relative s...
Parametric excitation of plasma oscillations in a Josephson tunnel junction
DEFF Research Database (Denmark)
Bak, Christen Kjeldahl; Kofoed, Bent; Pedersen, Niels Falsig
1975-01-01
Experimental evidence for subharmonic parametric excitation of plasma oscillations in Josephson tunnel junctions is presented. The experiments described are performed by measuring the microwave power necessary to switch a Josephson−tunnel junction biased in the zero−voltage state to a finite−volt......−voltage state. Journal of Applied Physics is copyrighted by The American Institute of Physics....
Efficient primary and parametric resonance excitation of bistable resonators
Ramini, Abdallah
2016-09-12
We experimentally demonstrate an efficient approach to excite primary and parametric (up to the 4th) resonance of Microelectromechanical system MEMS arch resonators with large vibrational amplitudes. A single crystal silicon in-plane arch microbeam is fabricated such that it can be excited axially from one of its ends by a parallel-plate electrode. Its micro/nano scale vibrations are transduced using a high speed camera. Through the parallel-plate electrode, a time varying electrostatic force is applied, which is converted into a time varying axial force that modulates dynamically the stiffness of the arch resonator. Due to the initial curvature of the structure, not only parametric excitation is induced, but also primary resonance. Experimental investigation is conducted comparing the response of the arch near primary resonance using the axial excitation to that of a classical parallel-plate actuation where the arch itself forms an electrode. The results show that the axial excitation can be more efficient and requires less power for primary resonance excitation. Moreover, unlike the classical method where the structure is vulnerable to the dynamic pull-in instability, the axial excitation technique can provide large amplitude motion while protecting the structure from pull-in. In addition to primary resonance, parametrical resonances are demonstrated at twice, one-half, and two-thirds the primary resonance frequency. The ability to actuate primary and/or parametric resonances can serve various applications, such as for resonator based logic and memory devices. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
Nonlinear cross-talk mitigation in polychromatic parametric sampling gate.
Ataie, Vahid; Wiberg, Andreas O J; Alic, Nikola; Radic, Stojan
2013-02-25
New technique for cancellation of nonlinear cross-talk in polychromatic parametric sampling gate is described and quantified. The method relies on a newly derived look-up table method that achieves equalization and suppresses nonlinear response associated with parametric sampling operation. The new cancellation scheme is implemented in a framework of a specific parametric photonics assisted analog-to-digital conversion (ADC) copy-and-sample-all (CaSA) architecture. A 20 dB improvement in total harmonic distortion is demonstrated experimentally.
Averaging in Parametrically Excited Systems – A State Space Formulation
Directory of Open Access Journals (Sweden)
Pfau Bastian
2016-01-01
Full Text Available Parametric excitation can lead to instabilities as well as to an improved stability behavior, depending on whether a parametric resonance or anti-resonance is induced. In order to calculate the stability domains and boundaries, the method of averaging is applied. The problem is reformulated in state space representation, which allows a general handling of the averaging method especially for systems with non-symmetric system matrices. It is highlighted that this approach can enhance the first order approximation significantly. Two example systems are investigated: a generic mechanical system and a flexible rotor in journal bearings with adjustable geometry.
In-plane Auto-Parametric Vibration of Inclined Cables under Random Transverse Excitation
Institute of Scientific and Technical Information of China (English)
WANG Bo; ZHANG Hai-long; XU Feng; GUO Cui-cui
2008-01-01
In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton's laws of motion and Galerkin's modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 1A-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square (RMS) response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to the auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.
A study of quasi-mode parametric excitations in lower-hybrid heating of tokamak plasmas
Villalon, E.; Bers, A.
1980-03-01
A detailed linear and non-linear analysis of quasi-mode parametric excitations, relevant to experiments in supplementary heating of tokamak plasmas, is presented. The linear analysis includes the full ion-cyclotron harmonic quasi-mode spectrum, while the nonlinear one, considering depletion of the pump electric field, is applied to the recent Alcator A heating experiment. The quasi-mode excitations are studied independently for the plasma edge and the main bulk of the plasma, and for the two typical regimes in overall density. It is concluded that the excited spectrum has a frequency close to the initial pump frequency, while the wave-number spectrum may be different from the initial linear spectrum.
Global chaos synchronization of coupled parametrically excited pendula
Indian Academy of Sciences (India)
O I Olusola; U E Vincent; A N Njah
2009-12-01
In this paper, we study the synchronization behaviour of two linearly coupled parametrically excited chaotic pendula. The stability of the synchronized state is examined using Lyapunov stability theory and linear matrix inequality (LMI); and some sufficient criteria for global asymptotic synchronization are derived from which an estimated critical coupling is determined. Numerical solutions are presented to verify the theoretical analysis. We also examined the transition to stable synchronous state and show that this corresponds to a boundary crisis of the chaotic attractor.
Resonator coupled Josephson junctions; parametric excitations and mutual locking
DEFF Research Database (Denmark)
Jensen, H. Dalsgaard; Larsen, A.; Mygind, Jesper
1991-01-01
Self-pumped parametric excitations and mutual locking in systems of Josephson tunnel junctions coupled to multimode resonators are reported. For the very large values of the coupling parameter, obtained with small Nb-Al2O3-Nb junctions integrated in superconducting microstrip resonators, the DC I......-V characteristic shows an equidistant series of current steps generated by subharmonic pumping of the fundamental resonator mode. This is confirmed by measurement of frequency and linewidth of the emitted Josephson radiation...
Control and characterization of spatio-temporal disorder in parametrically excited surface waves
Indian Academy of Sciences (India)
T Epsteing; J Fineberg
2005-06-01
The nonlinear interactions of parametrically excited surface waves have been shown to yield a rich family of nonlinear states. When the system is driven by two commensurate frequencies, a variety of interesting superlattice type states are generated via a number of different 3-wave resonant interactions. These states occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two different unstable modes generated by the two forcing frequencies. Near the system’s bicritical point, a well-defined region of phase space exists in which a highly disordered state, both in space and time, is observed. We first show that this state results from the competition between two distinct nonlinear superlattice states, each with different characteristic temporal and spatial symmetries. After characterizing the type of spatio-temporal disorder that is embodied in this disordered state, we will demonstrate that it can be controlled. Control to either of its neighboring nonlinear states is achieved by the application of a small-amplitude excitation at a third frequency, where the spatial symmetry of the selected pattern is determined by the temporal symmetry of the third frequency used. This technique can also excite rapid switching between different nonlinear states.
Resonant parametric excitations driven by lower-hybrid fields
Energy Technology Data Exchange (ETDEWEB)
Villalon, E.
1980-11-01
Three-wave parametric excitation in inhomogeneous plasmas is examined in a two-dimensional geometry relevant to supplementary rf heating of tokamaks. The stabilization of resonant parametric excitation due to a linear mismatch in wavenumbers and to the Landau-damping rates of the decay waves is analyzed, assuming that the magnitude of the pump field is constant in time and in the spatial region where the resonant interaction takes place. Both types of temporally growing modes and spatially amplified instabilities are studied, using a WKB analysis. It is shown that either by increasing the strength of the mismatch K' or the width of the pump L, the growth rate of the fastest growing normal mode will decrease. When the excited waves are slightly damped, it is shown that there exists a finite value of the product K'L, such that, above it, no temporal normal modes are excited. The amount of spatial amplification is also reduced by the mismatch in wavenumbers and by the damping rates of the excited waves. Because of the finite spatial extent of the pump electric field, the amplification length is found to be smaller than or equal to L, depending on the strength of the mismatch and damping rates.
Higher-order nonlinear effects in a Josephson parametric amplifier
Kochetov, Bogdan A.; Fedorov, Arkady
2015-12-01
Nonlinearity of the current-phase relationship of a Josephson junction is the key resource for a Josephson parametric amplifier (JPA) as well as for a Josephson traveling-wave parametric amplifier, the only devices in which the quantum limit for added noise has so far been approached at microwave frequencies. A standard approach to describe JPA takes into account only the lowest order (cubic) nonlinearity resulting in a Duffing-like oscillator equation of motion or in a Kerr-type nonlinearity term in the Hamiltonian. In this paper we derive the quantum expression for the gain of JPA including all orders of the Josephson junction nonlinearity in the linear response regime. We then analyze gain saturation effect for stronger signals within a semiclassical approach. Our results reveal nonlinear effects of higher orders and their implications for operation of a JPA.
Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators
Papariello, Luca; Zilberberg, Oded; Eichler, Alexander; Chitra, R.
2016-08-01
We propose a method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay among the parametric drive, external force, and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the attonewton range.
Nonlinear Excitations in Inflationary Power Spectra
Miranda, Vinicius; He, Chen; Motohashi, Hayato
2016-01-01
We develop methods to calculate the curvature power spectrum in models where features in the inflaton potential nonlinearly excite modes and generate high frequency features in the spectrum. The first nontrivial effect of excitations generating further excitations arises at third order in deviations from slow roll. If these further excitations are contemporaneous, the series can be resummed, showing the exponential sensitivity of the curvature spectrum to potential features. More generally, this exponential approximation provides a power spectrum template which nonlinearly obeys relations between excitation coefficients and whose parameters may be appropriately adjusted. For a large sharp step in the potential, it greatly improves the analytic power spectrum template and its dependence on potential parameters. For axionic oscillations in the potential, it corrects the mapping between the potential and the amplitude, phase and zero point of the curvature oscillations, which might otherwise cause erroneous infe...
Phonon-assisted nonlinear optical processes in ultrashort-pulse pumped optical parametric amplifiers
Isaienko, Oleksandr; Robel, István
2016-03-01
Optically active phonon modes in ferroelectrics such as potassium titanyl phosphate (KTP) and potassium titanyl arsenate (KTA) in the ~7-20 THz range play an important role in applications of these materials in Raman lasing and terahertz wave generation. Previous studies with picosecond pulse excitation demonstrated that the interaction of pump pulses with phonons can lead to efficient stimulated Raman scattering (SRS) accompanying optical parametric oscillation or amplification processes (OPO/OPA), and to efficient polariton-phonon scattering. In this work, we investigate the behavior of infrared OPAs employing KTP or KTA crystals when pumped with ~800-nm ultrashort pulses of duration comparable to the oscillation period of the optical phonons. We demonstrate that under conditions of coherent impulsive Raman excitation of the phonons, when the effective χ(2) nonlinearity cannot be considered instantaneous, the parametrically amplified waves (most notably, signal) undergo significant spectral modulations leading to an overall redshift of the OPA output. The pump intensity dependence of the redshifted OPA output, the temporal evolution of the parametric gain, as well as the pump spectral modulations suggest the presence of coupling between the nonlinear optical polarizations PNL of the impulsively excited phonons and those of parametrically amplified waves.
RESPONSE OF PARAMETRICALLY EXCITED DUFFING-VAN DER POL OSCILLATOR WITH DELAYED FEEDBACK
Institute of Scientific and Technical Information of China (English)
LI Xin-ye; CHEN Yu-shu; WU Zhi-qiang; SONG Tao
2006-01-01
The dynamical behaviour of a parametrically excited Duffing-van der Pol oscillator under linear-plus-nonlinear state feedback control with a time delay is concerned.By means of the method of averaging together with truncation of Taylor expansions, two slow-flow equations on the amplitude and phase of response were derived for the case of principal parametric resonance. It is shown that the stability condition for the trivial solution is only associated with the linear terms in the original systems besides the amplitude and frequency of parametric excitation. And the trivial solution can be stabilized by appreciate choice of gains and time delay in feedback control. Different from the case of the trivial solution, the stability condition for nontrivial solutions is also associated with nonlinear terms besides linear terms in the original system. It is demonstrated that nontrivial steady state responses may lose their stability by saddle-node (SN) or Hopf bifurcation (HB) as parameters vary. The simulations, obtained by numerically integrating the original system, are in good agreement with the analytical results.
Nonlinear dynamics of a parametrically driven sine-Gordon system
DEFF Research Database (Denmark)
Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm
1993-01-01
We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...
Kazachkov, Ivan V
2015-01-01
The results by development of physical, mathematical and numerical models for parametric excitation and suppression of oscillations on the interfaces separating continuous media, for carrying out computing, physical and natural experiments by revealing the new phenomena and parametric effects, and for their use in improvement the existing and creation the perspective highly efficient technological processes are presented. Scientific novelty of this work consists in development of the theory and applications of parametric excitation and suppression of oscillations on the boundaries of continua on the samples of three tasks classes: flat and radial spreading film flows of viscous incompressible liquids, conductive as well as non-conductive ones; surfaces of phase transition from a liquid state into a solid one; and heterogeneous granular media. The external actions considered are: alternating electromagnetic, vibration, acoustic and thermal fields. Along with linear the non-linear parametric oscillations are in...
Resonant parametric excitations driven by lower-hybrid fields
Villalon, E.
1980-11-01
Three-wave parametric excitation in inhomogeneous plasmas is examined in a two-dimensional geometry relevant to supplementary rf heating of tokamaks. The stabilization of resonant parametric excitation due to a linear mismatch in wavenumbers and to the Landau-damping rates of the decay waves is analyzed, assuming that the magnitude of the pump field is constant in time and in the spatial region where the resonant interaction takes place. Both types of temporally growing modes and spatially amplified instabilities are studied, using a WKB analysis. It is shown that by increasing the strength of the mismatch K prime or the width of the pump L, the growth rate of the fastest growing normal mode will decrease. The amount of spatial amplification is also reduced by the mismatch in wavenumbers and by the damping rates of the excited waves. Because of the finite spatial extent of the pump electric field, the amplification length is smaller than or equal to L, depending on the strength of the mismatch and damping rates.
Wei, Sha; Han, Qinkai; Peng, Zhike; Chu, Fulei
2016-05-01
Some system parameters in mechanical systems are always uncertain due to uncertainties in geometric and material properties, lubrication condition and wear. For a more reasonable estimation of dynamic analysis of the parametrically excited system, the effect of uncertain parameters should be taken into account. This paper presents a new non-probabilistic analysis method for solving the dynamic responses of parametrically excited systems under uncertainties and multi-frequency excitations. By using the multi-dimensional harmonic balance method (MHBM) and the Chebyshev inclusion function (CIF), an interval multi-dimensional harmonic balance method (IMHBM) is obtained. To illustrate the accuracy of the proposed method, a time-varying geared system of wind turbine with different kinds of uncertainties is demonstrated. By comparing with the results of the scanning method, it is shown that the presented method is valid and effective for the parametrically excited system with uncertainties and multi-frequency excitations. The effects of some uncertain system parameters including uncertain mesh stiffnesses and uncertain bearing stiffnesses on the frequency responses of the system are also discussed in detail. It is shown that the dynamic responses of the system are insensitive to the uncertain mesh stiffness and bearing stiffnesses of the planetary gear stage. The uncertain bearing stiffnesses of the intermediate and high-speed stages will lead to relatively large uncertainties in the dynamic responses around resonant regions. It will provide valuable guidance for the optimal design and condition monitoring of wind turbine gearboxes.
Localization of nonlinear excitations in curved waveguides
DEFF Research Database (Denmark)
Gaididei, Yu. B.; Christiansen, Peter Leth; Kevrekidis, P. G.;
2005-01-01
numerical simulations of the nonlinear problem and in this case localized excitations are found to persist. We found also interesting relaxational dynamics. Analogies of the present problem in context related to atomic physics and particularly to Bose–Einstein condensation are discussed....
Time reversal of parametrical driving and the stability of the parametrically excited pendulum
Stannarius, Ralf
2009-02-01
It is well known that the periodic driving of a parametrically excited pendulum can stabilize or destabilize its stationary states, depending upon the frequency, wave form, and amplitude of the parameter modulations. We discuss the effect of time reversal of the periodic driving function for the parametric pendulum at small elongations. Such a time reversal usually leads to different solutions of the equations of motion and to different stability properties of the system. Two interesting exceptions are discussed, and two conditions are formulated for which the character of the solutions of the system is not influenced by a time reversal of the driving function, even though the trajectories of the dynamic variables are different.
Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation
Macdonald, J. H. G.
2016-02-01
Cables are often prone to potentially damaging large amplitude vibrations. The dynamic excitation may be from external loading or motion of the cable ends, the latter including direct excitation, normally from components of end motion transverse to the cable, and parametric excitation induced by axial components of end motion causing dynamic tension variations. Geometric nonlinearity can be important, causing stiffening behaviour and nonlinear modal coupling. Previous analyses of the vibrations, often neglecting sag, have generally dealt with direct and parametric excitation separately or have reverted to numerical solutions of the responses. Here a nonlinear cable model is adopted, applicable to taut cables such as on cable-stayed bridges, that allows for cable inclination, small sag (such that the vibration modes are similar to those of a taut string), multiple modes in both planes and end motion and/or external forcing close to any natural frequency. Based on the method of scaling and averaging it is found that, for sinusoidal inputs and positive damping, non-zero steady state responses can only occur in the modes in each plane with natural frequencies close to the excitation frequency and those with natural frequencies close to half this frequency. Analytical solutions, in the form of non-dimensional polynomial equations, are derived for the steady state vibration amplitudes in up to three modes simultaneously: the directly excited mode, the corresponding nonlinearly coupled mode in the orthogonal plane and a parametrically excited mode with half the natural frequency. The stability of the solutions is also identified. The outputs of the equations are consistent with previous results, where available. Example results from the analytical solutions are presented for a typical inclined bridge cable subject to vertical excitation of the lower end, and they are validated by numerical integration of the equations of motion and against some previous experimental
Parametric vibrations of a restrained beam with an end mass under displacement excitation
Gürgöze, M.
1986-07-01
This paper is concerned with the stability and the steady state response of the main parametric resonance vibrations of a simply supported vertical beam. The beam carries a concentrated mass and is restrained at one end and subjected to a periodic axial displacement excitation at the other end. This system can be looked upon as a dynamic model of the vibrations of an engine valve mechanism. Non-linear terms arising from moderately large curvatures, longitudinal inertia of the beam elements and concentrated mass are included in the equation of motion. By using the one mode approximation and applying Galerkin's method, the governing partial differential equation is reduced to a non-linear ordinary differential equation with a periodic coefficient. The boundaries of the main parametric instability region of the linearized equation are obtained. The harmonic balance method is applied to solve the equation and an analytical expression for the dynamic response in the vicinity of the main parametric resonance is derived. The effects of various parameters on the boundaries of the instability region and the dynamic response are investigated.
Parametrically excited oscillation of stay cable and its control in cable-stayed bridges
Institute of Scientific and Technical Information of China (English)
孙炳楠; 汪至刚; 高赞明; 倪一清
2003-01-01
This paper presents a nonlinear dynamic model for simulation and analysis of a kind of parametrically excited vibration of stay cable caused by support motion in cable-stayed bridges. The sag, inclination angle of the stay cable are considered in the model, based on which, the oscillation mechanism and dynamic response characteristics of this kind of vibration are analyzed through numerical calculation. It is noted that parametrically excited oscillation of a stay cable with certain sag, inclination angle and initial static tension force may occur in cable-stayed bridges due to deck vibration under the condition that the natural frequency of a cable approaches to about half of the first model frequency of the bridge deck system. A new vibration control system installed on the cable anchorage is proposed as a possible damping system to suppress the cable parametric oscillation. The numerical calculation results showed that with the use of this damping system, the cable oscillation due to the vibration of the deck and/or towers will be considerably reduced.
Parametrically excited oscillation of stay cable and its control in cable-stayed bridges＂
Institute of Scientific and Technical Information of China (English)
孙炳楠; 汪至刚; 高赞明; 倪一清
2003-01-01
This paper presents a nonlinear dynamic model for simulation and analysis of a kind of parametrically excited vibration of stay cable caused by support motion in cable-stayed bridges. The sag, inclination angle of the stay cable are considered in the model, based on which, the oscillation mechanism and dynamic response characteristics of this kind of vibration are analyzed through numerical calculation. It is noted that parametrically excited oscillation of a stay cable with certain sag, inclination angle and initial static tension force may occur in cable-stayed bridges due to deck vibration under the condition that the natural frequency of a cable approaches to about half of the first model frequency of the bridge deck system. A new vibration control system installed on the cable anchorage is proposed as a possible damping system to suppress the cable parametric oscillation. The numerical calculation results showed that with the use of this damping system, the cable oscillation due to the vibration of the deck and/or towers will be considerably reduced.
Theory of double resonance parametric excitation in plasmas. II
Fried, B. D.; Adler, A.; Bingham, R.
1980-10-01
A simpler formalism than in the original paper on this subject is used to verify the earlier result that, for a pump frequency separation Delta approximately equal to twice the ion acoustic frequency Omega, the use of two long-wavelength pumps can reduce the threshold for parametric excitation of ion-acoustic waves when, and only when, the Langmuir wave damping rate gamma is much larger than Omega. The threshold is then reduced by a factor of order Omega/omega, the optimum value of Delta being 2 Omega-Gamma for equal pump amplitudes, where Gamma is the ion-acoustic wave damping rate and Gamma is much less than Omega. The analysis presented in a recent paper is shown to be valid only for gamma much less than Omega, where the threshold reduction is quite small, vanishing in the limit of weak ion-acoustic wave damping (Te/Ti much greater than 1).
Parametric and Non-Parametric Vibration-Based Structural Identification Under Earthquake Excitation
Pentaris, Fragkiskos P.; Fouskitakis, George N.
2014-05-01
The problem of modal identification in civil structures is of crucial importance, and thus has been receiving increasing attention in recent years. Vibration-based methods are quite promising as they are capable of identifying the structure's global characteristics, they are relatively easy to implement and they tend to be time effective and less expensive than most alternatives [1]. This paper focuses on the off-line structural/modal identification of civil (concrete) structures subjected to low-level earthquake excitations, under which, they remain within their linear operating regime. Earthquakes and their details are recorded and provided by the seismological network of Crete [2], which 'monitors' the broad region of south Hellenic arc, an active seismic region which functions as a natural laboratory for earthquake engineering of this kind. A sufficient number of seismic events are analyzed in order to reveal the modal characteristics of the structures under study, that consist of the two concrete buildings of the School of Applied Sciences, Technological Education Institute of Crete, located in Chania, Crete, Hellas. Both buildings are equipped with high-sensitivity and accuracy seismographs - providing acceleration measurements - established at the basement (structure's foundation) presently considered as the ground's acceleration (excitation) and at all levels (ground floor, 1st floor, 2nd floor and terrace). Further details regarding the instrumentation setup and data acquisition may be found in [3]. The present study invokes stochastic, both non-parametric (frequency-based) and parametric methods for structural/modal identification (natural frequencies and/or damping ratios). Non-parametric methods include Welch-based spectrum and Frequency response Function (FrF) estimation, while parametric methods, include AutoRegressive (AR), AutoRegressive with eXogeneous input (ARX) and Autoregressive Moving-Average with eXogeneous input (ARMAX) models[4, 5
Breatherlike excitations in discrete lattices with noise and nonlinear damping
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri B.; Johansson, Magnus
1997-01-01
We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrodinger equation in the regime of high nonlinearity, where temperature effects...
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.
Parametric interaction and intensification of nonlinear Kelvin waves
Novotryasov, Vadim
2008-01-01
Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\\omega_t$ or the inertial -- $\\omega_i$ frequency and oscillations of synoptic -- $\\Omega $ frequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum -- $\\omega_+ $ and dif -- $\\omega_-$ frequencies: $\\omega_\\pm =\\omega_{t,i}\\pm \\Omega$ have properties of propagating Kelvin waves suggesting permanent energy exchange from the synoptic band to the mesoscale $\\omega_\\pm $ band. The interaction may be responsible for the greater than predicted intensification, steepen and break of boundary trapped and equatorially trapped Kelvin waves, which can affect El Ni\\~{n}o. The problem on the parametric interaction of the nonlinear Kelvin wave at the frequency $\\omega $ and the low-frequency narrow-band nose with representative frequency $\\Omega\\ll\\omega $ is investigated with the theory of nonlinear week dispersion waves.
Nonlinear Zel'dovich effect: Parametric amplification from medium rotation
Faccio, Daniele
2016-01-01
The interaction of light with rotating media has attracted recent interest for both fundamental and applied studies including rotational Doppler shift measurements. It is also possible to obtain amplification through the scattering of light with orbital angular momentum from a rotating and absorbing cylinder, as proposed by Zel'dovich more than 40 years ago. This amplification mechanism has never been observed experimentally yet has connections to other fields such as Penrose superradiance in rotating black holes. Here we propose a nonlinear optics system whereby incident light carrying orbital angular momentum drives parametric interaction in a rotating medium. The crystal rotation is shown to take the phase-mismatched parametric interaction with negligible energy exchange at zero rotation to amplification for sufficiently large rotation rates. The amplification is shown to result from breaking of anti-PT symmetry induced by the medium rotation.
Nonlinear Zel'dovich Effect: Parametric Amplification from Medium Rotation
Faccio, Daniele; Wright, Ewan M.
2017-03-01
The interaction of light with rotating media has attracted recent interest for both fundamental and applied studies including rotational Doppler shift measurements. It is also possible to obtain amplification through the scattering of light with orbital angular momentum from a rotating and absorbing cylinder, as proposed by Zel'dovich more than forty years ago. This amplification mechanism has never been observed experimentally yet has connections to other fields such as Penrose superradiance in rotating black holes. Here we propose a nonlinear optics system whereby incident light carrying orbital angular momentum drives parametric interaction in a rotating medium. The crystal rotation is shown to take the phase-mismatched parametric interaction with negligible energy exchange at zero rotation to amplification for sufficiently large rotation rates. The amplification is shown to result from breaking of anti-P T symmetry induced by the medium rotation.
Nonlinear Resonance of Mechanically Excited Sessile Drops
Chang, Chun-Ti; Daniel, Susan; Steen, Paul
2013-11-01
The spectrum of frequencies and mode shapes for an inviscid drop on a planar substrate have recently been documented. For vertical excitation, zonal modes respond to the driving frequency harmonically and non-zonal modes subharmonically, consistent with the prior literature. In this study, we report observations from the regime of nonlinear response. Here, zonals can respond non-harmonically, both sub- and super-harmonic responses are reported. The principal challenge to generating and observing superharmonic resonances of higher zonal modes is a mode-mixing behavior. However, using a simple visual simulation based on the ray-tracing technique, the individual contributions to the mixed resonance behavior can be extracted. In summary, results from experiment and theory show that the zonal modes, which respond harmonically and can mix with non-zonal modes without interfering with one another in the linear regime, tend to respond sub- or superharmonically and compete with non-zonal modes in the nonlinear regime.
Nonlinear Excitation in a Ferrimagnetic Zigzag Chain
Institute of Scientific and Technical Information of China (English)
王为忠
2003-01-01
We study the nonlinear excitation(solitons)in a ferrimagnetic polymer chain by using a total Hamiltonian consisting of Su-Schrieffer-Heeger Hamiltonian and a Hubbard term.At half-filling,the distortion of lattices forms domain wall solitons,while the spin configuration forms envelope solitons.The soliton pair is obtained in a range of the electron-electron(e-e)interaction U,which depends on the electron-phonon(e-ph)interaction.The spin solitons corresponding to the left domain wall and the right domain wall of the displacement are quite different.
Optical detection of terahertz using nonlinear parametric upconversion.
Khan, M Jalal; Chen, Jerry C; Kaushik, Sumanth
2008-12-01
We extend our work to perform sensitive, room-temperature optical detection of terahertz (THz) by using nonlinear parametric upconversion. THz radiation at 700 GHz is mixed with pump light at 1,550 nm in a bulk GaAs crystal to generate an idler wave at 1,555.6 nm. The idler is separated, coupled into optical fiber, and detected using a gated Geiger-mode avalanche photodiode. The resulting THz detector has a power sensitivity of 4.5 pW/Hz and a timing resolution of 1 ns.
Lin, Z R; Nakamura, Y; Dykman, M I
2015-08-01
We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between the period-two states over the quasienergy barrier. We find the effective quantum activation energies for such transitions and their scaling with the difference of the driving amplitude from its critical value. We also find the scaling of the fluctuation correlation time with the quantum noise parameters in the critical region near the threshold. The results are extended to oscillators with nonlinear friction.
Lin, Z. R.; Nakamura, Y.; Dykman, M. I.
2015-08-01
We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between the period-two states over the quasienergy barrier. We find the effective quantum activation energies for such transitions and their scaling with the difference of the driving amplitude from its critical value. We also find the scaling of the fluctuation correlation time with the quantum noise parameters in the critical region near the threshold. The results are extended to oscillators with nonlinear friction.
Parametric excitation of multiple resonant radiations from localized wavepackets
Conforti, Matteo; Mussot, Arnaud; Kudlinski, Alexandre
2015-01-01
Fundamental physical phenomena such as laser-induced ionization, driven quantum tunneling, Faraday waves, Bogoliubov quasiparticle excitations, and the control of new states of matter rely on time-periodic driving of the system. A remarkable property of such driving is that it can induce the localized (bound) states to resonantly couple to the continuum. Therefore experiments that allow for enlightening and controlling the mechanisms underlying such coupling are of paramount importance. We implement such an experiment in a special fiber optics system characterized by a dispersion oscillating along the propagation coordinate, which mimics "time". The quasi-momentum associated with such periodic perturbation is responsible for the efficient coupling of energy from the localized wave-packets sustained by the fiber nonlinearity into free-running linear dispersive waves (continuum), at multiple resonant frequencies. Remarkably, the observed resonances can be explained by means of a unified approach, regardless of ...
Parametric characteristic of the random vibration response of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Xing-Jian Dong; Zhi-Ke Peng; Wen-Ming Zhang; Guang Meng; Fu-Lei Chu
2013-01-01
Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of non-linear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density (PSD) and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
A comparison of nonlinear media for parametric all-optical signal processing
DEFF Research Database (Denmark)
Martinez Diaz, Jordi; Bohigas Nadal, Jaume; Vukovic, Dragana;
2013-01-01
We systematically compare nonlinear media for parametric signal processing by determining the minimum pump power that is required for a given conversion efficiency in a degenerate four-wave mixing process, including the effect of nonlinear loss....
Nonlinear excitations in two-dimensional molecular structures with impurities
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Rasmussen, Kim; Christiansen, Peter Leth
1995-01-01
We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence of the imp......We study the nonlinear dynamics of electronic excitations interacting with acoustic phonons in two-dimensional molecular structures with impurities. We show that the problem is reduced to the nonlinear Schrodinger equation with a varying coefficient. The latter represents the influence...... excitations. Analytical results are in good agreement with numerical simulations of the nonlinear Schrodinger equation....
Mean square stability of a second-order parametric linear system excited by a colored Gaussian noise
Floris, Claudio
2015-02-01
The stochastic stability of a second-order linear parametric oscillator whose stiffness is perturbed by a stationary zero-mean colored Gaussian process is investigated in this paper referring to the stability in the second response moments (mean square stability). The stochastic perturbation is the output of a linear filter excited by a stationary Gaussian white noise stochastic process, and the hypothesis of weak excitation is not formulated. The first assumption allows using Itô's stochastic differential calculus. The moment equations of the response are written till the second order by means of Itô's differential rule. They form an infinite hierarchy, that is the equations for the moments of order r contain moments of order larger than r. In order to close the hierarchy, the cumulant neglect closure method is applied herein. The moment equation set is closed by neglecting the cumulants of third order. Nonlinear moment equations result: they are linearized, and the limit of stability is searched by studying the eigenvalues of the matrix of the coefficients of the linearized moment equations. Several numerical analyses are performed to evaluate the critical mean square value of the excitation when a system parameter is varied for the cases of both first and second-order parametric excitation. A first-order excitation, an Ornstein-Uhlenbeck process, does not cause stochastic resonance, while a second-order excitation does. The first result was not known previously.
Parametric excitation and squeezing in a many-body spinor condensate.
Hoang, T M; Anquez, M; Robbins, B A; Yang, X Y; Land, B J; Hamley, C D; Chapman, M S
2016-04-05
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states.
Excitation Thresholds for Nonlinear Localized Modes on Lattices
Weinstein, M I
1999-01-01
Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schrödinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schrödinger systems (DNLS). We prove that if $\\sigma\\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, the context of DNLS. We also discuss upper and lower bounds for excitation threshol...
Recursive design of nonlinear H _∞ excitation controller
Institute of Scientific and Technical Information of China (English)
卢强; 梅生伟; 申铁龙; 胡伟
2000-01-01
This work is concerned with the problem of L2 gain disturbance attenuation for nonlinear systems and nonlinear robust control for power systems. In terms of the recurrence design approach proposed, the nonnegative solution of dissipative inequality and the storage function of nonlinear H∞ control for a generator excitation system are acquired. From this storage function, the excitation controller is constructed. Moreover, simulation results manifest the effectiveness of this design method.
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.
Effective system properties and spectral density in random vibration with parametric excitation
DEFF Research Database (Denmark)
Krenk, Steen; Lin, Y. K.; Rüdinger, Finn
2002-01-01
The characteristic frequency and bandwidth of the random response to parametric excitation may be influenced by the excitation process. It is demonstrated that the effrective stiffness and damping properties can be expressed as conditional mean values for given displacement and energy levels...
Reduced-Order Modeling of Parametrically Excited Micro-Electro-Mechanical Systems (MEMS
Directory of Open Access Journals (Sweden)
Sangram Redkar
2010-01-01
Full Text Available Reduced-order modeling is a systematic way of constructing models with smaller number of states that can capture the “essential dynamics” of the large-scale systems, accurately. In this paper, reduced-order modeling and control techniques for parametrically excited MEMS are presented. The techniques proposed here use the Lyapunov-Floquet (L-F transformation that makes the linear part of transformed equations time invariant. In this work, three model reduction techniques for MEMS are suggested. First method is simply an application of the well-known Guyan-like reduction method to nonlinear systems. The second technique is based on singular perturbation, where the transformed system dynamics is partitioned as fast and slow dynamics and the system of differential equations is converted into a differential algebraic (DAE system. In the third technique, the concept of invariant manifold for time-periodic systems is used. The “time periodic invariant manifold” based technique yields “reducibility conditions”. This is an important result because it helps us to understand the various types of resonances present in the system. These resonances indicate a tight coupling between the system states, and in order to retain the dynamic characteristics, one has to preserve all these “resonant” states in the reduced-order model. Thus, if the “reducibility conditions” are satisfied, only then a nonlinear order reduction based on invariant manifold approach is possible. It is found that the invariant manifold approach yields the most accurate results followed by the nonlinear projection and linear technique. These methodologies are general, free from small parameter assumptions, and can be applied to a variety of MEM systems like resonators, sensors and filters. The reduced-order models can be used for parametric study, sensitivity analysis and/or controller design. The controller design is based on the reduced-order system. Thus, first the
Directory of Open Access Journals (Sweden)
Yong Zhao
1996-01-01
Full Text Available The large strain ratcheting in cyclic plasticity of a typical pressurized pipe elbow in a realistic nuclear piping system was investigated in a more quantitative manner than previously. The elbow was modeled using a fine mesh of shell elements that can provide the completed information of detailed time varying strain distributions in the whole elbow area. The nonlinear time history stress analyses performed were based on a pseudostatic concept using the vector-valued stochastic displacement response time series loaded at the elbow ends. The response time series were synthesized using a simulation approach based on the random vibration analyses of the piping system and its supporting building. After a finite element mesh convergence study, parametric analyses were conducted that included the effects due to the magnitude changes in excitation level, internal pressure, material yield stress, and material strain hardening.
Parametric excitation of electromagnetic fields by two pump waves
Energy Technology Data Exchange (ETDEWEB)
Brodin, G.; Lundberg, J.; Stenflo, L. (Umeaa Univ. (Sweden). Dept. of Plasma Physics)
1991-01-01
A collisionless plasma in the presence of two monochromatic electric fields is considered. By means of a kinetic analysis, a dispersion relation that governs the excitation of transverse electromagnetic fluctuations is derived and analysed. (orig.).
Wang, Yi-Ze; Li, Feng-Ming
2016-08-01
Structures under parametric load can be induced to the parametric instability in which the excitation frequency is located the instability region. In the present work, the parametric instability of double-walled carbon nanotubes is studied. The axial harmonic excitation is considered and the nonlocal continuum theory is applied. The critical equation is derived as the Mathieu form by the Galerkin's theory and the instability condition is presented with the Bolotin's method. Numerical calculations are performed and it can be seen that the van der Waals interaction can enhance the stability of double-walled nanotubes under the parametric excitation. The parametric instability becomes more obvious with the matrix stiffness decreasing and small scale coefficient increasing. The parametric instability is going to be more significant for higher mode numbers. For the nanosystem with the soft matrix and higher mode number, the small scale coefficient and the ratio of the length to the diameter have obvious influences on the starting point of the instability region.
Institute of Scientific and Technical Information of China (English)
韩东颖; 时培明; 赵东伟
2016-01-01
While considering parametric excitation nonlinearity,uncertainty and load torque,the nonlinear torsional vibration dynamic model of a mechanical and electrical transmission system in a strip-rolling mill is built.The problem of the strip-rolling mill's motor-speed robust tracking and non-fragile control of the DC motor is studied.As the nonlinearity of the strip-rolling mill's mechanical and electrical drive system is translated into parameter uncertainty,the sufficient condition that lets the system attain quadratic stability and outside-disturbance attenuation is obtained using H∞theory,Lyapunov stability theory and the LMI method.In order to achieve the given speed-signal tracking and non-fragile control,a feedforward and compensatory controller is designed.The results of the real strip-rolling mill's simulation example verify the effectiveness of the proposed method,and the non-fragility of the controller is reflected as the controller's parameter robustness.This means that the effect of the torsional vibration non-fragile control of the strip-rolling mill's mechanical and electrical drive system can be fulfilled by choosing the parameters of the controller directly.%建立了含参激非线性、不确定性、负载转矩的轧机机电传动系统扭振动力学模型，研究了板带轧机电机速度鲁棒跟踪非脆弱控制问题。将板带轧机机电传动系统的非线性按参数不确定性处理，通过 H∞理论、Lyapunov 稳定性理论和线性矩阵不等式（LMI）方法得到了通过状态反馈使得系统满足二次稳定、抑制外界干扰的充分条件；为了实现给定速度信号跟踪非脆弱控制，设计了前馈补偿器。轧机实例仿真结果验证了方法的有效性，并发现控制器的非脆弱性表现为控制器参数的鲁棒性，即可以通过控制器参数的直接选取达到板带轧机机电传动系统扭振非脆弱控制效果。
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Institute of Scientific and Technical Information of China (English)
M.M.Kamel; W.A.A.El-Ganaini; Y.S.Hamed
2009-01-01
Ultrasonic machining (USM) is of particular interest for the machining of non-conductive, brittle mate-rials such as engineering ceramics, In this paper, a multi-tool technique is used in USM to reduce the vibration in the tool holder and have reasonable amplitude for the tools. This can be done via dynamic absorbers. The coupling of four non-linear oscillators of the tool holder and tools representing ultrasonic cutting process are investigated. This leads to a four-degree-of-freedom system subjected to multi-external and multi-parametric excitation forces. The aim of this work is to control the tool holder behavior at simultaneous pri-mary, sub-harmonic and internal resonance condition. Mul-tiple scale perturbation method is used to obtain the solution up to the second order approximations. The different reso-nance cases are reported and studied numerically. The stabil-ity of the system is investigated by using both phase-plane and frequency response techniques. The effects of the differ-ent parameters of the tools on the system behavior are studied numerically. Comparison with the available published work is reported.
da Silva, Roberto; Peretti, Debora E
2016-01-01
In this paper, we explore the stability of an inverted pendulum under a generalized parametric excitation described by a superposition of $N$ cosines with different amplitudes and frequencies, based on a simple stability condition that does not require any use of Lyapunov exponent, for example. Our analysis is separated in 3 different cases: $N=1$, $N=2$, and $N$ very large. Our results were obtained via numerical simulations by fourth-order Runge Kutta integration of the non-linear equations. We also calculate the effective potential also for $N>2$. We show then that numerical integrations recover a wider region of stability that are not captured by the (approximated) analytical method. We also analyze stochastic stabilization here: firstly, we look the effects of external noise in the stability diagram by enlarging the variance, and secondly, when $N$ is large, we rescale the amplitude by showing that the diagrams for time survival of the inverted pendulum resembles the exact case for $N=1$. Finally, we fin...
Novel Localized Excitations of Nonlinear Coupled Scalar Fields
Institute of Scientific and Technical Information of China (English)
ZHU Ren-Gui; LI Jin-Hua; WANG An-Min; WU Huang-Jiao
2008-01-01
Some extended solution mapping relations of the nonlinear coupled scalar field and the well-known φ4 model are presented. Simultaneously, inspired by the new solutions of the famous φ4 model recently proposed by Jia, Huang and Lou, five kinds of new localized excitations of the nonlinear coupled scalar field (NCSF) system are obtained.
Directory of Open Access Journals (Sweden)
Frederico Martins Alves da Silva
2015-01-01
Full Text Available This work investigates the influence of Young’s modulus, shells thickness, and geometrical imperfection uncertainties on the parametric instability loads of simply supported axially excited cylindrical shells. The Donnell nonlinear shallow shell theory is used for the displacement field of the cylindrical shell and the parameters under investigation are considered as uncertain parameters with a known probability density function in the equilibrium equation. The uncertainties are discretized as Hermite-Chaos polynomials together with the Galerkin stochastic procedure that discretizes the stochastic equation in a set of deterministic equations of motion. Then, a general expression for the transversal displacement is obtained by a perturbation procedure which identifies all nonlinear modes that couple with the linear modes. So, a particular solution is selected which ensures the convergence of the response up to very large deflections. Applying the standard Galerkin method, a discrete system in time domain that considers the uncertainties is obtained and solved by fourth-order Runge-Kutta method. Several numerical strategies are used to study the nonlinear behavior of the shell considering the uncertainties in the parameters. Special attention is given to the influence of the uncertainties on the parametric instability and time response, showing that the Hermite-Chaos polynomial is a good numerical tool.
Metastable states in parametrically excited multimode Hamiltonian systems
Kirr, E
2003-01-01
Consider a linear autonomous Hamiltonian system with time periodic bound state solutions. In this paper we study their dynamics under time almost periodic perturbations which are small, localized and Hamiltonian. The analysis proceeds through a reduction of the original infinite dimensional dynamical system to the dynamics of two coupled subsystems: a dominant m-dimensional system of ordinary differential equations (normal form), governing the projections onto the bound states and an infinite dimensional dispersive wave equation. The present work generalizes previous work of the authors, where the case of a single bound state is considered. Here, the interaction picture is considerably more complicated and requires deeper analysis, due to a multiplicity of bound states and the very general nature of the perturbation's time dependence. Parametric forcing induces coupling of bound states to continuum radiation modes, bound states directly to bound states, as well as coupling among bound states, which is mediate...
Institute of Scientific and Technical Information of China (English)
HANG Chao; HUANG Guo-Xiang
2006-01-01
We investigate the nonlinear localized structures of optical pulses propagating in a one-dimensional photonic crystal with a quadratic nonlinearity. Using a method of multiple scales we show that the nonlinear evolution of a wave packet, formed by the superposition of short-wavelength excitations, and long-wavelength mean fields, generated by the self-interaction of the wave packet, are governed by a set of coupled high-dimensional nonlinear envelope equations, which can be reduced to Davey-Stewartson equations and thus support dromionlike high-dimensional nonlinear excitations in the system.
Broadband excitation and collection in fiber-optic nonlinear endomicroscopy
Prakash Ghimire, Navin; Bao, Hongchun; Gu, Min
2013-08-01
Broadband excitation and collection in a fiber-optic nonlinear endomicroscope are realized by using a single hollow-core double-clad photonic crystal fiber and a gradient index lens. Femtosecond pulses with central wavelengths in the range of 750-850 nm can be directly delivered through the core of the fiber for nonlinear excitation without pre-chirping. A gradient index lens with numerical aperture 0.8 designed to operate over the near-infrared wavelength range is used for focusing the laser beam from the fiber for nonlinear excitation and for collecting the fluorescent signal from the sample. This compact system is suitable to perform nonlinear imaging of multiple fluorophors in the wavelength range of 750-850 nm.
Institute of Scientific and Technical Information of China (English)
戎海武; 徐伟; 王向东; 孟光; 方同
2002-01-01
The principal resonance of Van der Pol-Duffing oscillator to combined determin istic and random parametric excitations is investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied. Jumps were shown to occur under some conditions. The effects of damping, detuning , bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analysis were verified by numerical results.
Directory of Open Access Journals (Sweden)
Albertus C. den Brinker
2007-01-01
Full Text Available This paper introduces a new audio and speech broadband coding technique based on the combination of a pulse excitation coder and a standardized parametric coder, namely, MPEG-4 high-quality parametric coder. After presenting a series of enhancements to regular pulse excitation (RPE to make it suitable for the modeling of broadband signals, it is shown how pulse and parametric codings complement each other and how they can be merged to yield a layered bit stream scalable coder able to operate at different points in the quality bit rate plane. The performance of the proposed coder is evaluated in a listening test. The major result is that the extra functionality of the bit stream scalability does not come at the price of a reduced performance since the coder is competitive with standardized coders (MP3, AAC, SSC.
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
Bishwajyoti Dey
2015-11-01
We discuss about the theory of nonlinear localized excitations, such as soliton and compactons in the gap of the linear spectrum of the nonlinear systems. We show how the gap originates in the linear spectrum using examples of a few systems, such as nonlinear lattices, Bose–Einstein condensates in optical lattice and systems represented by coupled nonlinear evolution equations. We then analytically show the excitation of solitons and compacton-like solutions in the gap of the linear spectrum of a system of coupled Korteweg–de Vries (KdV) equations with linear and nonlinear dispersions. Finally, we discuss about the theory of Feshbach resonance management and dispersion management of the soliton solutions.
Energy Technology Data Exchange (ETDEWEB)
Wu Xiaofeng [Center for Control and Optimizations, South China University of Technology, Guangzhou 510640 (China) and Guangzhou Naval Academy, Guangzhou 510430 (China)], E-mail: wuxiaof@21cn.com; Cai Jianping [Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275 (China); Wang Muhong [Guangzhou Naval Academy, Guangzhou 510430 (China)
2008-04-15
The paper deals with a linear state error feedback control technique which is utilized to synchronize two parametrically excited non-autonomous Duffing oscillators. Some sufficient criteria for global chaos synchronization are obtained by means of Lyapunov's direct method. A few examples are illustrated to verify the proposed theoretical results.
Directory of Open Access Journals (Sweden)
Michal Marszal
2014-01-01
Full Text Available This paper investigates dynamics of double pendulum subjected to vertical parametric kinematic excitation. It includes detailed bifurcation diagrams in two-parameter space (excitation’s frequency and amplitude for both oscillations and rotations in the domain of periodic solutions.
DEFF Research Database (Denmark)
Bak, Christen Kjeldahl; Kofoed, Bent; Pedersen, Niels Falsig;
1975-01-01
Experimental evidence for subharmonic, parametric excitation of plasma oscillations in Josephson tunnel junctions is presented. The experiments described are performed by measuring the microwave power necessary to switch a Josephson tunnel junction biased in the zero voltage state to a finite...
Non-Gaussian approach for parametric random vibration of non-linear structures
Ibrahim, R. A.; Soundararajan, A.
1984-01-01
The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.
Han, Xiujing; Bi, Qinsheng; Ji, Peng; Kurths, Jürgen
2015-07-01
We present a general method for analyzing mixed-mode oscillations (MMOs) in parametrically and externally excited systems with two low excitation frequencies (PEESTLEFs) for the case of arbitrary m:n relation between the slow frequencies of excitations. The validity of the approach has been demonstrated using the equations of Duffing and van der Pol, separately. Our study shows that, by introducing a slow variable and finding the relation between the slow variable and the slow excitations, PEESTLEFs can be transformed into a fast-slow form with a single slow variable and therefore MMOs observed in PEESTLEFs can be understood by the classical machinery of fast subsystem analysis of the transformed fast-slow system.
Directory of Open Access Journals (Sweden)
Jingjing Wu
2015-01-01
Full Text Available A robust particle filter (PF and its application to fault/defect detection of nonlinear system are investigated in this paper. First, an adaptive parametric model is exploited as the observation model for a nonlinear system. Second, by incorporating the parametric model, particle filter is employed to estimate more accurate hidden states for the nonlinear stochastic system. Third, by formulating the problem of defect detection within the hypothesis testing framework, the statistical properties of the proposed testing are established. Finally, experimental results demonstrate the effectiveness and robustness of the proposed detector on real defect detection and localization in images.
Zhukov, A. A.; Shapiro, D. S.; Remizov, S. V.; Pogosov, W. V.; Lozovik, Yu. E.
2017-02-01
We consider a superconducting qubit coupled to the nonstationary transmission line cavity with modulated frequency taking into account energy dissipation. Previously, it was demonstrated that in the case of a single nonadiabatical modulation of a cavity frequency there are two channels of a two-level system excitation which are due to the absorption of Casimir photons and due to the counterrotating wave processes responsible for the dynamical Lamb effect. We show that the parametric periodical modulation of the resonator frequency can increase dramatically the excitation probability. Remarkably, counterrotating wave processes under such a modulation start to play an important role even in the resonant regime. Our predictions can be used to control qubit-resonator quantum states as well as to study experimentally different channels of a parametric qubit excitation.
Yashkir, O. V.; Yashkir, Yu N.
1987-11-01
An investigation is made of nonlinear optical interaction of light propagating in a planar waveguide with surface polaritons. Reduced wave equations for the amplitudes of the waveguide modes and surface polaritons are used to study the characteristics of generation of surface polaritons of difference frequency, parametric frequency up-conversion of the polaritons, and stimulated Raman scattering by the polaritons. An analysis is made of the characteristic properties of the investigated nonlinear optical processes.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Design of triply-resonant microphotonic parametric oscillators based on Kerr nonlinearity.
Zeng, Xiaoge; Popović, Miloš A
2014-06-30
We propose optimal designs for triply-resonant optical parametric oscillators (OPOs) based on degenerate four-wave mixing (FWM) in microcavities. We show that optimal designs in general call for different external coupling to pump and signal/idler resonances. We provide a number of normalized performance metrics including threshold pump power and maximum achievable conversion efficiency for OPOs with and without two-photon (TPA) and free-carrier absorption (FCA). We find that the maximum achievable conversion efficiency is bound to an upper limit by nonlinear and free-carrier losses independent of pump power, while linear losses only increase the pump power required to achieve a certain conversion efficiency. The results of this work suggest unique advantages in on-chip implementations that allow explicit engineering of resonances, mode field overlaps, dispersion, and wavelength-and mode-selective coupling. We provide universal design curves that yield optimum designs, and give example designs of microring-resonator-based OPOs in silicon at the wavelengths 1.55 μm (with TPA) and 2.3 μm (no TPA) as well as in silicon nitride (Si(3)N(4)) at 1.55 μm. For typical microcavity quality factor of 10(6), we show that the oscillation threshold in excitation bus can be well into the sub-mW regime for silicon microrings and a few mW for silicon nitride microrings. The conversion efficiency can be a few percent when pumped at 10 times of the threshold. Next, based on our results, we suggest a family of synthetic "photonic molecule"-like, coupled-cavity systems to implement optimum FWM, where structure design for control of resonant wavelengths can be separated from that of optimizing nonlinear conversion efficiency, and where furthermore pump, signal, and idler coupling to bus waveguides can be controlled independently, using interferometric cavity supermode coupling as an example. Finally, consideration of these complex geometries calls for a generalization of the nonlinear
Purely nonlinear disorder-induced localizations and their parametric amplification
Folli, Viola; Conti, Claudio
2013-01-01
We investigate spatial localization in a quadratic nonlinear medium in the presence of randomness. By means of numerical simulations and theoretical analyses we show that, in the down conversion regime, the transverse random modulation of the nonlinear susceptibility generates localizations of the fundamental wave that grow exponentially in propagation. The localization length is optically controlled by the pump intensity which determines the amplification rate. The results also apply to cubic nonlinearities.
Institute of Scientific and Technical Information of China (English)
CHEN Liqun; Jean W.ZU; WU Jun
2004-01-01
To investigate the principal resonance in transverse nonlinear parametric vibration of an axially accelerating viscoelastic string, the method of multiple scales is applied directly to the nonlinear partial differential equation that governs the transverse vibration of the string. To derive the governing equation, Newton's second law, Lagrangean strain, and Kelvin's model are respectively used to account the dynamical relation, geometric nonlinearity and the viscoelasticity of the string material.Based on the solvability condition of eliminating the secular terms, closed form solutions are obtained for the amplitude and the existence conditions of nontrivial steady-state response of the principal parametric resonance. The Lyapunov linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions in the principal parametric resonance. Some numerical examples are presented to show the effects of the mean transport speed, the amplitude and the frequency of speed variation.
Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow
Choudhari, Meelan; Duck, Peter W.
1996-01-01
We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.
Nonlinear analysis of a structure loaded by a stochastic excitation
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
For a non-linear system excited by a stochastic load which is expressed as a time series, a recursive method based on the Z-transform is presented. To identify the obtained response time series, a discrete wavelet transform (DWT) technique is proposed.
Heteroclinic structure of parametric resonance in the nonlinear Schr\\"odinger equation
Conforti, M; Kudlinski, A; Rota-Nodari, S; Dujardin, G; De Bievre, S; Armaroli, A; Trillo, S
2016-01-01
We show that the nonlinear stage of modulational instability induced by parametric driving in the {\\em defocusing} nonlinear Schr\\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis.
Nonlinear Scaling Laws for Parametric Receiving Arrays. Part II. Numerical Analysis
1976-06-30
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Chaotic motions in the resonant separatrix band of a parametrically excited pendulum
Institute of Scientific and Technical Information of China (English)
AlbertC.J.LUO
2000-01-01
The energy increment spectrum method is developed for the numerical prediction of the appearance and disappearance of a primary (2M : 1)-librational or (M : 1)-rotational resonant separatrix band in a parametrically excited pendulum. The analytical conditions for the presence of such separatrix bands are also obtained. Illustrations of the analytical and numerical results for the appearance and destruction of the resonant bands are given for a comparison.
Reflections and mirror effect of parametrically-excited solitons at a boundary
Institute of Scientific and Technical Information of China (English)
王新龙
1995-01-01
Some of the up-to-date experimental results on the parametrically-excited solitons in arectangular trough of water are provided, including the periodical reflection of a soliton at an end wall of a trough, the collision dynamics of two solitons of like polarity and the existence of mirror effect at boundaries. Attempts are made to explain the observed phenomena and a conception of virtual solitons is proposed.
VISCO-ELASTIC SYSTEMS UNDER BOTH DETERMINISTIC AND BOUND RANDOM PARAMETRIC EXCITATION
Institute of Scientific and Technical Information of China (English)
徐伟; 戎海武; 方同
2003-01-01
The principal resonance of a visco-elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied by means of qualitative analysis. The contributions from the visco-elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations were analyzed. The theoretical analysis is verified by numerical results.
Institute of Scientific and Technical Information of China (English)
Xiao Li; Zhang Wei; Huang Yi-Dong; Peng Jiang-De
2008-01-01
High nonlinear microstructure fibre (HNMF) is preferred in nonlinear fibre optics, especially in the applications of optical parametric effects, due to its high optical nonlinear coefficient. However, polarization dependent dispersion will impact the nonlinear optical parametric process in HNMFs. In this paper, modulation instability (MI) method is used to measure the polarization dependent dispersion of a piece of commercial HNMF, including the group velocity dispersion, the dispersion slope, the fourth-order dispersion and group birefringence. It also experimentally demonstrates the impact of the polarization dependent dispersion on the continuous wave supercontinuum (SC) generation. On one axis MI sidebands with symmetric frequency dctunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift.
Nonlinear Container Ship Model for the Study of Parametric Roll Resonance
DEFF Research Database (Denmark)
Holden, Christian; Galeazzi, Roberto; Rodríguez, Claudio
2007-01-01
Parametric roll is a critical phenomenon for ships, whose onset may cause roll oscillations up to 40, leading to very dangerous situations and possibly capsizing. Container ships have been shown to be particularly prone to parametric roll resonance when they are sailing in moderate to heavy head...... seas. A Matlab/Simulinkr parametric roll benchmark model for a large container ship has been implemented and validated against a wide set of experimental data. The model is a part of a Matlab/Simulink Toolbox (MSS, 2007). The benchmark implements a 3rd-order nonlinear model where the dynamics of roll...... is strongly coupled with the heave and pitch dynamics. The implemented model has shown good accuracy in predicting the container ship motions, both in the vertical plane and in the transversal one. Parametric roll has been reproduced for all the data sets in which it happened, and the model provides realistic...
Nonlinear dynamics of a flexible portal frame under support excitation
de Paula, Aline Souza; Balthazar, José Manoel; Felix, Jorge Luis Palacios
2012-11-01
This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The problem is reduced to a mathematical model of four degrees of freedom and the equations of motion are derived via Lagrangian formulation. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a non-ideal support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincaŕ sections and bifurcation diagrams..
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.
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
Nonlinear Optical Spectroscopy of Excited States in Polyfluorene
Tong, M; Vardeny, Z V
2006-01-01
We used a variety of nonlinear optical (NLO) spectroscopies to study the singlet excited states order, and primary photoexcitations in polyfluorene; an important blue emitting p-conjugated polymer. The polarized NLO spectroscopies include ultrafast pump-probe photomodulation, two-photon absorption, and electroabsorption. For completeness we also measured the linear absorption and photoluminescence spectra. We found that the primary photoexcitations in polyfluorene are singlet excitons.
Bai, Cheng; Huang, Jin
2015-07-01
Fast settling, accurate positioning, and a large tilt angle range are important for MEMS mirrors. Here, residual vibration and the pull-in phenomenon-both major problems affecting the performance of an electrostatically actuated mirror-are investigated. Based on the analysis of a nonlinear proportional-derivative (PD) control with parametric uncertainties, a closed-loop feedback control strategy with a combined control scheme is proposed. This method, combining nonlinear PD control and sliding mode control (SMC), not only inherits the virtue of a good dynamic performance from the nonlinear PD control, but also further improves the robustness with SMC for such MEMS mirrors. Furthermore, this method can be convenient when tuning design gains of the controller to obtain a faster error convergence rate. Numerical simulation results show that with this combined control scheme not only the transient response of the MEMS mirror is improved but the influence of parametric uncertainties and external disturbance is also reduced.
Instability analysis of resonant standing waves in a parametrically excited boxed basin
Energy Technology Data Exchange (ETDEWEB)
Sirwah, Magdy A [Department of Mathematics, Faculty of Science, Tanta University, Tanta (Egypt)], E-mail: magdysirwah@yahoo.com
2009-06-15
Two-mode parametric excited interfacial waves of incompressible immiscible liquids in an infinite boxed basin subjected to a vertical excitation are studied. The method of multiple time scales is used to obtain uniform solutions of the second-order system as well as the third-order one, which in turn leads to the solvability conditions of the two orders including the cubic interaction terms. The different cases of resonance that arise among the natural frequencies together with the frequency of the vertical vibration of the box are demonstrated theoretically and numerical computations of one of these cases (the two-to-one internal resonance and the principal parametric resonance) have been performed in detail in order to investigate the behavior of the resonant waves, especially the qualitative one. The autonomous system of four first-order differential equations for the modulation of the amplitudes and phases of the resonant waves is derived. Some numerical applications are achieved to show the stability criteria of the excited liquids inside the considered basin.
Sensitivity of nonlinear photoionization to resonance substructure in collective excitation
Mazza, T.; Karamatskou, A.; Ilchen, M.; Bakhtiarzadeh, S.; Rafipoor, A. J.; O'Keeffe, P.; Kelly, T. J.; Walsh, N.; Costello, J. T.; Meyer, M.; Santra, R.
2015-04-01
Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources.
Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A
2015-01-01
Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.
Kwuimy, C A Kitio; Nataraj, C; Litak, G
2011-12-01
We consider the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos is analyzed using the Melnikov's criterion for a transition to permanent or transient nonperiodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincaré sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. Our attention is focussed on the effects of the asymmetric potential term and the driven frequency. It is shown that the threshold amplitude ∣γ(c)∣ of the excitation decreases for small values of the driven frequency ω and increases for large values of ω. This threshold value decreases with the asymmetric parameter α and becomes constant for sufficiently large values of α. γ(c) has its maximum value for asymmetric load in comparison with the symmetric load. Finally, we apply the Melnikov theorem to the controlled system to explore the gain control parameter dependencies.
Quantum mechanical treatment of parametric amplification in an absorptive nonlinear medium
Inoue, K.
2017-01-01
Generally, loss phenomena are known to affect the quantum properties of a light wave. This paper describes a quantum mechanical treatment of parametric amplification in an absorptive nonlinear medium. An expression of the quantum mechanical field operator in such a physical system is presented based on the Heisenberg equation, using which the quantum properties of traveling light suffering from medium absorption are quantitatively evaluated. Calculations using the obtained operator indicate that some degradation of noise performance is caused by the absorption. The influence of the absorption on the squeezing performance in phase-sensitive parametric amplification is also evaluated.
Ulvila, Ville; Halonen, Lauri; Vainio, Markku
2015-01-01
We present an experimental study of optical frequency comb generation based on cascaded quadratic nonlinearities inside a continuous-wave-pumped optical parametric oscillator. We demonstrate comb states which produce narrow-linewidth intermode beat note signals, and we verify the mode spacing uniformity of the comb at the Hz level. We also show that spectral quality of the comb can be improved by modulating the parametric gain at a frequency that corresponds to the comb mode spacing. We have reached a high average output power of over 4 W in the near-infrared region, at ~2 {\\mu}m.
Nonlinear self-excited oscillations of a ducted flame
Dowling, A. P.
1997-09-01
Self-excited oscillations of a confined flame, burning in the wake of a bluff-body flame-holder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic waves. According to linear theory, flow disturbances grow exponentially with time. A theory for nonlinear oscillations is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially ‘saturates’. The amplitudes of the pressure fluctuations are sufficiently small that the acoustic waves remain linear. The time evolution of the oscillations is determined by numerical integration and inclusion of nonlinear effects is found to lead to limit cycles of finite amplitude. The predicted limit cycles are compared with results from experiments and from linear theory. The amplitudes and spectra of the limit-cycle oscillations are in reasonable agreement with experiment. Linear theory is found to predict the frequency and mode shape of the nonlinear oscillations remarkably well. Moreover, we find that, for this type of nonlinearity, describing function analysis enables a good estimate of the limit-cycle amplitude to be obtained from linear theory.
Parametric resonance of flexible footbridges under crowd-induced lateral excitation
Piccardo, Giuseppe; Tubino, Federica
2008-03-01
The excessive lateral sway motion caused by crowds walking across footbridges has attracted great public attention in the past few years. Three possible mechanisms responsible for such lateral vibrations have been investigated in the literature: direct resonance, dynamic interaction, and internal resonance. In this paper, starting from a critical review of the mechanisms proposed in the literature, a parametric excitation mechanism is analyzed, based on a forcing model whose amplitude is a function of deck oscillations. A stability criterion is identified, depending on the ratio between the structural and excitation frequencies, on the ratio of the structural and pedestrian masses, and on the structural damping. The proposed mechanism can be achieved for very flexible footbridges, with a lateral natural frequency around 0.5 Hz, corresponding to a half of the lateral walking frequency. This situation can occur in modern structures, such as in the case of the London Millennium Footbridge.
Excitation of nonlinear ion acoustic waves in CH plasmas
Feng, Q S; Liu, Z J; Xiao, C Z; Wang, Q; He, X T
2016-01-01
Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $ k\\lambda_{De} $ increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $ T_i/T_e < 0.2 $ in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\\lambda_{De}$ increasing. When $k\\lambda_{De}$ is not large, such as $k\\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when $k\\lambda_{De}$ is large, such as $k\\lambda_{De}=0.7$, the linear ...
Experiments and theory on parametric instabilities excited in HF heating experiments at HAARP
Energy Technology Data Exchange (ETDEWEB)
Kuo, Spencer [New York University-Polytechnic School of Engineering, 5 Metrotech Center, Brooklyn, New York 11201 (United States); Snyder, Arnold [NorthWest Research Associates, P.O. Box 530, Stockton Springs, Maine 04981 (United States); Lee, M. C. [Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215 (United States); Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2014-06-15
Parametric instabilities excited by O-mode HF heater and the induced ionospheric modification were explored via HAARP digisonde operated in a fast mode. The impact of excited Langmuir waves and upper hybrid waves on the ionosphere are manifested by bumps in the virtual spread, which expand the ionogram echoes upward as much as 140 km and the downward range spread of the sounding echoes, which exceeds 50 km over a significant frequency range. The theory of parametric instabilities is presented. The theory identifies the ionogram bump located between the 3.2 MHz heater frequency and the upper hybrid resonance frequency and the bump below the upper hybrid resonance frequency to be associated with the Langmuir and upper hybrid instabilities, respectively. The Langmuir bump is located close to the upper hybrid resonance frequency, rather than to the heater frequency, consistent with the theory. Each bump in the virtual height spread of the ionogram is similar to the cusp occurring in daytime ionograms at the E-F2 layer transition, indicating that there is a small ledge in the density profile similar to E-F2 layer transitions. The experimental results also show that the strong impact of the upper hybrid instability on the ionosphere can suppress the Langmuir instability.
Experiments and theory on parametric instabilities excited in HF heating experiments at HAARP
Kuo, Spencer; Snyder, Arnold; Lee, M. C.
2014-06-01
Parametric instabilities excited by O-mode HF heater and the induced ionospheric modification were explored via HAARP digisonde operated in a fast mode. The impact of excited Langmuir waves and upper hybrid waves on the ionosphere are manifested by bumps in the virtual spread, which expand the ionogram echoes upward as much as 140 km and the downward range spread of the sounding echoes, which exceeds 50 km over a significant frequency range. The theory of parametric instabilities is presented. The theory identifies the ionogram bump located between the 3.2 MHz heater frequency and the upper hybrid resonance frequency and the bump below the upper hybrid resonance frequency to be associated with the Langmuir and upper hybrid instabilities, respectively. The Langmuir bump is located close to the upper hybrid resonance frequency, rather than to the heater frequency, consistent with the theory. Each bump in the virtual height spread of the ionogram is similar to the cusp occurring in daytime ionograms at the E-F2 layer transition, indicating that there is a small ledge in the density profile similar to E-F2 layer transitions. The experimental results also show that the strong impact of the upper hybrid instability on the ionosphere can suppress the Langmuir instability.
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations
Chen, Peng; Schwab, Christoph
2016-07-01
We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov-Galerkin high-fidelity (;HiFi;) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Peng, E-mail: peng@ices.utexas.edu [The Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, Stop C0200, Austin, TX 78712-1229 (United States); Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch [Seminar für Angewandte Mathematik, Eidgenössische Technische Hochschule, Römistrasse 101, CH-8092 Zürich (Switzerland)
2016-07-01
We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data
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.
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.
Variable selection in identification of a high dimensional nonlinear non-parametric system
Institute of Scientific and Technical Information of China (English)
Er-Wei BAI; Wenxiao ZHAO; Weixing ZHENG
2015-01-01
The problem of variable selection in system identification of a high dimensional nonlinear non-parametric system is described. The inherent difficulty, the curse of dimensionality, is introduced. Then its connections to various topics and research areas are briefly discussed, including order determination, pattern recognition, data mining, machine learning, statistical regression and manifold embedding. Finally, some results of variable selection in system identification in the recent literature are presented.
Numerical Tracking of Limit Points for Direct Parametric Analysis in Nonlinear Rotordynamics
Xie, Lihan; Baguet, Sébastien; Prabel, Benoit; Dufour, Régis
2016-01-01
International audience; A frequency-domain approach for direct parametric analysis of limit points of nonlinear dynamical systems is presented in this paper. Instead of computing responses curves for several values of a given system parameter, the direct tracking of limit points is performed. The whole numerical procedure is based on the Harmonic Balance Method and can be decomposed in three distinct steps. Firstly, a response curve is calculated by HBM combined with a continuation technique ...
Jing, Xingjian
2015-01-01
This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain. The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis a...
Resonances in nonlinear structure vibrations under multifrequency excitations
Energy Technology Data Exchange (ETDEWEB)
El-Bassiouny, A F [Faculty of Science, Mathematics Department, Benha University, Benha 1358 (Egypt); El-Latif, G M Abd [Faculty of Science, Mathematics Department, Sohag University, Sohag (Egypt)
2006-10-15
The response of a single-degree-of-freedom system with quadratic, cubic and quartic nonlinearities subjected to a sinusoidal excitation that involves multiple frequencies is considered. The method of multiple scales is used to construct a first order uniform expansion yielding two first-order nonlinear ordinary differential equations that are derived for the evolution of the amplitude and phase. These oscillations involve a subharmonic oscillation of order one-fourth and superharmonic oscillation of order two. Steady state responses and their stability are computed for selected values of the system parameters. The effects of these (quadratic, cubic, and quartic) nonlinearities on these oscillations are specifically investigated. With this study, it has been verified that the qualitative effects of these nonlinearities are different. Regions of hardening (softening) behaviour of the system exist for the case of subharmonic resonance. The response curve is not affected by decreasing the damping factor for the case of superharmonic resonance. It is shown that the response curve contracts or expands as the parameters vary. The multivalued region increases or decreases when some parameters vary.
Nonlinearity and trapping in excitation transfer Dimers and Trimers.
Barvik, I; Schanz, H; Barvik, Ivan; Esser, Bernd; Schanz, Holger
1995-01-01
We study the interplay between nonlinearity in exciton transport and trapping due to a sink site for the dimer and the trimer with chain configuration by a numerical integration of the discrete nonlinear Schroedinger equation. Our results for the dimer show, that the formation of a self trapped state due to the nonlinear coupling increases the life time of the exciton substantially. Self trapping can be enhanced by the sink for short times, but for long times it disappears. In the trimer consisting of a subdimer extended by a sink site exists a transition between states localized on the two sites of the subdimer before for larger nonlinear coupling self trapping on one site of the subdimer is observed. For large trapping rates the fear of death effect leads to an increasing life time of the excitation on both, the dimer and the trimer. The sink site is then effectively decoupled. We explain this effect using an asymptotic theory for strong trapping and demonstrate it by direct numerical computation.
Sabater, A. B.; Rhoads, J. F.
2017-02-01
The parametric system identification of macroscale resonators operating in a nonlinear response regime can be a challenging research problem, but at the micro- and nanoscales, experimental constraints add additional complexities. For example, due to the small and noisy signals micro/nanoresonators produce, a lock-in amplifier is commonly used to characterize the amplitude and phase responses of the systems. While the lock-in enables detection, it also prohibits the use of established time-domain, multi-harmonic, and frequency-domain methods, which rely upon time-domain measurements. As such, the only methods that can be used for parametric system identification are those based on fitting experimental data to an approximate solution, typically derived via perturbation methods and/or Galerkin methods, of a reduced-order model. Thus, one could view the parametric system identification of micro/nanosystems operating in a nonlinear response regime as the amalgamation of four coupled sub-problems: nonparametric system identification, or proper experimental design and data acquisition; the generation of physically consistent reduced-order models; the calculation of accurate approximate responses; and the application of nonlinear least-squares parameter estimation. This work is focused on the theoretical foundations that underpin each of these sub-problems, as the methods used to address one sub-problem can strongly influence the results of another. To provide context, an electromagnetically transduced microresonator is used as an example. This example provides a concrete reference for the presented findings and conclusions.
On the existence of localized excitations in nonlinear hamiltonian lattices
Flach, S
1994-01-01
We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase space of this map. Using dimensionality properties of separatrix manifolds of the mapping we show the persistence of NLE solutions under perturbations of the system, provided NLEs exist for the given system. For a class of nonintegrable Fermi-Pasta-Ulam chains we rigorously prove the existence of NLE solutions.
Damping by parametric excitation in a set of reduced-order cracked rotor systems
Kulesza, Zbigniew; Sawicki, Jerzy T.
2015-10-01
A common tool utilized for the stability analysis of parametrically excited linear systems, such as rotors with cracked shafts, is Floquet's method. The disadvantage is a long calculation time needed to evaluate the monodromy matrix and instability zones. An efficient alternative is the generalized Bolotin's method, where the instability zones are evaluated quickly, yet the matrices that must be calculated are of large dimensions. In the present paper, the stability analysis is conducted with both Floquet's method and the generalized Bolotin's method. However, the order of the model is reduced to two modes only and stability analyses are performed for the second-order systems obtained with various combinations of the reducing modes. Then, the results of such analyses are collected in an overall stability map. The stability map obtained in this way closely reconstructs the stability map calculated with the full-order model of the rotor, yet the calculation time needed to generate the collected map as well as the dimension of the problem are considerably reduced. The approach is demonstrated with a mathematical model of the machine with the breathing crack modeled using the rigid finite element method. The rotor is not rotating, yet the stiffness of the shaft is varied periodically to simulate the parametric excitation. An interesting indication of the developing shaft crack observed in the generated stability maps is the presence of anti-resonant zones, where the rotor vibration amplitudes quickly decay. It is anticipated that this phenomenon of increased damping at specific excitation frequencies may have potential application for shaft crack detection.
Gorinevsky, D
1995-01-01
Considers radial basis function (RBF) network approximation of a multivariate nonlinear mapping as a linear parametric regression problem. Linear recursive identification algorithms applied to this problem are known to converge, provided the regressor vector sequence has the persistency of excitation (PE) property. The main contribution of this paper is formulation and proof of PE conditions on the input variables. In the RBF network identification, the regressor vector is a nonlinear function of these input variables. According to the formulated condition, the inputs provide PE, if they belong to domains around the network node centers. For a two-input network with Gaussian RBF that have typical width and are centered on a regular mesh, these domains cover about 25% of the input domain volume. The authors further generalize the proposed solution of the standard RBF network identification problem and study affine RBF network identification that is important for affine nonlinear system control. For the affine RBF network, the author formulates and proves a PE condition on both the system state parameters and control inputs.
Directory of Open Access Journals (Sweden)
Souayeh Saoussen
2014-01-01
Full Text Available The collective nonlinear dynamics of a coupled array of nanocantilevers is investigated while taking into account the main sources of nonlinearities. The amplitude and phase equations of this device, subject to parametric and internal resonances, are analytically derived by means of a multi-modal Galerkin discretization coupled with a multiscale analysis. Based on the steady-state solutions of these equations, the frequency responses are numerically computed for a two-beam array. The effects of different parameters are investigated and several dynamical aspects are confirmed by numerical simulations. Particularly, we have demonstrated that the bifurcation topology transfer is imposed by the first nanocantilever and it can be general to the collective nonlinear dynamics of the NEMS array.
Abbasi, Mustafa; Sadeghi, Yahya; Sobhanian, Samad; Asgarian, Mohammad Ali
2016-03-01
The electron Bernstein wave (EBW) is typically the only wave in the electron cyclotron (EC) range that can be applied in spherical tokamaks for heating and current drive (H&CD). Spherical tokamaks (STs) operate generally in high- β regimes, in which the usual EC ordinary (O) and extraordinary (X) modes are cut off. As it was recently investigated the existence of EBWs at nonlinear regime thus the next step would be the probable nonlinear phenomena study which are predicted to be occurred within the high levels of injected power. In this regard, parametric instabilities are considered as the major channels for losses at the X-B conversion. Hence, we have to consider their effects at the UHR region which can reduce the X-B conversion efficiency. In the case of EBW heating (EBH) at high power density, the nonlinear effects can arise. Particularly at the UHR position, the group velocity is strongly reduced, which creates a high energy density and subsequently a high amplitude electric field. Therefore, a part of the input wave can decay into daughter waves via parametric instability (PI). Thus, via the present research, the excitations of ion Bernstein waves as the dominant decay channels are investigated and also an estimate for the threshold power in terms of experimental parameters related to the fundamental mode of instability is proposed.
Energy Technology Data Exchange (ETDEWEB)
Stefszky, Michael; Buchler, Ben C; Symul, Thomas; Lam, Ping Koy [Quantum Optics Group, Department of Quantum Science, The Australian National University, ACT 0200 (Australia); Mow-Lowry, Conor M; McKenzie, Kirk; Chua, Sheon; McClelland, David E, E-mail: michael.stefszky@anu.edu.au [Centre for Gravitational Physics, Department of Quantum Science, The Australian National University, ACT 0200 (Australia)
2011-01-14
A squeezed light source requires properties such as high squeezing amplitude, high bandwidth and stability over time, ideally using as few resources, such as laser power, as possible. We compare three nonlinear materials, two of which have not been well characterized for squeezed state production, and also investigate the viability of doubly-resonant optical parametric oscillator cavities in achieving these requirements. A model is produced that provides a new way of looking at the construction of an optical parametric oscillator/optical parametric amplifier setup where second harmonic power is treated as a limited resource. The well-characterized periodically poled potassium titanyl phosphate (PPKTP) is compared in an essentially identical setup to two relatively new materials, periodically poled stoichiometric lithium tantalate (PPSLT) and 1.7% magnesium oxide doped periodically poled stoichiometric lithium niobate (PPSLN). Although from the literature PPSLT and PPSLN present advantages such as a higher damage threshold and a higher nonlinearity, respectively, PPKTP was still found to have the most desirable properties. With PPKTP, 5.8 dB of squeezing below the shot noise limit was achieved. With PPSLT, 5.0 dB of squeezing was observed but the power required to see this squeezing was much higher than expected. A technical problem with the PPSLN limited the observed squeezing to around 1.0 dB. This problem is discussed.
Nonlinear Container Ship Model for the Study of Parametric Roll Resonance
Directory of Open Access Journals (Sweden)
Christian Holden
2007-10-01
Full Text Available Parametric roll is a critical phenomenon for ships, whose onset may cause roll oscillations up to +-40 degrees, leading to very dangerous situations and possibly capsizing. Container ships have been shown to be particularly prone to parametric roll resonance when they are sailing in moderate to heavy head seas. A Matlab/Simulink parametric roll benchmark model for a large container ship has been implemented and validated against a wide set of experimental data. The model is a part of a Matlab/Simulink Toolbox (MSS, 2007. The benchmark implements a 3rd-order nonlinear model where the dynamics of roll is strongly coupled with the heave and pitch dynamics. The implemented model has shown good accuracy in predicting the container ship motions, both in the vertical plane and in the transversal one. Parametric roll has been reproduced for all the data sets in which it happened, and the model provides realistic results which are in good agreement with the model tank experiments.
Nonlinear Optical Properties of Novel C60 Derivatives under Picosecond Laser Excitation
Institute of Scientific and Technical Information of China (English)
MAO Yan-Li; CHENG Yong-Guang; LIU Jun-Hui; LIN Bing-chen; HUO Yan-Ping; ZENG He-Ping
2007-01-01
We investigate the third-order nonlinear optical properties of six novel fullerene derivatives under picosecond laser excitation by Z-scan technique.The experimental results reveal that all the derivatives have very large nonlinear absorption coefficient under 532 nm pulses excitation and great third-order nonlinear refraction index under 1064 nm pulses excitation.The molecular second hyperpolarizabilities are obtained from the experimental results.
Kim, I. K.; Lee, S. I.
2013-09-01
The nonlinear dynamics of a resonating carbon nanotube (CNT) cantilever having an attached mass at the tip ("tip mass") were investigated by incorporating electrostatic forces and intermolecular interactions between the CNT and a conducting plane surface. This work enables applications of CNT resonating sensors for tiny mass detection and provides a better understanding of the dynamics of CNT cantilevers. The effect of tip mass on a resonating CNT cantilever is normally characterized by the fundamental frequency shift in the linear resonance regime. However, there are more complex dynamics in the nonlinear resonance regime, such as secondary resonances with parametric excitation. The latter have been limited to nano-cantilevers without tip mass or to axially excited micro-beams. To analyze the nonlinear dynamics, we developed a differential equation model that includes both geometric and inertial nonlinear terms for the large vibration amplitudes at increasing drive forces. In our approach, we used Galerkin discretization techniques and numerical integration methods. The CNT cantilever exhibited complex nonlinear responses due to the applied AC and DC voltages and various tip masses. The nonlinear model had a softer response for increasing tip mass than those of the linear model with the same driving conditions. At low applied voltages, the cantilever had linear amplitude and phase responses at primary and secondary superharmonic resonance frequencies. The response branches were softened at the primary resonance through saddle-node (SN) bifurcation from harmonic electrostatic excitation at higher applied voltages. After SN bifurcation, the lower branch of the solution near resonance became unstable. In addition, theoretical analyses were performed on more complex nonlinear responses and stability changes with tip mass variations, such as period-doubling (PD) bifurcation at subharmonic resonance frequencies.
Notake, Takashi; Nawata, Kouji; Kawamata, Hiroshi; Matsukawa, Takeshi; Qi, Feng; Minamide, Hiroaki
2012-11-01
We developed a difference frequency generation (DFG) source with an organic nonlinear optical crystal of DAST or BNA selectively excited by a dual-wavelength β-BaB(2)O(4) optical parametric oscillator (BBO-OPO). The dual-wavelength BBO-OPO can independently oscillate two lights with different wavelengths from 800 to 1800 nm in a cavity. THz-wave generation by using each organic crystal covers ultrawide range from 1 to 30 THz with inherent intensity dips by crystal absorption modes. The reduced outputs can be improved by switching over the crystals with adequately tuned pump wavelengths of the BBO-OPO.
Institute of Scientific and Technical Information of China (English)
WANG Huanlei; ZHU Xiaofeng; GONG Xiufen; ZHANG Dong
2003-01-01
Based on the finite amplitude insert-substitu- tion method, a novel technique to reconstruct the acoustic nonlinear parameter B/A tomography for biological tissues in reflection mode via the difference frequency wave generated by a parametric array is developed in this paper. An experimental system is established, and the beam pattern of the difference frequency wave is measured and compared with that excited directly from a transmitter at the same frequency. B/A tomography for several biological tissues including normal and pathological tissues, is experimentally obtained with satisfying quality. Results indicate that B/A imaging using this mode may become a novel modality in ultrasonic diagnosis.
Wang, Xiang; Cannon, Patrick; Zhou, Chen; Honary, Farideh; Ni, Binbin; Zhao, Zhengyu
2016-04-01
Recent ionospheric modification experiments performed at Tromsø, Norway, have indicated that X-mode pump wave is capable of stimulating high-frequency enhanced plasma lines, which manifests the excitation of parametric instability. This paper investigates theoretically how the observation can be explained by the excitation of parametric instability driven by X-mode pump wave. The threshold of the parametric instability has been calculated for several recent experimental observations at Tromsø, illustrating that our derived equations for the excitation of parametric instability for X-mode heating can explain the experimental observations. According to our theoretical calculation, a minimum fraction of pump wave electric field needs to be directed along the geomagnetic field direction in order for the parametric instability threshold to be met. A full-wave finite difference time domain simulation has been performed to demonstrate that a small parallel component of pump wave electric field can be achieved during X-mode heating in the presence of inhomogeneous plasma.
Detection of Parametric Roll Resonance on Ships from Indication of Nonlinear Energy Flow
DEFF Research Database (Denmark)
Galeazzi, Roberto; Blanke, Mogens; Poulsen, Niels Kjølstad
2009-01-01
The detection of the onset of parametric roll resonance on ships is of a central importance in order to activate specific control strategies able to counteract the large roll motion. One of the main priorities is to have detectors with a small detection time, such that warnings can be issued when...... the roll oscillations are about 5◦. This paper proposes two different detection approaches: the first one based on sinusoidal detection in white gaussian noise; the second one utilizes an energy flow indicator in order to catch the onset of parametric roll based upon the transfer of energy from heave...... and pitch to roll. Both detectors have been validated against experimental data of a scale model of a container vessel excited with both regular and irregular waves. The detector based on the energy flow indicator proved to be very robust to different scenarios (regular/irregular waves) since it does...
DEFF Research Database (Denmark)
Gaididei, Yu. B.; Christiansen, Peter Leth
2008-01-01
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered...... and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under...
Phase locking and quantum statistics in a parametrically driven nonlinear resonator
Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.
2016-04-01
We discuss phase-locking phenomenon at low-level of quanta and quantum statistics for parametrically driven nonlinear Kerr resonator (PDNR). Oscillatory mode of PDNR is created in the process of a degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. We calculate the distribution of photon-number states, the second-order correlation function of photons, the Wigner functions of cavity mode showing two-fold symmetry in phase space, and we analyze formation of phase-locked states in the regular as well as the quantum chaotic regime of the PDNR.
Parametric nonlinear lumped element model for circular CMUTs in collapsed mode.
Aydoğdu, Elif; Ozgurluk, Alper; Atalar, Abdullah; Köymen, Hayrettin
2014-01-01
We present a parametric equivalent circuit model for a circular CMUT in collapsed mode. First, we calculate the collapsed membrane deflection, utilizing the exact electrical force distribution in the analytical formulation of membrane deflection. Then we develop a lumped element model of collapsed membrane operation. The radiation impedance for collapsed mode is also included in the model. The model is merged with the uncollapsed mode model to obtain a simulation tool that handles all CMUT behavior, in transmit or receive. Large- and small-signal operation of a single CMUT can be fully simulated for any excitation regime. The results are in good agreement with FEM simulations.
Non-linear processes in thin titanium nitride transmission lines for parametric amplification
Vissers, Michael; Gao, Jiansong; Chaudhuri, Suptarshi; Bockstiegel, Clint; Sandberg, Martin; Pappas, David P.
2013-03-01
Nitride superconductors, such as titanium nitride and niobium titanium nitride, are a non-linear, low dissipation medium at microwave frequencies. The lossless nonlinearity may be probed and utilized. Important applications include generation of higher harmonics, e.g. 3f, and a microwave version of the optical paramagnetic amplifier, i.e. the degenerate-pump case of four-photon mixing (FPM). An amplifier based on these principles should allow for very wide bandwidth, low noise (quantum limited) and high dynamic range devices. These measurements are performed via a single layer, 3 meter long TiN spiral and measured at temperatures below 100 mK. Initial results of the design, fabrication, testing, and impedance optimization of a titanium nitride based parametric amplifier are presented.
Generation of broadband spontaneous parametric fluorescence using multiple bulk nonlinear crystals
Okano, Masayuki; Tanaka, Akira; Subashchandran, Shanthi; Takeuchi, Shigeki; 10.1364/OE.20.013977
2012-01-01
We propose a novel method for generating broadband spontaneous parametric fluorescence by using a set of bulk nonlinear crystals (NLCs). We also demonstrate this scheme experimentally. Our method employs a superposition of spontaneous parametric fluorescence spectra generated using multiple bulk NLCs. A typical bandwidth of 160 nm (73 THz) with a degenerate wavelength of 808 nm was achieved using two beta-barium-borate (BBO) crystals, whereas a typical bandwidth of 75 nm (34 THz) was realized using a single BBO crystal. We also observed coincidence counts of generated photon pairs in a non-collinear configuration. The bandwidth could be further broadened by increasing the number of NLCs. Our demonstration suggests that a set of four BBO crystals could realize a bandwidth of approximately 215 nm (100 THz).We also discuss the stability of Hong-Ou-Mandel two-photon interference between the parametric fluorescence generated by this scheme. Our simple scheme is easy to implement with conventional NLCs and does not...
Generation of broadband spontaneous parametric fluorescence using multiple bulk nonlinear crystals.
Okano, Masayuki; Okamoto, Ryo; Tanaka, Akira; Subashchandran, Shanthi; Takeuchi, Shigeki
2012-06-18
We propose a novel method for generating broadband spontaneous parametric fluorescence by using a set of bulk nonlinear crystals (NLCs). We also demonstrate this scheme experimentally. Our method employs a superposition of spontaneous parametric fluorescence spectra generated using multiple bulk NLCs. A typical bandwidth of 160 nm (73 THz) with a degenerate wavelength of 808 nm was achieved using two β-barium-borate (BBO) crystals, whereas a typical bandwidth of 75 nm (34 THz) was realized using a single BBO crystal. We also observed coincidence counts of generated photon pairs in a non-collinear configuration. The bandwidth could be further broadened by increasing the number of NLCs. Our demonstration suggests that a set of four BBO crystals could realize a bandwidth of approximately 215 nm (100 THz). We also discuss the stability of Hong-Ou-Mandel two-photon interference between the parametric fluorescence generated by this scheme. Our simple scheme is easy to implement with conventional NLCs and does not require special devices.
Yashkir, O. V.; Yashkir, Yu N.
1987-06-01
A theoretical investigation is made of nonlinear excitation of planar waveguide modes at frequencies ω when external plane optical waves of frequency ω1 are incident on the waveguide surface. The general formulas for the efficiency of the excitation of modes by a monochromatic wave are obtained and analyzed for the case of self-interaction of the ω = ω1 + ω1 - ω1 type and by a biharmonic wave in the case of generation of the difference frequency ω = ω1 - ω1'. The efficiency of parametric conversion of waveguide modes ω accompanied by an increase of the frequency to the range ω' is considered for the case when the sum frequency ω + ω1 = ω1' is generated. The numerical method developed by the authors is used to analyze the characteristic features of these processes in some specific cases.
Institute of Scientific and Technical Information of China (English)
周良强; 陈芳启; 陈予恕
2007-01-01
研究了具有参数激励约简的扰动KdV方程的混沌动力学行为.利用改进的Melnikov方法分析了由于同宿轨道的横截相交而产生的混沌行为.对周期外激励、周期线性参数激励和周期非线性参数激励下的扰动KdV方程的混沌行为进行了比较,发现划分混沌区与非混沌区的临界曲线是互不相同的.尤其是对非线性参数激励系统,存在"死频率".当这类系统受到该频率激励时,不论激励的振幅多大,混沌也不会发生.用时间积分法对上述系统进行了数值计算,结果与理论分析一致.%The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries (KdV) equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones.
Energy Technology Data Exchange (ETDEWEB)
Aulova, T V; Kravtsov, Nikolai V; Lariontsev, E G; Chekina, S N [D.V. Skobel' tsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
2012-08-31
The dynamics of solid-state ring laser (SSRL) radiation with periodic pump modulation is studied experimentally and simulated numerically in the case of parametric excitation of relaxation oscillations at the subharmonic of a modulating signal. Parametric processes are investigated by modulating the pump in two regimes of the SSRL operation: steady-state regime of unidirectional lasing and self-modulation regime of the first kind. Significant differences in the dynamics of radiation for these regimes are found. It is established that when the laser operates in the self-modulation regime, a first-order parametric instability can result in the appearance of the dynamic chaos regime. (control of laser radiation parameters)
Boscolo, Ilario; Stellato, Marco; Vercellati, Stefano
2014-01-01
The spring-mass system studied in undergraduate physics laboratories may exhibit complex dynamics due to the simultaneous action of gravitational and elastic forces in addition to air friction. In the first part of this paper, we describe a laboratory experiment aimed at beginner students which also gives those with a more advanced background an opportunity to explore more complex aspects of the motions involved. If students are not given predefined apparatus but are allowed instead to design their own set-up for the experiment, they may also learn something about the thought processes and experimental procedures used in physics. In the second part of this paper, we present a systematic study of the parametric behavior of the system because teachers have to master its dynamics. The non-linear interaction between the vertical and the pendular oscillations in a vertical spring-mass system depends on the ratio between the frequencies of the two motions and on the motion's excitation. Systematic experimental inve...
Directory of Open Access Journals (Sweden)
Ayman A. El-Badawy
2000-01-01
Full Text Available We investigated the design of a neural-network-based adaptive control system for a smart structural dynamic model of the twin tails of an F-15 tail section. A neural network controller was developed and tested in computer simulation for active vibration suppression of the model subjected to parametric excitation. First, an emulator neural network was trained to represent the structure to be controlled and thus used in predicting the future responses of the model. Second, a neurocontroller to determine the necessary control action on the structure was developed. The control was implemented through the application of a smart material actuator. A strain gauge sensor was assumed to be on each tail. Results from computer-simulation studies have shown great promise for control of the vibration of the twin tails under parametric excitation using artificial neural networks.
Nonlinear PET parametric image reconstruction with MRI information using kernel method
Gong, Kuang; Wang, Guobao; Chen, Kevin T.; Catana, Ciprian; Qi, Jinyi
2017-03-01
Positron Emission Tomography (PET) is a functional imaging modality widely used in oncology, cardiology, and neurology. It is highly sensitive, but suffers from relatively poor spatial resolution, as compared with anatomical imaging modalities, such as magnetic resonance imaging (MRI). With the recent development of combined PET/MR systems, we can improve the PET image quality by incorporating MR information. Previously we have used kernel learning to embed MR information in static PET reconstruction and direct Patlak reconstruction. Here we extend this method to direct reconstruction of nonlinear parameters in a compartment model by using the alternating direction of multiplier method (ADMM) algorithm. Simulation studies show that the proposed method can produce superior parametric images compared with existing methods.
Lattice topology and spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays
Leykam, Daniel; Sukhorukov, Andrey A; Desyatnikov, Anton S
2015-01-01
We analyze spontaneous parametric down-conversion in various experimentally feasible 1D quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons. These selection rules are in addition to, and independent of existing control using the pump beam's spatial profile and phase matching conditions. In finite lattices, nontrivial topology produces single photon edge modes, resulting in "hybrid" biphoton edge modes, with one photon localized at the edge and the other propagating into the bulk. When the single photon band gap is sufficiently large, these hybrid biphoton modes reside in a band gap of the bulk biphoton Bloch wave spectrum. Numerical simulations support our analytical results.
Lattice topology and spontaneous parametric down-conversion in quadratic nonlinear waveguide arrays
Leykam, Daniel; Solntsev, Alexander S.; Sukhorukov, Andrey A.; Desyatnikov, Anton S.
2015-09-01
We analyze spontaneous parametric down-conversion in various experimentally feasible one-dimensional quadratic nonlinear waveguide arrays, with emphasis on the relationship between the lattice's topological invariants and the biphoton correlations. Nontrivial topology results in a nontrivial "winding" of the array's Bloch waves, which introduces additional selection rules for the generation of biphotons, independent of existing control using the pump beam's spatial profile and phase-matching conditions. In finite lattices, nontrivial topology produces single-photon edge modes, resulting in "hybrid" biphoton edge modes, with one photon localized at the edge and the other propagating into the bulk. When the single-photon band gap is sufficiently large, these hybrid biphoton modes reside in a band gap of the bulk biphoton Bloch wave spectrum. Numerical simulations support our analytical results.
Vavulin, D. N.; Sukhorukov, A. A.
2016-08-01
We present an analytical description of the process of spontaneous four-wave mixing in a cubic nonlinear fiber with linear losses. We consider the generation of photon pairs in the fiber when in the input of fiber is fed the pumping wave and single signal photon. The focus of attention is on three cases: when the signal photon propagates in the fiber without generating of biphotons; when the photon pair is generated; and when the photon is lost in the fiber. We also consider the cascade processes, but do not give them an analytical description because of their smallness. Description of the biphotons generation process we provide using the Schrodinger-type equation, and take into account the losses in the fiber through the introduction of the virtual beam splitters. We demonstrate the effectiveness of the generation of photon pairs through parametric processes.
Fiber optical parametric oscillator based on highly nonlinear dispersion-shifted fiber
Institute of Scientific and Technical Information of China (English)
Sigang YANG; Kenneth K. Y. WONG; Minghua CHEN; Shizhong XIE
2013-01-01
The development of fiber optical parametric oscillators （FOPO） based on highly nonlinear dispersion- shifted fiber is reviewed in this paper. Firstly, the background and motivation are introduced, and it is pointed out that the FOPO is promising to act as optical source in non-conventional wavelength bands. Subsequently, the context focuses principally on the problem of inherent multiple-longitudinal-mode characteristic of FOPO and the corresponding solutions to it. The primary technique is by locking the phase of multiple longitudinal modes. The first reported actively mode locked FOPO is also presented in this article. However, it is not probable to realize passively mode locked FOPO because of the random phase dithering of the pump required for suppressing stimulated Brillouin scattering. Furthermore, a regeneratively mode locked FOPO is demonstrated, which can generate wide band tunable radiation in non- conventional wavelengths. Besides mode locked FOPO, the single-longitudinal-mode FOPO is also introduced. Finally, potential future directions are discussed.
Institute of Scientific and Technical Information of China (English)
LIM; C.W.
2010-01-01
Nonlinear combination parametric resonance is investigated for an axially accelerating viscoelastic string.The governing equation of in-planar motion of the string is established by introducing a coordinate transform in the Eulerian equation of a string with moving boundaries.The string under investigation is constituted by the standard linear solid model in which the material,not partial,time derivative was used.The governing equation leads to the Mote model for transverse vibration by omitting the longitudinal component and higher order terms.The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string.The two models are respectively analyzed via the method of multiple scales for principal parametric resonance.The amplitudes and the existence conditions of steady-state response and its stability can be numerically determined.Numerical calculations demonstrate the effects of the string material parameters,the initial tension,and the axial speed fluctuation amplitude.The outcomes of the two models are qualitatively and quantitatively compared.
NONLINEAR DYNAMIC INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES UNDER PERIODIC EXCITATION
Institute of Scientific and Technical Information of China (English)
Yiming Fu; Rengui Bi; Pu Zhang
2009-01-01
A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waais forces as well as the non-coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube (DWNT) can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.
Angelis, Georgios I; Matthews, Julian C; Kotasidis, Fotis A; Markiewicz, Pawel J; Lionheart, William R; Reader, Andrew J
2014-11-01
Estimation of nonlinear micro-parameters is a computationally demanding and fairly challenging process, since it involves the use of rather slow iterative nonlinear fitting algorithms and it often results in very noisy voxel-wise parametric maps. Direct reconstruction algorithms can provide parametric maps with reduced variance, but usually the overall reconstruction is impractically time consuming with common nonlinear fitting algorithms. In this work we employed a recently proposed direct parametric image reconstruction algorithm to estimate the parametric maps of all micro-parameters of a two-tissue compartment model, used to describe the kinetics of [[Formula: see text]F]FDG. The algorithm decouples the tomographic and the kinetic modelling problems, allowing the use of previously developed post-reconstruction methods, such as the generalised linear least squares (GLLS) algorithm. Results on both clinical and simulated data showed that the proposed direct reconstruction method provides considerable quantitative and qualitative improvements for all micro-parameters compared to the conventional post-reconstruction fitting method. Additionally, region-wise comparison of all parametric maps against the well-established filtered back projection followed by post-reconstruction non-linear fitting, as well as the direct Patlak method, showed substantial quantitative agreement in all regions. The proposed direct parametric reconstruction algorithm is a promising approach towards the estimation of all individual microparameters of any compartment model. In addition, due to the linearised nature of the GLLS algorithm, the fitting step can be very efficiently implemented and, therefore, it does not considerably affect the overall reconstruction time.
Directory of Open Access Journals (Sweden)
Ajit Desai
2010-01-01
Full Text Available Aeroelastic stability remains an important concern for the design of modern structures such as wind turbine rotors, more so with the use of increasingly flexible blades. A nonlinear aeroelastic system has been considered in the present study with parametric uncertainties. Uncertainties can occur due to any inherent randomness in the system or modeling limitations, and so forth. Uncertainties can play a significant role in the aeroelastic stability predictions in a nonlinear system. The analysis has been put in a stochastic framework, and the propagation of system uncertainties has been quantified in the aeroelastic response. A spectral uncertainty quantification tool called Polynomial Chaos Expansion has been used. A projection-based nonintrusive Polynomial Chaos approach is shown to be much faster than its classical Galerkin method based counterpart. Traditional Monte Carlo Simulation is used as a reference solution. Effect of system randomness on the bifurcation behavior and the flutter boundary has been presented. Stochastic bifurcation results and bifurcation of probability density functions are also discussed.
Transversal parametric oscillation and its external stability in photorefractive sillenite crystals
DEFF Research Database (Denmark)
Podivilov, E.V.; Pedersen, H.C.; Johansen, P.M.
1998-01-01
We develop the nonlinear theory of transversal parametric oscillation in photorefractive sillenite crystals. The theory is nonlinear in the sense that the nonlinear feedback from the parametric space-charge field waves, above threshold of their excitation, is taken into account. In this manner...... of transversal parametric oscillation is stable within certain regions of external and internal parameters. This is opposed to the degenerate case (K/2 subharmonic generation), which is unstable....
Effects of introducing nonlinear components for a random excited hybrid energy harvester
Zhou, Xiaoya; Gao, Shiqiao; Liu, Haipeng; Guan, Yanwei
2017-01-01
This work is mainly devoted to discussing the effects of introducing nonlinear components for a hybrid energy harvester under random excitation. For two different types of nonlinear hybrid energy harvesters subjected to random excitation, the analytical solutions of the mean output power, voltage and current are derived from Fokker-Planck (FP) equations. Monte Carlo simulation exhibits qualitative agreement with FP theory, showing that load values and excitation’s spectral density have an effect on the total mean output power, piezoelectric (PE) power and electromagnetic power. Nonlinear components affect output characteristics only when the PE capacitance of the hybrid energy harvester is non-negligible. Besides, it is also demonstrated that for this type of nonlinear hybrid energy harvesters under random excitation, introducing nonlinear components can improve output performances effectively.
Nonlinear Analysis of Mechanical Systems Under Combined Harmonic and Stochastic Excitation
1993-05-27
autonomous system is studied. The effect of studied by several authors in the past ( Caprino et a]. periodic parametric excitations is examined on systems...Resonance," (in preparation). 3. Caprino , S., Maffei, C., and Negrini, P., 1984, "Hopf 17. Namachchivaya, N. Sri, and Malhotra, N., 1! Bifurcation with
Localized excitations in nonlinear complex systems current state of the art and future perspectives
Cuevas-Maraver, Jesús; Frantzeskakis, Dimitri; Karachalios, Nikos; Kevrekidis, Panayotis; Palmero-Acebedo, Faustino
2014-01-01
The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.
Some Comments on the Nonlinear Dynamics of a Portal Frame under Base Excitation
Directory of Open Access Journals (Sweden)
Aline Souza de Paula
2013-01-01
Full Text Available This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a nonlinear electrical support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincaré sections and bifurcation diagrams.
A parametric FE modeling of brake for non-linear analysis
Directory of Open Access Journals (Sweden)
Ibrahim Ahmed, Yasser Fatouh, Wael Aly
2014-01-01
Full Text Available A parametric modeling of a drum brake based on 3-D Finite Element Methods (FEM for non-contact analysis is presented. Many parameters are examined during this study such as the effect of drum-lining interface stiffness, coefficient of friction, and line pressure on the interface contact. Firstly, the modal analysis of the drum brake is also studied to get the natural frequency and instability of the drum to facilitate transforming the modal elements to non-contact elements. It is shown that the Unsymmetric solver of the modal analysis is efficient enough to solve this linear problem after transforming the non-linear behavior of the contact between the drum and the lining to a linear behavior. A SOLID45 which is a linear element is used in the modal analysis and then transferred to non-linear elements which are Targe170 and Conta173 that represent the drum and lining for contact analysis study. The contact analysis problems are highly non-linear and require significant computer resources to solve it, however, the contact problem give two significant difficulties. Firstly, the region of contact is not known based on the boundary conditions such as line pressure, and drum and friction material specs. Secondly, these contact problems need to take the friction into consideration. Finally, it showed a good distribution of the nodal reaction forces on the slotted lining contact surface and existing of the slot in the middle of the lining can help in wear removal due to the friction between the lining and the drum. Accurate contact stiffness can give a good representation for the pressure distribution between the lining and the drum. However, a full contact of the front part of the slotted lining could occur in case of 20, 40, 60 and 80 bar of piston pressure and a partially contact between the drum and lining can occur in the rear part of the slotted lining.
Yin, L; Daughton, W; Albright, B J; Bezzerides, B; DuBois, D F; Kindel, J M; Vu, H X
2006-02-01
The parametric coupling involving backward stimulated scattering of a laser and electron beam acoustic modes (BAM) is described as observed in particle-in-cell (PIC) simulations. The BAM modes evolve from Langmuir waves (LW) as the electron velocity distribution is nonlinearly modified to be non-Maxwellian by backward stimulated Raman scattering (BSRS). With a marginal damping rate, BAM can be easily excited and allow an extended chirping in frequency to occur as later SRS pulses encounter modified distributions. Coincident with the emergence of this non-Maxwellian distribution is a rapid increase in BSRS reflectivities with laser intensities. Both the reflectivity scaling with laser intensity and the observed spectral features from PIC simulations are consistent with recent Trident experiments.
Chefranov, Sergey G
2013-01-01
The condition of internal gravity waves (IGW) parametric excitation in the rotating fluid layer heated from above, with the layer vibration along the vertical axis or with periodic modulation in time of the vertical temperature distribution, is obtained. We show the dual role of the molecular dissipative effects that may lead not only to the wave oscillations damping, but also to emergence of hydrodynamic dissipative instability (DI) in some frequency band of IGW. This DI also may take place for the localized in horizontal plane tornado-like disturbances, horizontal scale of which does not exceed the character vertical scale for the fluid layer of the finite depth. Investigated parametric resonance mechanism of IGW generation in ocean and atmosphere during and before earthquakes allows monitoring of such waves (with double period with respect to the period of vibration or temperature gradient modulation) as precursors of these devastating phenomena.
Non trivial effect of strong high-frequency excitation on a nonlinear controlled system
DEFF Research Database (Denmark)
Fidlin, A.; Thomsen, Jon Juel
2004-01-01
due to control is usually high compared to uncontrolled systems. A standard optimal controller for a standard nonlinear system (a movable cart used to balance a pendulum vertically) is shown to exhibit pronounced bias error in presence of HF-excitation. The bias increases with increased excitation...
Non-linear excitation of quantum emitters in two-dimensional hexagonal boron nitride
Schell, Andreas W; Takashima, Hideaki; Takeuchi, Shigeki; Aharonovich, Igor
2016-01-01
Two-photon absorption is an important non-linear process employed for high resolution bio-imaging and non-linear optics. In this work we realize two-photon excitation of a quantum emitter embedded in a two-dimensional material. We examine defects in hexagonal boron nitride and show that the emitters exhibit similar spectral and quantum properties under one-photon and two-photon excitation. Furthermore, our findings are important to deploy two-dimensional hexagonal boron nitride for quantum non-linear photonic applications.
Nonlinear optical studies in semiconductor-doped glasses under femtosecond pulse excitation
Indian Academy of Sciences (India)
C P Singh; K S Bindra; S M Oak
2010-12-01
Nonlinear optical studies in semiconductor-doped glasses (SDGs) are performed under femtosecond laser pulse excitation. Z-scan experiments with 800 nm wave- length pulses are used to excite SDG samples in the resonance and non-resonance regimes. Schott colour glass filter OG 515 shows stronger two-photon absorption than GG 420 and both the samples exhibit positive nonlinearity. However, in resonantly excited RG 850 the intensity-dependent Z-scan shows transition from saturable to reverse saturable absorption behaviour with the increase in intensity.
Damage detection in structures through nonlinear excitation and system identification
Hajj, Muhammad R.; Bordonaro, Giancarlo G.; Nayfeh, Ali H.; Duke, John C., Jr.
2008-03-01
Variations in parameters representing natural frequency, damping and effective nonlinearities before and after damage initiation in a beam carrying a lumped mass are assessed. The identification of these parameters is performed by exploiting and modeling nonlinear behavior of the beam-mass system and matching an approximate solution of the representative model with quantities obtained from spectral analysis of measured vibrations. The representative model and identified coefficients are validated through comparison of measured and predicted responses. Percentage variations of the identified parameters before and after damage initiation are determined to establish their sensitivities to the state of damage of the beam. The results show that damping and effective nonlinearity parameters are more sensitive to damage initiation than the system's natural frequency. Moreover, the sensitivity of nonlinear parameters to damage is better established using a physically-derived parameter rather than spectral amplitudes of harmonic components.
Nonlinear variable structure excitation and steam valving controllers for power system stability
Institute of Scientific and Technical Information of China (English)
Ben WANG; Zongyuan MAO
2009-01-01
A set of novel nonlinear variable structure excitation and steam-valving controllers are proposed in this paper.On the basis of the classical dynamic equations of a generator,excitation control and steam valving control are si-multaneously considered.Design of these controllers combines the differential geometry theory with the variable structure controlling theory.The mathematical model in the form of "an affine nonlinear system" is set up for the control design of a large-scale power plant.The dynamic performance of the nonlinear variable structure controllers proposed for a single ma-chine connected to an infinite bus power system is simulated.Simulation results show that the nonlinear variable structure excitation and steam-valving controllers give satisfactory dynamic performance and good robustness.
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China); E-mail: Jiaoruili@mail.nwpu.edu.cn; Xu Wei [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2005-12-01
Stochastic stabilization of first-passage failure of Rayleigh oscillator under Gaussian White-Noise parametric excitation is studied. The equation of motion of the system is first reduced to an averaged Ito stochastic differential equation by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function of first-passage failure is established. The conditional reliability function, and the conditional probability density are obtained by solving the backward Kolmogorov equation with boundary conditions. Finally, the cost function and optimal control forces are determined by the requirements of stabilizing the system by evaluating the maximal Lyapunov exponent. The numerical results show that the procedure is effective and efficiency.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
Nonlinear optical sub-bandgap excitation of ZnO-based photonic resonators
Energy Technology Data Exchange (ETDEWEB)
Bader, Christina A.; Zeuner, Franziska; Bader, Manuel H. W.; Zentgraf, Thomas; Meier, Cedrik [Department of Physics and Center for Optoelectronics and Photonics Paderborn (CeOPP), Universität Paderborn, Warburger Str. 100, 33098 Paderborn (Germany)
2015-12-07
Zinc oxide (ZnO) is a versatile candidate for photonic devices due to its highly efficient optical emission. However, for pumping of ZnO photonic devices UV-sources are required. Here, we investigate the alternative usage of widely available pulsed near-infrared (NIR)-sources and compare the efficiency of linear and nonlinear excitation processes. We found that bulk ZnO, ZnO thin films grown by molecular beam epitaxy, and ZnO/SiO{sub 2} microdisk devices exhibit strong nonlinear response when excited with NIR pulses (λ ≈ 1060 nm). In addition, we show that the ZnO/SiO{sub 2} microdisks exhibit sharp whispering gallery modes over the blue-yellow part of the visible spectrum for both excitation conditions and high Q-factors up to Q = 4700. The results demonstrate that nonlinear excitation is an efficient way to pump ZnO photonic devices.
Armstrong, D J; Alford, W J; Raymond, T D; Smith, A V
1996-04-20
Absolute magnitudes of the effective nonlinearity, deff, were measured for seven KTP and six BBO crystals. The d(eff), were derived from the parametric gain of an 800-nm signal wave in the sample crystals when they were pumped by the frequency-doubled, spatially filtered light from an injectionseeded, Q-switched Nd:YAG laser. The KTP crystals, all type II phase matched with propagation in the X-Z plane, had d(eff) values ranging from 1.97 to 3.50 pm/V. Measurements of gain as a function of phase velocity mismatch indicate that two of the KTP crystals clearly contain multiple ferroelectric domains. For five type I phase-matched BBO crystals, d(eff) ranged from 1.76 to 1.83 pm/V, and a single type II phase-matched BBO crystal had a d(eff) of 1.56 pm/V. The uncertainty in our measurements of d(eff) values is ±5% for KTP and ±10% for BBO.
Nonlinear response of metallic acGNR to an elliptically-polarized terahertz excitation field
Wang, Yichao
2016-01-01
We present a theoretical description of the nonlinear response induced by an elliptically-polarized terahertz beam normally-incident on intrinsic and extrinsic metallic armchair graphene nanorib- bons. Our results show that using a straightforward experimental setup, it should be possible to observe novel polarization-dependent nonlinearities at low excitation field strengths of the or- der of 10 4 V/m. At low temperatures the Kerr nonlinearities in extrinsic nanoribbons persist to significantly higher excitation frequencies than they do for linear polarizations, and at room tem- peratures, the third-harmonic nonlinearities are enhanced by 2-3 orders of magnitude. Finally, the Fermi-level and temperature dependence of the nonlinear response is characterized.
Gusakov, E Z
2016-01-01
Novel mechanism leading to excitation of absolute two plasmon parametric decay instability (TPDI) of a pump extraordinary (X) wave is discussed. It is shown that the upper hybrid (UH) plasmon can be 3D trapped in the presence of both a nonmonotonous density profile and a finite-size pump beam in a plane perpendicular to the plasma inhomogeneity direction. This leads to excitation of the absolute TPDI of the pump X wave, which manifests itself in temporal exponential growth of the trapped daughter UH wave amplitude and is perhaps the most dangerous instability for mm-waves, widely utilized nowadays in tokamak and stellarators for local plasma heating and current drive and being considered for application in ITER.
Slabko, Vitaly V; Popov, Alexander K; Tkachenko, Viktor A; Myslivets, Sergey A
2016-09-01
Three-wave mixing of ordinary and backward electromagnetic waves in a pulsed regime is investigated in the metamaterials that enable the coexistence and phase-matching of such waves. It is shown that the opposite direction of phase velocity and energy flux in backward waves gives rise to extraordinary transient processes due to greatly enhanced optical parametric amplification and frequency up- and down-shifting nonlinear reflectivity. The differences are illustrated through comparison with the counterparts in ordinary, co-propagating settings.
Interference control of nonlinear excitation in a multiatom cavity QED system
Yang, Guoqing; Zou, Bichen; Zhu, Yifu
2014-01-01
We show that by manipulating quantum interference in a multi-atom cavity QED system, the nonlinear excitation of the cavity-atom polariton can be resonantly enhanced while the linear excitation is suppressed. Under appropriate conditions, it is possible to selectively enhance or suppress the polariton excitation with two free-pace laser fields. We report an experiment with cold Rb atoms in an optical cavity and present experimental results that demonstrate such interference control of the cavity QED excitation and its direct applications for studies of all-optical switching and cross-phase modulation of the cavity transmitted light.
Interference control of nonlinear excitation in a multi-atom cavity quantum electrodynamics system.
Yang, Guoqing; Tan, Zheng; Zou, Bichen; Zhu, Yifu
2014-12-01
We show that by manipulating quantum interference in a multi-atom cavity quantum electrodynamics (CQED) system, the nonlinear excitation of the cavity-atom polariton can be resonantly enhanced while the linear excitation is suppressed. Under the appropriate conditions, it is possible to selectively enhance or suppress the polariton excitation with two free-pace laser fields. We report on an experiment with cold Rb atoms in an optical cavity and present experimental results that demonstrate such interference control of the CQED excitation and its direct application to studies of all-optical switching and cross-phase modulation of the cavity-transmitted light.
RESPONSE OF NONLINEAR OSCILLATOR UNDER NARROW-BAND RANDOM EXCITATION
Institute of Scientific and Technical Information of China (English)
戎海武; 王向东; 孟光; 徐伟; 方同
2003-01-01
The principal resonance of Duffing oscillator to narrow-band random parametricexcitation was investigated. The method of multiple scales was used to determine theequations of modulation of amplitude and phase. The behavior, stability and bifurcation ofsteady state response were studied by means of qualitative analyses. The effects of damping,detuning, bandwidth and magnitudes of deterministic and random excitations wereanalyzed. The theoretical analyses were verified by numerical results. Theoretical analysesand numerical simulations show that when the intensity of the random excitation increases,the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle.Under some conditions the system may have two ,steady state solutions.
Nonlinear processes upon two-photon interband picosecond excitation of PbWO4 crystal
Lukanin, V. I.; Karasik, A. Ya
2016-09-01
A new experimental method is proposed to study the dynamics of nonlinear processes occurring upon two-photon interband picosecond excitation of a lead tungstate crystal and upon its excitation by cw probe radiation in a temporal range from several nanoseconds to several seconds. The method is applied to the case of crystal excitation by a sequence of 25 high-power picosecond pulses with a wavelength of 523.5 nm and 633-nm cw probe radiation. Measuring the probe beam transmittance during crystal excitation, one can investigate the influence of two-photon interband absorption and the thermal nonlinearity of the refractive index on the dynamics of nonlinear processes in a wide range of times (from several nanoseconds to several seconds). The time resolution of the measuring system makes it possible to distinguish fast and slow nonlinear processes of electronic or thermal nature, including the generation of a thermal lens and thermal diffusion. An alternative method is proposed to study the dynamics of induced absorption transformation and, therefore, the dynamics of the development of nonlinear rocesses upon degenerate two-photon excitation of the crystal in the absence of external probe radiation.
Nonlinear Dynamics of Self-excitation in Autoparametric Systems
2003-01-01
Various types of self-excited oscillators are implemented into an autoparametric system, and the study of the solutions, stabilities and bifurcations, shows very different results. First, we implement the Rayleigh type oscillator into a suitable autoparametric system. The bifurcation analysis of the
Three types magnetic moment distribution of nonlinear excitations in a Heisenberg helimagnet
Energy Technology Data Exchange (ETDEWEB)
Qi, Jian-Wen [School of Physics, Northwest University, Xi' an 710069 (China); Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi' an 710069 (China); Li, Zai-Dong [Department of Applied Physics, Hebei University of Technology, Tianjin 300401 (China); Yang, Zhan-Ying, E-mail: zyyang@nwu.edu.cn [School of Physics, Northwest University, Xi' an 710069 (China); Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi' an 710069 (China); Yang, Wen-Li [Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi' an 710069 (China); Institute of Modern Physics, Northwest University, Xi' an 710069 (China)
2017-06-15
Highlights: • Three different types of soliton excitations under the spin-wave background are demonstrated in spin chain system. • The magnetic moment distributions corresponding to these solitons are characterized in detail. • The formation mechanisms of those excitations are explained by the magnon density distribution. - Abstract: We study the nonlinear spin dynamics of an anisotropic Heisenberg helimagnet in a fourth-order integrable nonlinear Schrödinger equation. We demonstrate that there are three types of nonlinear spin excitations on a spin-wave background in the Heisenberg helimagnet, notably including anti-dark soliton, W-shaped soliton, and multi-peak soliton. The magnetic moment distribution that corresponds to each of these are characterized in detail. Additionally, the formation mechanism is clarified by the magnon density distribution.
Parametric resonance of intrinsic localized modes in coupled cantilever arrays
Kimura, Masayuki; Matsushita, Yasuo; Hikihara, Takashi
2016-08-01
In this study, the parametric resonances of pinned intrinsic localized modes (ILMs) were investigated by computing the unstable regions in parameter space consisting of parametric excitation amplitude and frequency. In the unstable regions, the pinned ILMs were observed to lose stability and begin to fluctuate. A nonlinear Klein-Gordon, Fermi-Pasta-Ulam-like, and mixed lattices were investigated. The pinned ILMs, particularly in the mixed lattice, were destabilized by parametric resonances, which were determined by comparing the shapes of the unstable regions with those in the Mathieu differential equation. In addition, traveling ILMs could be generated by parametric excitation.
Institute of Scientific and Technical Information of China (English)
Zhang Li-Ping; Xue Ju-Kui; Li Yan-Long
2011-01-01
Both linear and nonlinear excitation in dusty plasmas have been investigated including the nonadiabatic dust charge fluctuation and Gaussian size distribution dust particles.A linear dispersion relation and a Korteweg-de VriesBurgers equation governing the dust acoustic shock waves are obtained.The relevance of the instability of wave and the wave evolution to the dust size distribution and nonadiabatic dust charge fluctuation is illustrated both analytically and numerically.The numerical results show that the Gaussian size distribution of dust particles and the nonadiabatic dust charge fluctuation have strong common influence on the propagation of both linear and nonlinear excitations.
Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse
Energy Technology Data Exchange (ETDEWEB)
Grishkov, V. E.; Uryupin, S. A., E-mail: uryupin@sci.lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)
2017-03-15
Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron–ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.
Nonlinear Conductivity and Collective Charge Excitations in the Lowest Landau Level
Auerbach, Assa; Arovas, Daniel P.
2017-07-01
For weakly disordered fractional quantum Hall phases, the nonlinear photoconductivity is related to the charge susceptibility of the clean system by a Floquet boost. Thus, it may be possible to probe collective charge modes at finite wave vectors by electrical transport. Incompressible phases, irradiated at slightly above the magnetoroton gap, are predicted to exhibit negative photoconductivity and zero resistance states with spontaneous internal electric fields. Nonlinear conductivity can probe composite fermions' charge excitations in compressible filling factors.
Active Vibration Control of a Nonlinear Beam with Self- and External Excitations
Directory of Open Access Journals (Sweden)
J. Warminski
2013-01-01
Full Text Available An application of the nonlinear saturation control (NSC algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with nonlinear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controller's parameters for effective vibrations suppression are presented.
Siu-Siu, Guo; Qingxuan, Shi
2017-03-01
In this paper, single-degree-of-freedom (SDOF) systems combined to Gaussian white noise and Gaussian/non-Gaussian colored noise excitations are investigated. By expressing colored noise excitation as a second-order filtered white noise process and introducing colored noise as an additional state variable, the equation of motion for SDOF system under colored noise is then transferred artificially to multi-degree-of-freedom (MDOF) system under white noise excitations with four-coupled first-order differential equations. As a consequence, corresponding Fokker-Planck-Kolmogorov (FPK) equation governing the joint probabilistic density function (PDF) of state variables increases to 4-dimension (4-D). Solution procedure and computer programme become much more sophisticated. The exponential-polynomial closure (EPC) method, widely applied for cases of SDOF systems under white noise excitations, is developed and improved for cases of systems under colored noise excitations and for solving the complex 4-D FPK equation. On the other hand, Monte Carlo simulation (MCS) method is performed to test the approximate EPC solutions. Two examples associated with Gaussian and non-Gaussian colored noise excitations are considered. Corresponding band-limited power spectral densities (PSDs) for colored noise excitations are separately given. Numerical studies show that the developed EPC method provides relatively accurate estimates of the stationary probabilistic solutions, especially the ones in the tail regions of the PDFs. Moreover, statistical parameter of mean-up crossing rate (MCR) is taken into account, which is important for reliability and failure analysis. Hopefully, our present work could provide insights into the investigation of structures under random loadings.
Nonlinear Schroedinger excitations scattering on local barrier in one dimension
Kovrizhin, D L
2001-01-01
The task on the excitations scattering of the Bose condensate under consideration on the unidimensional barrier is nontrivial one even in the case of a low barrier because the barrier itself and change in the condensate density in its vicinity play the similar important role. It is shown that if any repulsive barrier for a bare particle within the range of the waves high lengths is impermeable, than the coefficient of the delta-functional transmission for the phonons within this range strives to the unity and the barrier becomes transparent
The pseudoforce approach to fully nonlinear plasma excitations
Akbari-Moghanjoughi, M.
2017-08-01
In this paper, we develop a technique to study the dynamic structure of oscillations in plasmas. We consider the hydrodynamic model and reduce the system of closed equations to the system of differential equations with integrable Hamiltonian. Then, using the analogy of pseudoparticle oscillation in the pseudoforce field, we generalize the Hamiltonian to include the dissipation and external driving force effects. The developed method is used to study various features of electron-ion plasmas with different equations of state for ions. It is shown that this method can be used in the analysis of superposed fully nonlinear oscillations and even the sheath structure of plasmas. The generalized pseudoforce equation is then used to study the dynamics of damped periodically forced nonlinear ion acoustic oscillations in plasmas with adiabatic and isothermal ion fluids. We found striking differences in dynamics of oscillations in these plasmas. The fundamental difference in the dynamic character of oscillations between adiabatic and isothermal ion fluids is described based on the fast ion fluid response to external perturbations in the case of adiabatic ion fluid compression. The current approach may be easily extended to more complex situations with different species and in the presence of electromagnetic interactions.
Optical nonlinearities in GaSe and InSe crystals upon laser excitation
Kyazym-zade, A. G.; Salmanov, V. M.; Guseinov, A. G.; Gasanova, L. G.; Mamedov, R. M.
2014-04-01
The nonlinear absorption of light and its temporal evolution in the vicinity of exciton resonance in layered GaSe and InSe crystals under high optical excitation have been experimentally investigated. The decisive factor for the observed temporal dependence of the absorption coefficient and its dependence on the excitation intensity is screening excitons by nonequilibrium-carrier plasma. It is shown that the increase in the transmittance in the absorption-band edge in GaSe with a simultaneous blue shift of the band edge is caused by filling the energy bands under high optical excitation.
da Silva, Roberto; Prado, Sandra D.; Fernandes, Henrique A.
2017-10-01
In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of N sines with different frequencies and phases. We show that when the amplitude is scaled with the frequency we obtain the stabilization of the real inverted pendulum, i.e., with values of g according to planet Earth (g ≈ 9.8 m/s2) for high frequencies. By randomly sorting the frequencies, we obtain a critical amplitude in light of perturbative theory in classical mechanics which is numerically tested by exploring its validity regime in many alternatives. We also analyse the effects when different values of N as well as the pendulum size l are taken into account.
Stochastic stability of mechanical systems under renewal jump process parametric excitation
DEFF Research Database (Denmark)
Iwankiewicz, R.; Nielsen, Søren R.K.; Larsen, Jesper Winther
2005-01-01
if the state space is augmented by the products of the original state variables and the excitation variable. Asymptotic mean and mean-square stability as well as asymptotic sample (Lyapunov) stability with probability 1 are investigated. The Lyapunov exponents have been evaluated both by the direct simulation...
Localized Excitations in a Sixth-Order (1+1)-Dimensional Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
SHEN Shou-Feng
2005-01-01
In this letter, by means of the Lax pair, Darboux transformation, and variable separation approach, a new exact solution of a sixth-order (1+ 1)-dimensional nonlinear evolution equation, which includes some arbitrary functions,is obtained. Abundant new localized excitations can be found by selecting appropriate functions and they are illustrated both analytically and graphically.
Bentley, Sean J; Heebner, John E; Boyd, Robert W
2006-04-01
We describe observations of various transverse instabilities that occur when two laser beams intersect in nonlinear optical liquids. Patterns that we observe include two types of conical emission and the generation of a linear array of spots. These results can be understood in terms of the physical processes of self-diffraction, two-beam-excited conical emission, and seeded modulational instability.
Excited state nonlinear integral equations for an integrable anisotropic spin-1 chain
Energy Technology Data Exchange (ETDEWEB)
Suzuki, J [Department of Physics, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka (Japan)
2004-12-17
We propose a set of nonlinear integral equations to describe the excited states of an integrable the spin-1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study of the supersymmetric sine-Gordon model.
Directory of Open Access Journals (Sweden)
Mervan Pašić
2014-01-01
Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.
Linear and Nonlinear Bullets of the Bogoliubov-de Gennes Excitations
Kumar, S.; Perego, A. M.; Staliunas, K.
2017-01-01
We report on the focalization of Bogoliubov-de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov-de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear "bullets"). These traveling Bogoliubov-de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice.
Directory of Open Access Journals (Sweden)
Rong Haiwu
2014-01-01
Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
Rigatos, G; Rigatou, E; Djida, J D
2015-01-01
The derivative-free nonlinear Kalman filter is proposed for state estimation and fault diagnosis in distributed parameter systems of the wave-type and particularly in the Peyrard-Bishop-Dauxois model of DNA dynamics. At a first stage, a nonlinear filtering approach is introduced for estimating the dynamics of the Peyrard-Bishop-Dauxois 1D nonlinear wave equation, through the processing of a small number of measurements. It is shown that the numerical solution of the associated partial differential equation results in a set of nonlinear ordinary differential equations. With the application of a diffeomorphism that is based on differential flatness theory it is shown that an equivalent description of the system is obtained in the linear canonical (Brunovsky) form. This transformation enables to obtain local estimates about the state vector of the DNA model through the application us of the standard Kalman filter recursion. At a second stage, the local statistical approach to fault diagnosis is used to perform fault diagnosis for this distributed parameter system by processing with statistical tools the differences (residuals) between the output of the Kalman filter and the measurements obtained from the distributed parameter system. Optimal selection of the fault threshold is succeeded by using the local statistical approach to fault diagnosis. The efficiency of the proposed filtering approach in the problem of fault diagnosis for parametric change detection, in nonlinear wave-type models of DNA dynamics, is confirmed through simulation experiments.
Nonlinear dynamics of a sliding beam on two supports under sinusoidal excitation
Indian Academy of Sciences (India)
R J Somnay; R A Ibrahim
2006-08-01
This study deals with the nonlinear dynamics associated with large deformation of a beam sliding on two-knife edge supports under external excitation. The beam is referred to as a Gospodnetic–Frisch-Fay beam, after the researchers who reported its static deformation in closed form. The freedom of the beam to slide on its supports imparts a nonlinear characteristic to the force-deﬂection response. The restoring elastic force of the beam possesses characteristics similar to those of the roll-restoring moment of ships. The Gospodnetic–Frisch-Fay exact solution is given in terms of elliptic functions. A curve ﬁt of the exact solution up to eleventh-order is constructed to establish the governing equation of motion under external excitation. The dynamic stability of the unperturbed beam is examined for the damped and undamped cases. The undamped case reveals periodic orbits and one homoclinic orbit depending on the value of the initial conditions. The response to a sinusoidal excitation at a frequency below the linear natural frequency is numerically estimated for different excitation amplitude and different values of initial conditions covered by the area of the homoclinic orbit. The safe basins of attraction are plotted for different values of excitation amplitude. It is found that the safe region of operation is reduced as the excitation amplitude increases.
Saturation of radiation-induced parametric instabilities by excitation of Langmuir turbulence
Energy Technology Data Exchange (ETDEWEB)
Dubois, D.F.; Rose, H.A. [Los Alamos National Lab., NM (United States); Russell, D. [Lodestar Research Inc., Boulder, CO (United States)
1995-12-01
Progress made in the last few years in the calculation of the saturation spectra of parametric instabilities which involve Langmuir daughter waves will be reviewed. These instabilities include the ion acoustic decay instability, the two plasmon decay instability (TPDI), and stimulated Raman scattering (SRS). In particular I will emphasize spectral signatures which can be directly compared with experiment. The calculations are based on reduced models of driven Laugmuir turbulence. Thomson scattering from hf-induced Langmuir turbulence in the unpreconditioned ionosphere has resulted in detailed agreement between theory and experiment at early times. Strong turbulence signatures dominate in this regime where the weak turbulence approximation fails completely. Recent experimental studies of the TPDI have measured the Fourier spectra of Langmuir waves as well as the angular and frequency, spectra of light emitted near 3/2 of the pump frequency again permitting some detailed comparisons with theory. The experiments on SRS are less detailed but by Thomson scattering the secondary decay of the daughter Langmuir wave has been observed. Scaling laws derived from a local model of SRS saturation are compared with full simulations and recent Nova experiments.
Directory of Open Access Journals (Sweden)
M. P. Markakis
2010-01-01
Full Text Available Through a suitable ad hoc assumption, a nonlinear PDE governing a three-dimensional weak, irrotational, steady vector field is reduced to a system of two nonlinear ODEs: the first of which corresponds to the two-dimensional case, while the second involves also the third field component. By using several analytical tools as well as linear approximations based on the weakness of the field, the first equation is transformed to an Abel differential equation which is solved parametrically. Thus, we obtain the two components of the field as explicit functions of a parameter. The derived solution is applied to the two-dimensional small perturbation frictionless flow past solid surfaces with either sinusoidal or parabolic geometry, where the plane velocities are evaluated over the body's surface in the case of a subsonic flow.
PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito' s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted.Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.
Energy transport in weakly nonlinear wave systems with narrow frequency band excitation.
Kartashova, Elena
2012-10-01
A novel discrete model (D model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of energy transport between modes, namely, intermittency and energy cascade, and gives the conditions under which each regime will take place. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc., are given and depend strongly on the choice of excitation parameters. The energy spectra of a cascade may be computed, yielding discrete and continuous energy spectra. The model does not require statistical assumptions, as all effects are derived from the interaction of distinct modes. In the example given-surface water waves with dispersion function ω(2)=gk and small nonlinearity-the D model predicts asymmetrical growth of side-bands for Benjamin-Feir instability, while the transition from discrete to continuous energy spectrum, excitation parameters properly chosen, yields the saturated Phillips' power spectrum ~g(2)ω(-5). The D model can be applied to the experimental and theoretical study of numerous wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.
Directory of Open Access Journals (Sweden)
Yan-Lei Zhang
2016-01-01
Full Text Available Nonlinear vibration of a fluid-conveying pipe subjected to a transverse external harmonic excitation is investigated in the case with two-to-one internal resonance. The excitation amplitude is in the same magnitude of the transverse displacement. The fluid in the pipes flows in the speed larger than the critical speed so that the straight configuration becomes an unstable equilibrium and two curved configurations bifurcate as stable equilibriums. The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. The method of multiple scales is applied to analyze approximately the gyroscopic system. A set of first-order ordinary differential equations governing the modulations of the amplitude and the phase are derived via the method. In the supercritical regime, the subharmonic, superharmonic, and combination resonances are examined in the presence of the 2 : 1 internal resonance. The steady-state responses and their stabilities are determined. The various jump phenomena in the amplitude-frequency response curves are demonstrated. The effects of the viscosity, the excitation amplitude, the nonlinearity, and the flow speed are observed. The analytical results are supported by the numerical integration.
Nonlinear dynamic analysis of atomic force microscopy under deterministic and random excitation
Energy Technology Data Exchange (ETDEWEB)
Pishkenari, Hossein Nejat [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Behzad, Mehdi [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)], E-mail: m_behzad@sharif.edu; Meghdari, Ali [Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2008-08-15
The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. This paper is devoted to the analysis of nonlinear behavior of amplitude modulation (AM) and frequency modulation (FM) modes of atomic force microscopy. For this, the microcantilever (which forms the basis for the operation of AFM) is modeled as a single mode approximation and the interaction between the sample and cantilever is derived from a van der Waals potential. Using perturbation methods such as averaging, and Fourier transform nonlinear equations of motion are analytically solved and the advantageous results are extracted from this nonlinear analysis. The results of the proposed techniques for AM-AFM, clearly depict the existence of two stable and one unstable (saddle) solutions for some of exciting parameters under deterministic vibration. The basin of attraction of two stable solutions is different and dependent on the exciting frequency. From this analysis the range of the frequency which will result in a unique periodic response can be obtained and used in practical experiments. Furthermore the analytical responses determined by perturbation techniques can be used to detect the parameter region where the chaotic motion is avoided. On the other hand for FM-AFM, the relation between frequency shift and the system parameters can be extracted and used for investigation of the system nonlinear behavior. The nonlinear behavior of the oscillating tip can easily explain the observed shift of frequency as a function of tip sample distance. Also in this paper we have investigated the AM-AFM system response under a random excitation. Using two different methods we have obtained the statistical properties of the tip motion. The results show that we can use the mean square value of tip motion to image the sample when the excitation signal is random.
Nonlinear excitation kinetics of biased quantum wells. Coherent dynamical screening effect
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Jepsen, Peter Uhd
2006-01-01
In this paper we describe a strongly nonlinear process of ultrafast photoexcitation of a biased quantum well. This process is governed by coherent dynamical screening, where the instantaneously polarized photoexcited carriers screen initial bias field. This results in a dynamic modification...... of the bandstructure of the quantum well, which is totally coherent with the temporal intensity distribution of the excitation laser pulse. We developed a time-resolved theoretical model of coherent dynamical screening, which predicts interesting fundamental consequences, such as nonlinear absorption and ultra......-broadband THz emission. The results of our THz and optical experiments are in good agreement with the theoretical model....
Nonlinear Analysis of Cable Vibration of a Multispan Cable-Stayed Bridge under Transverse Excitation
Kun Lin; Dujian Zou; Minghai Wei
2014-01-01
The nonlinear vibrations of cable in a multispan cable-stayed bridge subjected to transverse excitation are investigated. The MECS (multielements cable system) model, where multielements per cable stay are used, is built up and used to analyze the model properties of the multispan cable-stayed bridges. Then, a simplified two-degrees-of-freedom (2-DOFs) model, where the tower or the deck is reduced to a beam, is proposed to analyze the nonlinear dynamic behaviors of the beam and cable. The res...
Excitation Forces on Point Absorbers Exposed to High Order Non-linear Waves
DEFF Research Database (Denmark)
Viuff, Thomas Hansen; Andersen, Morten Thøtt; Kramer, Morten
2013-01-01
of proper methods to calculate design pressure distributions has led to structural failures such as buckling in the shells in wave energy prototypes. As a step towards understanding the complex loading from high order non-linear waves, this paper presents a practical approach to estimate wave excitation...... forces accounting for both non-linearity and diffraction effects. The method is validated by laboratory experiments using a hemispherical point absorber with a 6-axis force transducer, but the technique is believed to be applicable for most types of submerged or semi-submerged floating devices...
Mode competition in a system of two parametrically driven pendulums with nonlinear coupling
Banning, E.J.; Weele, van der J.P.; Ross, J.C.; Kettenis, M.M.
1997-01-01
This paper is part three in a series on the dynamics of two coupled, parametrically driven pendulums. In the previous parts Banning and van der Weele (1995) and Banning et al. (1997) studied the case of linear coupling; the present paper deals with the changes brought on by the inclusion of a nonlin
Weakly nonlinear ion-acoustic excitations in a relativistic model for dense quantum plasma.
Behery, E E; Haas, F; Kourakis, I
2016-02-01
The dynamics of linear and nonlinear ionic-scale electrostatic excitations propagating in a magnetized relativistic quantum plasma is studied. A quantum-hydrodynamic model is adopted and degenerate statistics for the electrons is taken into account. The dispersion properties of linear ion acoustic waves are examined in detail. A modified characteristic charge screening length and "sound speed" are introduced, for relativistic quantum plasmas. By employing the reductive perturbation technique, a Zakharov-Kuznetzov-type equation is derived. Using the small-k expansion method, the stability profile of weakly nonlinear slightly supersonic electrostatic pulses is also discussed. The effect of electron degeneracy on the basic characteristics of electrostatic excitations is investigated. The entire analysis is valid in a three-dimensional as well as in two-dimensional geometry. A brief discussion of possible applications in laboratory and space plasmas is included.
Multi-Index Nonlinear Coordinated Control for Battery Energy Storage System and Generator Excitation
Lingyi, Kong; Liying, Liao
A multi-index nonlinear coordinated control scheme for BESS and generator excitation is proposed. The proposed multi-index nonlinear coordinated controller can effectively coordinate the dynamic and steady-state performance of the controlled system. It can enhance the stability of the system, improve the dynamic characteristics of state variables, and can improve the control accuracy of output variables such as terminal voltage, active power output of the generator. Simulation results show that to control BESS and generator coordinately has the advantage of enhancing the stability of the system. With the ability of BESS to control the active power and reactive power, and the regulate of generator excitation, the dynamic characteristics of state variables can changes more smoothness, responds more speediness.
Key components for nano-assembled plasmon-excited single molecule non-linear devices
Kewes, Günter; Mazzamuto, Giacomo; Neitzke, Oliver; Schönfeld, Rolf-Simon; Schell, Andreas W; Probst, Jürgen; Wolters, Janik; Löchel, Bernd; Toninelli, Costanza; Benson, Oliver
2015-01-01
Tremendous enhancement of light-matter interaction in plasmon-excited molecular hybrid devices allows for non-linearities on the level of single emitters and few photons. This promises a plethora of novel applications like single photon transistors. Nevertheless, building the components of such devices is technologically extremely challenging. We tackle this task by lithographically fabricating on-chip plasmonic waveguides, efficiently connected to far-field in- and out-coupling ports via low-loss dielectric waveguides. Furthermore, a nano-assembling technology is developed, enabling the controlled coupling of single organic emitters to the plasmonic waveguides. Dibenzoterrylene fluorescent molecules hosted in anthracene crystals are investigated for this purpose. Here we present all key-components and technologies for a plasmon-excited single molecule non-linear device.
Institute of Scientific and Technical Information of China (English)
Changshui Feng; Weiqiu Zhu
2008-01-01
A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Ito equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov (FPK) equation associated with the completed averaged Ito equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.
The coordinated control of SVC and excitation of generators in power systems with nonlinear loads
Energy Technology Data Exchange (ETDEWEB)
Ruan, Yingqin; Wang, Jie [Department of Electrical Engineering, Shanghai Jiaotong University, 1954 Hua Shan Road, Shanghai 200030 (China)
2005-10-01
Based on the feedback linearized technique and control of differential and algebraic systems, the exact linearization design is presented in this paper for SVC (static var compensator) and generator excitation controllers in power systems with nonlinear loads. It can improve both the power angle stability of generators and the voltage behavior at the SVC location. Simulation results indicate that this control method has a good effect and superiority. (author)
Orientation-dependent excitations of lattice soliton trains with hybrid nonlinearity.
Hu, Yi; Lou, Cibo; Liu, Sheng; Zhang, Peng; Zhao, Jianlin; Xu, Jingjun; Chen, Zhigang
2009-04-01
We demonstrate selective excitation of soliton trains residing in different gaps or within the same Bloch band of a new type of photonic lattice merely by changing the orientation of an input probe beam. A self-focusing and -defocusing hybrid nonlinearity as established in a nonconventionally biased photorefractive crystal leads to controlled soliton transitions from different band edges or subband edges, in good agreement with our theoretical analysis.
Exciting traffic jams: nonlinear phenomena behind traffic jam formation on highways.
Orosz, Gábor; Wilson, R Eddie; Szalai, Róbert; Stépán, Gábor
2009-10-01
A nonlinear car-following model is studied with driver reaction time delay by using state-of-the-art numerical continuations techniques. These allow us to unveil the detailed microscopic dynamics as well as to extract macroscopic properties of traffic flow. Parameter domains are determined where the uniform flow equilibrium is stable but sufficiently large excitations may trigger traffic jams. This behavior becomes more robust as the reaction time delay is increased.
Exciting traffic jams: Nonlinear phenomena behind traffic jam formation on highways
Orosz, Gábor; Wilson, R. Eddie; Szalai, Róbert; Stépán, Gábor
2009-10-01
A nonlinear car-following model is studied with driver reaction time delay by using state-of-the-art numerical continuations techniques. These allow us to unveil the detailed microscopic dynamics as well as to extract macroscopic properties of traffic flow. Parameter domains are determined where the uniform flow equilibrium is stable but sufficiently large excitations may trigger traffic jams. This behavior becomes more robust as the reaction time delay is increased.
Application of the bispectrum for detection of small nonlinearities excited sinusoidally
Courtney, C. R. P.; Neild, S. A.; Wilcox, P. D.; Drinkwater, B. W.
2010-09-01
The nonlinear behaviour of damaged systems excited by vibration or ultrasound offers potential as a technique for damage detection in machine condition monitoring and non-destructive testing applications. The bispectrum, a third-order spectrum, has properties that lend themselves to the measurement of nonlinearities in systems. The properties of interest are insensitivity to Gaussian noise and ability to detect quadratic phase coupling. However, thus far analysis of the statistics of bispectrum estimation has been mainly aimed at stochastic systems. Many applications to vibration and ultrasound involve primarily deterministic, periodic excitations in the presence of stochastic noise. This paper considers the properties of a bispectrum estimate when applied to a system with weak quadratic nonlinearity excited by the superposition of two sinusoids in the presence of additive Gaussian noise. This is compared, using signal-to-noise ratios, to the powerspectrum, with the results validated using numerical data. Also addressed is the effect of quadratic phase coupling on such a system (in the absence of noise).
Guo, Tieding; Kang, Houjun; Wang, Lianhua; Zhao, Yueyu
2016-12-01
Cable dynamics under ideal longitudinal support motions/excitations assumes that the support's mass, stiffness and mechanical energy are infinite. However, for many long/slender support structures, their finite mass and stiffness should be taken into account and the cable-support dynamic interactions should be modelled and evaluated. These moving supports are non-ideal support excitations, deserving a proper coupling analysis. For systems with a large support/cable mass ratio, using the multiple scale method and asymptotic approximations, a cable-support coupled reduced model, with both cable's geometric nonlinearity and cable-support coupling nonlinearity included, is established asymptotically and validated numerically in this paper. Based upon the reduced model, cable's nonlinear responses under non-ideal support excitations(and also the coupled responses) are found, with stability and bifurcation characteristics determined. By finding the modifications caused by the support/cable mass ratio, boundary damping, and internal detuning, full investigations into coupling-induced dynamic effects on the cable are conducted. Finally, the approximate analytical results based on the reduced model are verified by numerical results from the original full model.
Excited-state dynamics and nonlinear optical response of Ge nanocrystals embedded in silica matrix
Razzari, Luca; Gnoli, Andrea; Righini, Marcofabio; Dâna, Aykutlu; Aydinli, Atilla
2006-05-01
We use a dedicated Z-scan setup, arranged to account for cumulative effects, to study the nonlinear optical response of Ge nanocrystals embedded in silica matrix. Samples are prepared with plasma-enchanced chemical-vapor deposition and post-thermal annealing. We measure a third-order nonlinear refraction coefficient of γ =1×10-16m2/W. The nonlinear absorption shows an intensity-independent coefficient of β =4×10-10m/W related to fast processes. In addition, we measure a second β component around 10-9m /W with a relaxation time of 300μs that rises linearly with the laser intensity. We associate its origin to the absorption of excited carriers from a surface-defect state with a long depopulation time.
Fast and slow dynamics in a nonlinear elastic bar excited by longitudinal vibrations
Favrie, Nicolas; Payan, Cédric
2014-01-01
Heterogeneous materials, such as rocks and concrete, have a complex dynamics including hysteresis, nonlinear elasticity and viscoelasticity. It is very sensitive to microstructural changes and damage. The goal of this paper is to propose a physical model describing the longitudinal vibrations of this class of material, and to develop a numerical strategy for solving the evolution equations. The theory relies on the coupling between two processes with radically-different time scales: a fast process at the frequency of the excitation, governed by nonlinear elasticity and viscoelasticity; a slow process, governed by the evolution of defects. The evolution equations are written as a nonlinear hyperbolic system with relaxation. A time-domain numerical scheme is developed, based on a splitting strategy. The numerical simulations show qualitative agreement with the features observed experimentally by Dynamic Acousto-Elastic Testing.
Nonlinear Phenomena and Resonant Parametric Perturbation Control in QR-ZCS Buck DC-DC Converters
Hsieh, Fei-Hu; Liu, Feng-Shao; Hsieh, Hui-Chang
The purpose of this study is to investigate the chaotic phenomena and to control in current-mode controlled quasi-resonant zero-current-switching (QR-ZCS) DC-DC buck converters, and to present control of chaos by resonant parametric perturbation control methods. First of all, MATLAB/SIMULINK is used to derive a mathematical model for QR-ZCS DC-DC buck converters, and to simulate the converters to observe the waveform of output voltages, inductance currents and phase-plane portraits from the period-doubling bifurcation to chaos by changing the load resistances. Secondly, using resonant parametric perturbation control in QR-ZCS buck DC-DC converters, the simulation results of the chaotic converter form chaos state turn into stable state period 1, and improve ripple amplitudes of converters under the chaos, to verify the validity of the proposes method.
Devi, Anita; De, Arijit K
2016-09-19
The use of low-power high-repetition-rate ultrafast pulsed excitation in stable optical trapping of dielectric nanoparticles has been demonstrated in the recent past; the high peak power of each pulse leads to instantaneous trapping of a nanoparticle with fast inertial response and the high repetition-rate ensures repetitive trapping by successive pulses However, with such high peak power pulsed excitation under a tight focusing condition, nonlinear optical effects on trapping efficiency also become significant and cannot be ignored. Thus, in addition to the above mentioned repetitive instantaneous trapping, trapping efficiency under pulsed excitation is also influenced by the optical Kerr effect, which we theoretically investigate here. Using dipole approximation we show that with an increase in laser power the radial component of the trapping potential becomes progressively more stable but the axial component is dramatically modulated due to increased Kerr nonlinearity. We justify that the relevant parameter to quantify the trapping efficiency is not the absolute depth of the highly asymmetric axial trapping potential but the height of the potential barrier along the beam propagation direction. We also discuss the optimal excitation parameters leading to the most stable dipole trap. Our results show excellent agreement with previous experiments.
Nonlinear Response of High Arch Dams to Nonuniform Seismic Excitation Considering Joint Effects
Directory of Open Access Journals (Sweden)
Masoomeh Akbari
2013-01-01
Full Text Available Nonuniform excitation due to spatially varying ground motions on nonlinear responses of concrete arch dams is investigated. A high arch dam was selected as numerical example, reservoir was modelled as incompressible material, foundation was assumed as mass-less medium, and all contraction and peripheral joints were modelled considering the ability of opening/closing. This study used Monte-Carlo simulation approach for generating spatially nonuniform ground motion. In this approach, random seismic characteristics due to incoherence and wave passage effects were investigated and finally their effects on structural response were compared with uniform excitation at design base level earthquake. Based on the results, nonuniform input leads to some differences than uniform input. Moreover using nonuniform excitation increase, stresses on dam body.
Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators
Alexeeva, N V; Tsironis, G P
2000-01-01
Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.
National Research Council Canada - National Science Library
de Paor, A. M
1998-01-01
Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field...
Naseri, Tayebeh; Moradi, Ronak
2017-01-01
Some optical properties including the linear and nonlinear susceptibility and electromagnetically induced phase grating (EIG) in graphene under Raman excitation is studied. A single-layer graphene nanostructure driven by coherent and incoherent fields is investigated theoretically. It is revealed that by adjusting the amplitude of control and incoherent fields, the linear and nonlinear absorption as well as Kerr nonlinearity of the medium can be optimized. It is realized that the enhanced Kerr nonlinearity can occur with zero linear absorption and nonlinear amplification. Furthermore, it should be noted that EIG in graphene is studied for the first time. The results indicate that the diffraction efficiency of the phase grating is dramatically enhanced by controlling the amplitude of coherent and incoherent fields, and an efficient electromagnetically induced phase grating can be obtained. A novel result shows a considerable improvement of the intensity of higher-order diffractions and switching between different orders of grating via incoherent pumping field. Therefore, this model can be used in real experiments for the development of new types of nanoelectronic devices used for the realization of all-optical switching processes.
Li, Xiao-Dong; Lv, Mang-Mang; Ho, John K. L.
2016-07-01
In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.
Institute of Scientific and Technical Information of China (English)
曾志刚; 叶敏
2012-01-01
在之前的研究中我们以ABS树脂为基材,填充1％ ～ 10％的金红石纳米二氧化钛制成纳米复合材料系列梁样本,并搭建了参数激励非线性振动实验系统.采用实验建模的方法,建立了粘弹性屈曲梁的动力学控制方程.在此基础上,进一步研究了系统的稳定性和分岔特性,利用多尺度方法对系统的幅频响应和解的稳定性进行了分析,并采用数值模拟分析参数激励幅值对系统分叉行为的影响,同时研究了系统通往混沌的道路,获得了丰富的动力学现象.%A series of composite materical samples were synthesized by using acrylonitrile-butadine styrene copolymer (ABS) resin as basic material and adding rutile nanscaled titania from 1% to 10% as reinforced material. A test platform for nonlinear parametrically excited vibrations was set up. Adopting a modeling method with tests, the dynamic governing equation of a viscoelastic composite beam was built. Furthermore, the stability and bifuraction of the system were further discussd. The multi-scale analysis method was used to analyze the amplitude and frequency response characteristics of the system and the stability of the solutions to the dynamic equation. The effect of the parametric excitation amplitude on the bifurcation behavior of the system was analyzed with numerical simulation. The way to chaos for the system was studied. The results showed that there are rich nonlinear dynamic pehnomena in the system.
Indian Academy of Sciences (India)
P K Karmakar
2007-04-01
Application of inertia-induced acoustic excitation theory offers a new resonant excitation source channel of acoustic turbulence in the transonic domain of plasma flow. In bi-ion plasmas like colloidal plasma, two well-defined transonic points exist corresponding to the parent ion and the dust grain-associated acoustic modes. As usual, the modified ion acoustic mode (also known as dust ion-acoustic (DIA) wave) dynamics associated with parent ion inertia is excitable for both nanoscale- and micronscale-sized dust grains. It is found that the so-called (ion) acoustic mode (also known as dust-acoustic (DA) wave) associated with nanoscale dust grain inertia is indeed resonantly excitable through the active role of weak but finite parent ion inertia. It is interestingly conjectured that the same excitation physics, as in the case of normal plasma sound mode, operates through the active inertial role of plasma thermal species. Details of the nonlinear acoustic mode analyses of current interest in transonic domains of such impure plasmas in hydrodynamic flow are presented.
Adaptive neural control for a class of nonlinearly parametric time-delay systems.
Ho, Daniel W C; Li, Junmin; Niu, Yugang
2005-05-01
In this paper, an adaptive neural controller for a class of time-delay nonlinear systems with unknown nonlinearities is proposed. Based on a wavelet neural network (WNN) online approximation model, a state feedback adaptive controller is obtained by constructing a novel integral-type Lyapunov-Krasovskii functional, which also efficiently overcomes the controller singularity problem. It is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.
Nonlinear Analysis of Cable Vibration of a Multispan Cable-Stayed Bridge under Transverse Excitation
Directory of Open Access Journals (Sweden)
Kun Lin
2014-01-01
Full Text Available The nonlinear vibrations of cable in a multispan cable-stayed bridge subjected to transverse excitation are investigated. The MECS (multielements cable system model, where multielements per cable stay are used, is built up and used to analyze the model properties of the multispan cable-stayed bridges. Then, a simplified two-degrees-of-freedom (2-DOFs model, where the tower or the deck is reduced to a beam, is proposed to analyze the nonlinear dynamic behaviors of the beam and cable. The results of MECS model analysis show that the main tower in the multispan cable-stayed bridge is prone to the transverse vibration, and the local vibration of cables only has a little impact on the frequency values of the global modes. The results of simplified model analysis show that the energy can be transformed between the modes of the beam and cable when the nature frequencies of them are very close. On the other hand, with the transverse excitation changing, the cable can exhibit richer quasi-periodic or chaotic motions due to the nonlinear terms caused by the coupled mode between the beam and cable.
Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
Iubini, Stefano; Boada, Octavi; Omar, Yasser; Piazza, Francesco
2015-11-01
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Parametric and Non-Parametric System Modelling
DEFF Research Database (Denmark)
Nielsen, Henrik Aalborg
1999-01-01
considered. It is shown that adaptive estimation in conditional parametric models can be performed by combining the well known methods of local polynomial regression and recursive least squares with exponential forgetting. The approach used for estimation in conditional parametric models also highlights how....... For this purpose non-parametric methods together with additive models are suggested. Also, a new approach specifically designed to detect non-linearities is introduced. Confidence intervals are constructed by use of bootstrapping. As a link between non-parametric and parametric methods a paper dealing with neural...... the focus is on combinations of parametric and non-parametric methods of regression. This combination can be in terms of additive models where e.g. one or more non-parametric term is added to a linear regression model. It can also be in terms of conditional parametric models where the coefficients...
Institute of Scientific and Technical Information of China (English)
李高峰; 杨志安; 赵雪娟; 王丽
2011-01-01
以温度场中斜梁受简谐激励的非线性振动方程为基础，应用非线性振动的多尺度法，求得非线性振动系统主参数共振的一次近似解，并进行定常解稳定性分析和数值计算；分析了温度、长度、面积、激励等参数对主参数共振幅频响应曲线的影响。数值结果表明，系统主参数共振的共振区很窄，随着温度和长度的减小，系统主参数共振的共振区增大。%Based on nonlinear vibration equation of inclined beam subjected to harmonic excitation in temperature field, the first approximate solution of primary parametric resonance of the nonlinear vibration system is obtained by means of the method of multiple scales for nonlinear oscillations. Results of numerical analysis of the influence of temperature and the ratio of length to height on amplitude frequency response curves are as follows. An analysis is made of stability of steady state solutions and the resonant region of the primary paratric resonance system is narrow. With the decreasing of the temperature and the ratio of length to height, the resonant region of primary parametric resonance of the system increases.
The Nonlinear Dynamic Relationship of Exchange Rates: Parametric and Nonparametric Causality testing
Bekiros, S.D.; Diks, C.
2007-01-01
The present study investigates the long-term linear and nonlinear causal linkages among six currencies, namely EUR/USD, GBP/USD, USD/JPY, USD/CHF, AUD/USD and USD/CAD. The prime motivation for choosing these exchange rates comes from the fact that they are the most liquid and widely traded, covering
Stefszky, Michael; Mow-Lowry, Conor M.; McKenzie, Kirk; Chua, Sheon; Buchler, Ben C.; Symul, Thomas; McClelland, David E.; Lam, Ping Koy
2011-01-01
A squeezed light source requires properties such as high squeezing amplitude, high bandwidth and stability over time, ideally using as few resources, such as laser power, as possible. We compare three nonlinear materials, two of which have not been well characterized for squeezed state production,
Stefszky, Michael; Mow-Lowry, Conor M.; McKenzie, Kirk; Chua, Sheon; Buchler, Ben C.; Symul, Thomas; McClelland, David E.; Lam, Ping Koy
2011-01-01
A squeezed light source requires properties such as high squeezing amplitude, high bandwidth and stability over time, ideally using as few resources, such as laser power, as possible. We compare three nonlinear materials, two of which have not been well characterized for squeezed state production, a
Non-linear Ion-wake Excitation by Ultra-relativistic Electron Wakefields
Sahai, Aakash A
2015-01-01
The excitation of a non-linear ion-wake by a train of ultra-relativistic plasmons is modeled and its use for a novel regime of positron acceleration is explored. Its channel-like structure is independent of the energy-source driving the bubble-shaped slowly-propagating high phase-velocity electron density waves. The back of the bubble electron compression sucks-in the ions and the space-charge within the bubble expels them, forming a near-void channel with on-axis and bubble-edge density-spikes. The channel-edge density-spike is driven radially outwards as a non-linear ion acoustic-wave by the wake electron thermal pressure. OSIRIS PIC simulations are used to study the ion-wake structure, its evolution and its use for positron acceleration.
Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations
Energy Technology Data Exchange (ETDEWEB)
Aydogmus, F., E-mail: fatma.aydogmus@gmail.com [Istanbul University, Department of Physics, Faculty of Science (Turkey)
2015-02-15
The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.
Excitation of turbulence in accretion disks of binary stars by non-linear perturbations
Kurbatov, E. P.; Bisikalo, D. V.
2017-06-01
Accretion disks in binary systems can experience hydrodynamical influences at both their inner and outer edges. The former is typical for protoplanetary disks around young T Tauri stars, while the latter is typical for circumstellar disks in close binaries. This influence excites perturbations with various scales and amplitudes in the disk. The nonlinear evolution of perturbations with a finite, but small amplitude against the background of a sub-Keplerian flow is investigated. Nonlinear effects at the fronts of perturbation waves lead to the formation of discontinuities in the density and radial velocity; i.e., to formation of shocks. The tangential flow in the neighborhood of the shock becomes equivalent to a flow in a boundary layer. Due to an instability of the tangential flow, the disk becomes turbulent. The characteristics of the turbulence depend on the parameters of the perturbations, but the Shakura-Syunyaev α parameter does not exceed 0.1.
Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation
Institute of Scientific and Technical Information of China (English)
SHI Peiming; LIU Bin; HOU Dongxiao
2009-01-01
Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.
Multidimensional Plasma Wake Excitation in the Non-linear Blowout Regime
Vieira, J; Silva, L O
2016-01-01
Plasma accelerators can sustain very high acceleration gradients. They are promising candidates for future generations of particle accelerators for sev- eral scientific, medical and technological applications. Current plasma based acceleration experiments operate in the relativistic regime, where the plasma response is strongly non-linear. We outline some of the key properties of wake- field excitation in these regimes. We outline a multidimensional theory for the excitation of plasma wakefields in connection with current experiments. We then use these results and provide design guidelines for the choice of laser and plasma parameters ensuring a stable laser wakefield accelerator that maximizes the quality of the accelerated electrons. We also mention some of the future challenges associated with this technology.
Institute of Scientific and Technical Information of China (English)
Chang-shui FENG; Wei-qiu ZHU
2009-01-01
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged Ito stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov (FPK) equation associated with the averaged Ito equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus-trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
RESPONSE ANALYSIS OF RANDOMLY EXCITED NONLINEAR SYSTEMS WITH SYMMETRIC WEIGHTING PREISACH HYSTERESIS
Institute of Scientific and Technical Information of China (English)
应祖光
2003-01-01
An approximate method for analyzing the response of nonlinear systems with the Preisach hysteresis of the non-local memory under a stationary Gaussian excitation is presented based on the covariance and switching probability analysis. The covariance matrix equation of the Preisach hysteretic system response is derived. The cross correlation function of the Preisach hysteretic force and response in the covariance equation is evaluated by the switching probability analysis and the Gaussian approximation to the response process. Then an explicit expression of the correlation function is given for the case of symmetric Preisach weighting functions. The numerical result obtained is in good agreement with that from the digital simulation.
Energy Technology Data Exchange (ETDEWEB)
Chen, Jia Nen; Liu, Jun [Tianjin Key Laboratory of the Design and Intelligent Control of the Advanced Mechatronical System, Tianjin University of Technology, Tianjin (China); Zhang, Wei; Yao, Ming Hui [College of Mechanical Engineering, Beijing University of Technology, Beijing (China); Sun, Min [School of Science, Tianjin Chengjian University, Tianjin (China)
2016-09-15
Nonlinear vibrations of carbon fiber reinforced composite sandwich plate with pyramidal truss core are investigated. The governing equation of motion for the sandwich plate is derived by using a Zig-Zag theory under consideration of geometrically nonlinear. The natural frequencies of sandwich plates with different dimensions are calculated and compared with those obtained from the classic laminated plate theory and Reddy's third-order shear deformation plate theory. The frequency responses and waveforms of the sandwich plate when 1:3 internal resonance occurs are obtained, and the characteristics of the internal resonance are discussed. The influences of layer number of face sheet, strut radius, core height and inclination angle on the nonlinear responses of the sandwich plate are analyzed. The results demonstrate that the strut radius and inclination angle mainly affect the resonance frequency band of the sandwich plate, and the layer number and core height not only influence the resonance frequency band but also significantly affect the response amplitude.
Parametric optimal bounded feedback control for smart parameter-controllable composite structures
Ying, Z. G.; Ni, Y. Q.; Duan, Y. F.
2015-03-01
Deterministic and stochastic parametric optimal bounded control problems are presented for smart composite structures such as magneto-rheological visco-elastomer based sandwich beam with controllable bounded parameters subjected to initial disturbances and stochastic excitations. The parametric controls by actively adjusting system parameters differ from the conventional additive controls by systemic external inputs. The dynamical programming equations for the optimal parametric controls are derived based on the deterministic and stochastic dynamical programming principles. The optimal bounded functions of controls are firstly obtained from the equations with the bounded control constraints based on the bang-bang control strategy. Then the optimal bounded parametric control laws are obtained by the inversion of the nonlinear functions. The stability of the optimally controlled systems is proved according to the Lyapunov method. Finally, the proposed optimal bounded parametric feedback control strategy is applied to single-degree-of-freedom and two-degree-of-freedom dynamic systems with nonlinear parametric bounded control terms under initial disturbances and earthquake excitations and then to a magneto-rheological visco-elastomer based sandwich beam system with nonlinear parametric bounded control terms under stochastic excitations. The effective vibration suppression is illustrated with numerical results. The proposed optimal parametric control strategy is applicable to other smart composite structures with nonlinear controllable parameters.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
Institute of Scientific and Technical Information of China (English)
ZHOU Shihua; SONG Guiqiu; REN Zhaohui; WEN Bangchun
2016-01-01
Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.
Zhou, Shihua; Song, Guiqiu; Ren, Zhaohui; Wen, Bangchun
2016-03-01
Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom(8-DOF) nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system(SGRBS) is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.
Energy Technology Data Exchange (ETDEWEB)
Delaune, X.; Piteau, Ph.; Borsoi, L. [CEA Saclay, Laboratoire d' Etudes de Dynamique, CEA, DEN, DM2S, SEMT, 91 - Gif-sur-Yvette (France); Antunes, J.; Debut, V. [Applied Dynamics Laboratory, Instituto Tecnologico e Nuclear, ITN/ADL, Estrada Nacional 10, 2686 Sacavem Codex (Portugal)
2010-06-15
Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information which is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this field using wave-propagation techniques, we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results prove quite sensitive to noise and modeling error problems. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of non-measured noise perturbations. In particular, a method is proposed to improve the identification of contact forces at the supports when the system is excited by an unknown distributed turbulence force field. The important topic of dealing with the imperfect knowledge of the modal parameters used to build the inverted transfer functions is addressed elsewhere. Here, the extensive identifications presented are based on the exact modal parameters and performed on realistic numerical simulations of gap-supported tubes subjected to flow excitation. We can thus confront the identified dynamical support contact forces and vibratory motions at the gap-support with the actual values stemming from the original nonlinear computations, with overall satisfying results. (authors)
The Nonlinear Behavior of Vibrational Conveyers with Single-Mass Crank-and-Rod Exciters
Directory of Open Access Journals (Sweden)
G. Füsun Alışverişçi
2012-01-01
Full Text Available The single-mass, crank-and-rod exciters vibrational conveyers have a trough supported on elastic stands which are rigidly fastened to the trough and a supporting frame. The trough is oscillated by a common crank drive. This vibration causes the load to move forward and upward. The moving loads jump periodically and move forward with relatively small vibration. The movement is strictly related to vibrational parameters. This is applicable in laboratory conditions in the industry which accommodate a few grams of loads, up to those that accommodate tons of loading capacity. In this study I explore the transitional behavior across resonance, during the starting of a single degree of freedom vibratory system excited by crank-and-rod. A loaded vibratory conveyor is more safe to start than an empty one. Vibrational conveyers with cubic nonlinear spring and ideal vibration exciter have been analyzed analytically for primary and secondary resonance by the Method of Multiple Scales, and numerically. The approximate analytical results obtained in this study have been compared with the numerical results and have been found to be well matched.
List, Nanna Holmgaard; Zaleśny, Robert; Murugan, N Arul; Kongsted, Jacob; Bartkowiak, Wojciech; Ågren, Hans
2015-09-08
We establish the relationships between the metric of charge transfer excitation (Δr) for the bright ππ* state and the two-photon absorption probability as well as the first hyperpolarizability for two families of push-pull π-conjugated systems. As previously demonstrated by Guido et al. (J. Chem. Theory Comput. 2013, 9, 3118-3126), Δr is a measure for the average hole-electron distance upon excitation and can be used to discriminate between short- and long-range electronic excitations. We indicate two new benefits from using this metric for the analyses of nonlinear optical properties of push-pull systems. First, the two-photon absorption probability and the first hyperpolarizability are found to be interrelated through Δr; if β ∼ (Δr)(k), then roughly, δ(TPA) ∼ (Δr)(k+1). Second, a simple power relation between Δr and the molecular hyperpolarizabilities of push-pull systems offers the possibility of estimating properties for longer molecular chains without performing calculations of high-order response functions explicitly. We further demonstrate how to link the hyperpolarizabilities with the chain length of the push-pull π-conjugated systems through the metric of charge transfer.
Fan, Xiaopeng; Zheng, Weihao; Liu, Hongjun; Zhuang, Xiujuan; Fan, Peng; Gong, Yanfang; Li, Honglai; Wu, Xueping; Jiang, Ying; Zhu, Xiaoli; Zhang, Qinglin; Zhou, Hong; Hu, Wei; Wang, Xiao; Duan, Xiangfeng; Pan, Anlian
2017-06-01
Recombination dynamics during photoluminescence (PL) in two-dimensional (2D) semiconducting transition metal dichalcogenides (TMDs) are complicated and can be easily affected by the surroundings because of their atomically thin structures. Herein, we studied the excitation power and temperature dependence of the recombination dynamics on the chemical vapor deposition-grown monolayer WS2via a combination of Raman, PL, and time-resolved PL spectroscopies. We found a red shift and parabolic intensity increase in the PL emission of the monolayer WS2 with the increasing excitation power and the decay time constants corresponding to the recombination of trions and excitons from transient PL dynamics. We attributed the abovementioned nonlinear changes in the PL peak positions and intensities to the combination of increasing carrier interaction and band structure renormalization rather than to the thermal effect from a laser. Furthermore, the excitation power-dependent Raman measurements support our conclusion. These findings and understanding will provide important information for the development of TMD-based optoelectronics and photonics.
Institute of Scientific and Technical Information of China (English)
Xiaodong WANG; Yushu CHEN; Lei HOU
2015-01-01
The bifurcation analysis of a simple electric power system involving two synchronous generators connected by a transmission network to an infinite-bus is carried out in this paper. In this system, the infinite-bus voltage are considered to maintain two fluctuations in the amplitude and phase angle. The case of 1:3 internal resonance between the two modes in the presence of parametric principal resonance is considered and examined. The method of multiple scales is used to obtain the bifurcation equations of this system. Then, by employing the singularity method, the transition sets determining different bifurcation patterns of the system are obtained and analyzed, which reveal the effects of the infinite-bus voltage amplitude and phase fluctuations on bifurcation patterns of this system. Finally, the bifurcation patterns are all examined by bifurcation diagrams. The results obtained in this paper will contribute to a better understanding of the complex nonlinear dynamic behaviors in a two-machine infinite-bus (TMIB) power system.
Premraj, D.; Suresh, K.; Palanivel, J.; Thamilmaran, K.
2017-09-01
A periodically forced series LCR circuit with Chua's diode as a nonlinear element exhibits slow passage through Hopf bifurcation. This slow passage leads to a delay in the Hopf bifurcation. The delay in this bifurcation is a unique quantity and it can be predicted using various numerical analysis. We find that when an additional periodic force is added to the system, the delay in bifurcation becomes chaotic which leads to an unpredictability in bifurcation delay. Further, we study the bifurcation of the periodic delay to chaotic delay in the slow passage effect through strange nonchaotic delay. We also report the occurrence of strange nonchaotic dynamics while varying the parameter of the additional force included in the system. We observe that the system exhibits a hitherto unknown dynamical transition to a strange nonchaotic attractor. With the help of Lyapunov exponent, we explain the new transition to strange nonchaotic attractor and its mechanism is studied by making use of rational approximation theory. The birth of SNA has also been confirmed numerically, using Poincaré maps, phase sensitivity exponent, the distribution of finite-time Lyapunov exponents and singular continuous spectrum analysis.
Hard and Soft Excitation Regimes of Kerr Frequency Combs
Matsko, Andrey B; Ilchenko, Vladimir S; Seidel, David; Maleki, Lute
2011-01-01
We theoretically study the stability conditions and excitation regimes of hyper-parametric oscillation and Kerr frequency comb generation in continuously pumped nonlinear optical resonators possessing anomalous group velocity dispersion. We show that both hard and soft excitation regimes are possible in the resonators. Selection between the regimes is achieved via change in the parameters of the pumping light.
A. M. de Paor
1998-01-01
International audience; Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ? has the value 1 is proved via ...
de Paor, A. M.
Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.
Directory of Open Access Journals (Sweden)
Zhi-Wen Zhu
2015-01-01
Full Text Available A kind of high-aspect-ratio shape memory alloy (SMA composite wing is proposed to reduce the wing’s fluttering. The nonlinear dynamic characteristics and optimal control of the SMA composite wings subjected to in-plane stochastic excitation are investigated where the great bending under the flight loads is considered. The stochastic stability of the system is analyzed, and the system’s response is obtained. The conditions of stochastic Hopf bifurcation are determined, and the probability density of the first-passage time is obtained. Finally, the optimal control strategy is proposed. Numerical simulation shows that the stability of the system varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the reliability of the system is improved through optimal control, and the first-passage time is delayed. Finally, the effects of the control strategy are proved by experiments. The results of this paper are helpful for engineering applications of SMA.
Institute of Scientific and Technical Information of China (English)
ZHENGChun-Long; ZHANGJie-Fang; CHENLi-Qun
2003-01-01
Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
Nonlinear TeraHertz Coherent Excitation of Vibrational Modes of Liquids
Allodi, Marco A; Blake, Geoffrey A
2015-01-01
We report the first coherent excitation of intramolecular vibrational modes via the nonlinear interaction of a TeraHertz (THz) light field with molecular liquids. A TeraHertz-TeraHertz-Raman pulse sequence prepares the coherences with a broadband, high-energy, (sub)picosecond TeraHertz pulse, that are then measured in a TeraHertz Kerr effect spectrometer via phase-sensitive, heterodyne detection with an optical pulse. The spectrometer reported here has broader TeraHertz frequency coverage and an increased sensitivity relative to previously reported TeraHertz Kerr effect experiments. Vibrational coherences are observed in liquid diiodomethane at 3.66 THz (122 cm$^{-1}$), and in carbon tetrachloride at 6.50 THz (217 cm$^{-1}$), in exact agreement with literature values of those intramolecular modes. This work opens the door to 2D spectroscopies, nonlinear in TeraHertz field, that can study the dynamics of condensed-phase molecular systems, as well as coherent control at TeraHertz frequencies.
Directory of Open Access Journals (Sweden)
A.M. Elnaggar
2016-01-01
Full Text Available An analysis of primary, superharmonic of order five, and subharmonic of order one-three resonances for non-linear s.d.o.f. system with two distinct time-delays under an external excitation is investigated. The method of multiple scales is used to determine two first order ordinary differential equations which describe the modulation of the amplitudes and the phases. Steady-state solutions and their stabilities in each resonance are studied. Numerical results are obtained by using the Software of Mathematica, which presented in a group of figures. The effect of the feedback gains and time-delays on the non-linear response of the system is discussed and it is found that: an appropriate feedback can enhance the control performance. A suitable choice of the feedback gains and time-delays can enlarge the critical force amplitude, and reduce the peak amplitude of the response (or peak amplitude of the free oscillation term for the case of primary resonance (superharmonic resonance. Furthermore, a proper feedback can eliminate saddle-node bifurcation, thereby eliminating jump and hysteresis phenomena taking place in the corresponding uncontrolled system. For subharmonic resonance, an adequate feedback can reduce the regions of subharmonic resonance response.
Yang, Yongge; Xu, Wei; Sun, Yahui; Xiao, Yanwen
2017-01-01
This paper aims to investigate the stochastic bifurcations in the nonlinear vibroimpact system with fractional derivative under random excitation. Firstly, the original stochastic vibroimpact system with fractional derivative is transformed into equivalent stochastic vibroimpact system without fractional derivative. Then, the non-smooth transformation and stochastic averaging method are used to obtain the analytical solutions of the equivalent stochastic system. At last, in order to verify the effectiveness of the above mentioned approach, the van der Pol vibroimpact system with fractional derivative is worked out in detail. A very satisfactory agreement can be found between the analytical results and the numerical results. An interesting phenomenon we found in this paper is that the fractional order and fractional coefficient of the stochastic van der Pol vibroimpact system can induce the occurrence of stochastic P-bifurcation. To the best of authors' knowledge, the stochastic P-bifurcation phenomena induced by fractional order and fractional coefficient have not been found in the present available literature which studies the dynamical behaviors of stochastic system with fractional derivative under Gaussian white noise excitation.
Nonlinear Resonant Excitation of Fast Sausage Waves in Current-Carrying Coronal Loops
Mikhalyaev, B. B.; Bembitov, D. B.
2014-11-01
We consider a model of a coronal loop that is a cylindrical magnetic tube with two surface electric currents. Its principal sausage mode has no cut-off in the long-wavelength limit. For typical coronal conditions, the period of the mode is between one and a few minutes. The sausage mode of flaring loops could cause long-period pulsations observed in microwave and hard X-ray ranges. There are other examples of coronal oscillations: long-period pulsations of active-region quiet loops in the soft X-ray emission are observed. We assume that these can also be caused by sausage waves. The question arises of how the sausage waves are generated in quiet loops. We assume that they can be generated by torsional oscillations. This process can be described in the framework of the nonlinear three-wave interaction formalism. The periods of interacting torsional waves are similar to the periods of torsional oscillations observed in the solar atmosphere. The timescale of the sausage-wave excitation is not much longer than the periods of interacting waves, so that the sausage wave is excited before torsional waves are damped.
Institute of Scientific and Technical Information of China (English)
张长友; 朱昌明; 林忠钦
2004-01-01
This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieus equation with cubic nonlinearity. According to the theory of the Mathieus equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.%论述了一种抑制载重绳索参数激励横向振动的简便方法. 假设绳索底端的质量受到一个垂直简谐激励并忽略载重绳索高阶振型的影响, 载重绳索的运动方程可以用一个带有立方非线性项的Mathieu方程来描述. 根据Mathieu方程的有关理论, 在载重绳索系统中, 当索端质量垂直振动的频率接近绳索横向振动固有频率2倍时, 一旦索端质量垂直振动的幅度超过某个临界数值时, 绳索将产生参数共振. 为了避免这种现象, 建议在索端质量上加装一个减振器以削减索端质量的垂直振动, 进而抑制绳索的横向振动. 实验验证了该减振方案的有效性.
DEFF Research Database (Denmark)
Turchinovich, Dmitry; Monozon, B. S.; Jepsen, Peter Uhd
2006-01-01
calculations, in particular, predict the strongly nonlinear dependency of the effective optical absorption coefficient on the excitation pulse fluence, and ultrabroadband terahertz emission. Our theoretical model is free of fitting parameters. Calculations performed for internally biased InFaN/GaN quantum...
Parametric versus non-parametric simulation
Dupeux, Bérénice; Buysse, Jeroen
2014-01-01
Most of ex-ante impact assessment policy models have been based on a parametric approach. We develop a novel non-parametric approach, called Inverse DEA. We use non parametric efficiency analysis for determining the farm’s technology and behaviour. Then, we compare the parametric approach and the Inverse DEA models to a known data generating process. We use a bio-economic model as a data generating process reflecting a real world situation where often non-linear relationships exist. Results s...
Elsaesser, Thomas; Reimann, Klaus; Woerner, Michael
2015-06-01
Intense terahertz (THz) electric field transients with amplitudes up to several megavolts/centimeter and novel multidimensional techniques are the key ingredients of nonlinear THz spectroscopy, a new area of basic research. Both nonlinear light-matter interactions including the non-perturbative regime and THz driven charge transport give new insight into the character and dynamics of low-energy excitations of condensed matter and into quantum kinetic phenomena. This article provides an overview of recent progress in this field, combining an account of technological developments with selected prototype results for liquids and solids. The potential of nonlinear THz methods for future studies of low-frequency excitations of condensed-phase molecular systems is discussed as well.
Indian Academy of Sciences (India)
Fatih Goktepe; H Serdar Kuyuk; Erkan Celebi
2014-04-01
Earthquakes have caused colossal casualties and severe damages to engineering structures and especially leading to substantial economic loss to the underground structures and/or infrastructures. Pipelines are one of most important component of lifeline engineering. For instance, the Southern Caucasus- Eastern Turkey energy corridors are formed by several key pipelines carrying crude oil and natural gas from Azerbaijan, via Georgia, to world markets through Mediterranean Sea. Many project accomplished recently and construction of new corridors are still going on. They should be protected from earthquake disaster especially when they pass through high seismicity zones. The installation of wave impeding barriers (WIB) below the vulnerable infrastructures as pipelines established in soft soil can be used to reduce the effect of the earthquake induced ground borne vibrations. In this paper, a WIB as artificial bedrock based on the cut-off frequency of a soil layer over bedrock is proposed as isolation measurement in order to mitigate the dynamic response of the buried pipelines under earthquake strong ground motion. The computational simulation of the wave propagation problem is directly achieved by employing nonlinear 2D finite element modelling for prediction of screening performance of WIB on the dynamic response of vibrating coupled soil-pipeline system. Energy absorbing boundaries along the truncated interfaces of the unbounded nature of the underlying soil media are implemented in the time domain along with Newmark’s integration. An extensive parametric investigation and systematic computations are performed with different controlling parameters. The obtained numerical results point out that WIB can be very promising as an isolator to protect pipelines when they establish for a certain depth.
Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo
Directory of Open Access Journals (Sweden)
R. Hide
1997-01-01
Full Text Available In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions. New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ (where τ denotes time by a steady applied couple. The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ by a torque xf (x due to Lorentz forces associated with the electric current x(τ in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD geodynamo. The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1 - βzf(x, dy/dt = α(1 - x² - κy, dz/dt = xf (x -λz, where f (x = 1 - ε + εσx, in cases when the dimensionless parameters (α, β, κ, λ, σ are all positive and 0 ≤ ε ≤ 1. Within those regions of (α, β, κ, λ, σ parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0 to occur at all, there are in general extensive regions where x(τ exhibits large amplitude regular or irregular (chaotic fluctuations. But these fluctuating r
Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo
Hide, R.
In the interpretation of geomagnetic polarity reversals with their highly variable frequency over geological time it is necessary, as with other irregularly fluctuating geophysical phenomena, to consider the relative importance of forced contributions associated with changing boundary conditions and of free contributions characteristic of the behaviour of nonlinear systems operating under fixed boundary conditions. New evidence -albeit indirect- in favour of the likely predominance of forced contributions is provided by the discovery reported here of the possibility of complete quenching by nonlineax effects of current fluctuations in a self-exciting homopolar dynamo with its single Faraday disk driven into rotation with angular speed y(τ) (where τ denotes time) by a steady applied couple. The armature of an electric motor connected in series with the coil of the dynamo is driven into rotation' with angular speed z(τ) by a torque xf (x) due to Lorentz forces associated with the electric current x(τ) in the system (just as certain parts of the spectrum of eddies within the liquid outer core are generated largely by Lorentz forces associated with currents generated by the self-exciting magnetohydrodynamic (MHD) geodynamo). The discovery is based on bifurcation analysis supported by computational studies of the following (mathematically novel) autonomous set of nonlinear ordinary differential equations: dx/dt = x(y - 1) - βzf(x), dy/dt = α(1 - x²) - κy, dz/dt = xf (x) -λz, where f (x) = 1 - ɛ + ɛσx, in cases when the dimensionless parameters (α, β, κ, λ, σ) are all positive and 0 ≤ ɛ ≤ 1. Within those regions of (α, β, κ, λ, σ) parameter space where the applied couple, as measured by α, is strong enough for persistent dynamo action (i.e. x ≠ 0) to occur at all, there are in general extensive regions where x(τ) exhibits large amplitude regular or irregular (chaotic) fluctuations. But these fluctuating régimes shrink in size as increases
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead in an exponenti......We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead...
Two-parametric scaling law and figures of merit of excited-state absorption of organic dyes
Koldunov, Modest F.; Koldunov, Leonid M.
2017-02-01
Sequential theoretical analysis of the excited-state absorption of organic dyes is carried out. It is established that the transmission dependence on laser radiation intensity of optical elements activated by organic dyes is described by the scaling law. It contains two parameters (the critical intensity and the contrast parameter) which are figures of merit of the excited state absorption of dye. Requirements to experimental conditions needed for correctly determination of figures of merit of the excited-state absorption efficiency of organic dyes are formulated. It is shown that there is a good agreement between experimental data of the sample transmission dependence on laser radiation intensity with the result of its calculation based on the scaling law. Figures of merit for several organic dyes are obtained.
Energy Technology Data Exchange (ETDEWEB)
Zhu, Zhi-Wen [Department of Mechanics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072 (China); Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control 92 Weijin Road, Nankai District, Tianjin 300072 (China); Zhang, Qing-Xin [Department of Mechanics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072 (China); Xu, Jia, E-mail: xujia_ld@163.com [Department of Mechanics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072 (China)
2014-11-03
A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters.
Directory of Open Access Journals (Sweden)
Anton eIlango
2014-05-01
Full Text Available Midbrain dopamine neurons are implicated in motivation and learning. However, it is unclear how phasic excitation of dopamine neurons, which is implicated in learning, is involved in motivation. Here we used a self-stimulation procedure to examine how mice seek for optogenetically-induced phasic excitation of dopamine neurons, with an emphasis on the temporal dimension. TH-Cre transgenic mice received adeno-associated viral vectors encoding channelrhodopsin-2 into the ventral tegmental area, resulting in selective expression of the opsin in dopamine neurons. These mice were trained to press on a lever for photo-pulse trains that phasically excited dopamine neurons. They learned to self-stimulate in a fast, constant manner, and rapidly reduced pressing during extinction. We first determined effective parameters of photo-pulse trains in self-stimulation. Lever-press rates changed as a function of the manipulation of pulse number, duration, intensity and frequency. We then examined effects of interval and ratio schedules of reinforcement on photo-pulse train reinforcement, which was contrasted with food reinforcement. Reinforcement with food inhibited lever pressing for a few seconds, after which pressing was robustly regulated in a goal-directed manner. In contrast, phasic excitation of dopamine neurons robustly potentiated the initiation of lever pressing; however, this effect did not last more than 1 s and quickly diminished. Indeed, response rates markedly decreased when lever pressing was reinforced with inter-reinforcement interval schedules of 3 or 10 s or ratio schedules requiring multiple responses per reinforcement. Thus, phasic excitation of dopamine neurons briefly potentiates the initiation of approach behavior with apparent lack of long-term motivational regulation.
Ilango, Anton; Kesner, Andrew J; Broker, Carl J; Wang, Dong V; Ikemoto, Satoshi
2014-01-01
Midbrain dopamine neurons are implicated in motivation and learning. However, it is unclear how phasic excitation of dopamine neurons, which is implicated in learning, is involved in motivation. Here we used a self-stimulation procedure to examine how mice seek for optogenetically-induced phasic excitation of dopamine neurons, with an emphasis on the temporal dimension. TH-Cre transgenic mice received adeno-associated viral vectors encoding channelrhodopsin-2 into the ventral tegmental area, resulting in selective expression of the opsin in dopamine neurons. These mice were trained to press on a lever for photo-pulse trains that phasically excited dopamine neurons. They learned to self-stimulate in a fast, constant manner, and rapidly reduced pressing during extinction. We first determined effective parameters of photo-pulse trains in self-stimulation. Lever-press rates changed as a function of the manipulation of pulse number, duration, intensity, and frequency. We then examined effects of interval and ratio schedules of reinforcement on photo-pulse train reinforcement, which was contrasted with food reinforcement. Reinforcement with food inhibited lever pressing for a few seconds, after which pressing was robustly regulated in a goal-directed manner. In contrast, phasic excitation of dopamine neurons robustly potentiated the initiation of lever pressing; however, this effect did not last more than 1 s and quickly diminished. Indeed, response rates markedly decreased when lever pressing was reinforced with inter-reinforcement interval schedules of 3 or 10 s or ratio schedules requiring multiple responses per reinforcement. Thus, phasic excitation of dopamine neurons briefly potentiates the initiation of approach behavior with apparent lack of long-term motivational regulation.
Directory of Open Access Journals (Sweden)
A. M. de Paor
1998-01-01
Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.
Chaos control of a class of parametrically excited Duffing's system using a random phase
Energy Technology Data Exchange (ETDEWEB)
Li Longsuo, E-mail: lilongsuo@126.com [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China); Yu Hedan [Pharmaceutical College, Heilongjiang University of Chinese Medicine, Harbin 150001 (China)
2011-07-15
Highlights: > The chaotic dynamical behavior first has been controlled by random phase. > It can be proved that chaos has been suppressed from the Lyapunov exponents. > It is verified that chaos has been suppressed from Poincare map. - Abstract: As the analysis of the chaotic dynamical behavior of a parametric Duffing's system, we show that chaos can be suppressed by addition the Gauss white noise phase and determined by the sign of the top Lyapunov exponent, which is based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. Also Poincare map analysis is carried out to confirm the obtained results. So random phase can be realized as one of the methods of chaos control.
Halevy, A; Dovrat, L; Eisenberg, H S; Becker, P; Bohatý, L
2011-01-01
We describe the full characterization of the biaxial nonlinear crystal BiB3O6 (BiBO) as a polarization entangled photon source using non-collinear type-II parametric down-conversion. We consider the relevant parameters for crystal design, such as cutting angles, polarization of the photons, effective nonlinearity, spatial and temporal walk-offs, crystal thickness and the effect of the pump laser bandwidth. Experimental results showing entanglement generation with high rates and a comparison to the well investigated beta-BaB2O4 (BBO) crystal are presented as well. Changing the down-conversion crystal of a polarization entangled photon source from BBO to BiBO enhances the generation rate as if the pump power was increased by more than three times. Such an improvement is currently required for the generation of multiphoton entangled states.
Halevy, A; Megidish, E; Dovrat, L; Eisenberg, H S; Becker, P; Bohatý, L
2011-10-10
We describe the full characterization of the biaxial nonlinear crystal BiB₃O₆ (BiBO) as a polarization entangled photon source using non-collinear type-II parametric down-conversion. We consider the relevant parameters for crystal design, such as cutting angles, polarization of the photons, effective nonlinearity, spatial and temporal walk-offs, crystal thickness and the effect of the pump laser bandwidth. Experimental results showing entanglement generation with high rates and a comparison to the well investigated β-BaB₂O₄ (BBO) crystal are presented as well. Changing the down-conversion crystal of a polarization entangled photon source from BBO to BiBO enhances the generation rate as if the pump power was increased by 2.5 times. Such an improvement is currently required for the generation of multiphoton entangled states.
Energy Technology Data Exchange (ETDEWEB)
Rouzaud, C., E-mail: crouzaud@adm.estp.fr [LMT (ENS Cachan, CNRS, Université Paris Saclay) 61 avenue du Président Wilson, 94235 Cachan (France); Université Paris-Est, Institut de Recherche en Constructibilité, ESTP 28 avenue du Président Wilson, 94230 Cachan (France); AREVA, 10 rue Juliette Récamier, 69006 Lyon (France); Gatuingt, F. [LMT (ENS Cachan, CNRS, Université Paris Saclay) 61 avenue du Président Wilson, 94235 Cachan (France); Hervé, G. [Université Paris-Est, Institut de Recherche en Constructibilité, ESTP 28 avenue du Président Wilson, 94230 Cachan (France); Moussallam, N. [AREVA, 10 rue Juliette Récamier, 69006 Lyon (France); Dorival, O. [Icam, Site de Toulouse, 75 avenue de Grande-Bretagne, 31076 Toulouse Cedex 3 (France); Université de Toulouse, Institut Clément Ader (ICA), INSA, UPS, Mines Albi, ISAE 135 avenue de Rangueil, 31077 Toulouse Cedex (France)
2016-03-15
Highlights: • Structures could resist to the induced accelerations which they might undergo. • The characterization of non-linearities in the signal of an aircraft impact. • The non linear impact area are studied through a sensitivity analysis. • This analysis should allow to achieve a link between aircraft impact parameters. - Abstract: In the process of nuclear power plant design, the safety of structures is an important aspect. Civil engineering structures have to resist the accelerations induced by, for example, seismic loads or shaking loads resulting from the aircraft impact. This is even more important for the in-structures equipments that have also to be qualified against the vibrations generated by this kind of hazards. In the case of aircraft crash, as a large variety of scenarios has to be envisaged, it is necessary to use methods that are less CPU-time consuming and that consider appropriately the nonlinearities. The analysis presented in this paper deals with the problem of the characterization of nonlinearities (damaged area, transmitted force) in the response of a structure subjected to an aircraft impact. The purpose of our study is part of the development of a new decoupled nonlinear and elastic way for calculating the shaking of structures following an aircraft impact which could be very numerically costly if studied with classical finite element methods. The aim is to identify which parameters control the dimensions of the nonlinear zone and so will have a direct impact on the induced vibrations. In a design context, several load cases (and simulations) are analyzed in order to consider a wide range of impact (different loading surfaces, momentum) and data sets of the target (thickness, reinforcements). In this work, the nonlinear area generated by the impact is localized and studied through a parametric analysis associated with a sensitivity analysis to identify the boundaries between the elastic domain and this nonlinear area.
Chikh-Touami, Hocine; Kremer, Régis; Lee, Hsin-Jung; Lee, Min Won; Peng, Lung-Han; Boudrioua, Azzedine
2017-06-01
We investigated angle-resolved optical parametric generation (OPG) in 2D periodically poled lithium tantalate (PPLT) with a 8.52 μm square lattice structure. Substantial parametric gain was observed at two specific incident angles of {0.8}\\circ and {1.6}\\circ , with the signal/idler wave propagating collinearly/non-collinearly to a 532 nm pump. These phenomena are due to simultaneous quasi-phase-matching OPG processes involved contribution from the reciprocal lattice vectors of ({{K}}{1,{0}} and {{K}}{1,{1}}) or ({{K}}{1,{0}} and {{K}}{1,{2}}), respectively. These configurations raise the parametric gain to comparable to that of the 1D QPM structure.
Nonlinear properties of the lattice network-based nonlinear CRLH transmission lines
Institute of Scientific and Technical Information of China (English)
王正斌; 吴昭质; 高超
2015-01-01
The nonlinear properties of lattice network-based (LNB) composite right-/left-handed transmission lines (CRLH TLs) with nonlinear capacitors are experimentally investigated. Harmonic generation, subharmonic generation, and parametric excitation are clearly observed in an unbalanced LNB CRLH TL separately. While the balanced design of the novel nonlinear TL shows that the subharmonic generation and parametric processes can be suppressed, and almost the same power level of the higher harmonics can be achieved over a wide bandwidth range, which are difficult to find in the conventional CRLH TLs.
Daniels, Jonathan S.; Anderson, Erik P.; Lee, Thomas H.; Pourmand, Nader
2009-01-01
Impedance biosensors detect the binding of a target to an immobilized probe by quantifying changes in the impedance of the electrode-electrolyte interface. The interface's I-V relationship is inherently nonlinear, varying with DC bias, and target binding can alter the degree of nonlinearity. We propose and demonstrate a method to simultaneously measure the nonlinearity and conventional small-signal impedance using intermodulation products from a two-tone input. Intermodulation amplitudes accurately reflect the impedance's manually-measured voltage dependence. We demonstrate that changes in nonlinearity can discriminate protein binding. Our measurements suggest that target binding can alter nonlinearity via the voltage dependence of the ionic double layer. PMID:19164024
Norris, G; McConnell, G
2010-03-01
A novel bi-directional pump geometry that nonlinearly increases the nonlinear optical conversion efficiency of a synchronously pumped optical parametric oscillator (OPO) is reported. This bi-directional pumping method synchronizes the circulating signal pulse with two counter-propagating pump pulses within a linear OPO resonator. Through this pump scheme, an increase in nonlinear optical conversion efficiency of 22% was achieved at the signal wavelength, corresponding to a 95% overall increase in average power. Given an almost unchanged measured pulse duration of 260 fs under optimal performance conditions, this related to a signal wavelength peak power output of 18.8 kW, compared with 10 kW using the traditional single-pass geometry. In this study, a total effective peak intensity pump-field of 7.11 GW/cm(2) (corresponding to 3.55 GW/cm(2) from each pump beam) was applied to a 3 mm long periodically poled lithium niobate crystal, which had a damage threshold intensity of 4 GW/cm(2), without impairing crystal integrity. We therefore prove the application of this novel pump geometry provides opportunities for power-scaling of synchronously pumped OPO systems together with enhanced nonlinear conversion efficiency through relaxed damage threshold intensity conditions.
Effective properties of mechanical systems under high-frequency excitation at multiple frequencies
DEFF Research Database (Denmark)
Thomsen, Jon Juel
2008-01-01
Effects of strong high-frequency excitation at multiple frequencies (multi-HFE) are analyzed for a class of generally nonlinear systems. The effects are illustrated for a simple pendulum system with a vibrating support, and for a parametrically excited flexible beam. For the latter, theoretical p...
Combined parametric-nonparametric identification of block-oriented systems
Mzyk, Grzegorz
2014-01-01
This book considers a problem of block-oriented nonlinear dynamic system identification in the presence of random disturbances. This class of systems includes various interconnections of linear dynamic blocks and static nonlinear elements, e.g., Hammerstein system, Wiener system, Wiener-Hammerstein ("sandwich") system and additive NARMAX systems with feedback. Interconnecting signals are not accessible for measurement. The combined parametric-nonparametric algorithms, proposed in the book, can be selected dependently on the prior knowledge of the system and signals. Most of them are based on the decomposition of the complex system identification task into simpler local sub-problems by using non-parametric (kernel or orthogonal) regression estimation. In the parametric stage, the generalized least squares or the instrumental variables technique is commonly applied to cope with correlated excitations. Limit properties of the algorithms have been shown analytically and illustrated in simple experiments.
Size-dependent nonlinear absorption and refraction of Ag nanoparticles excited by femtosecond lasers
Institute of Scientific and Technical Information of China (English)
Fan Guang-Hua; Qu Shi-Liang; Guo Zhong-Yi; Wang Qiang; Li Zhong-Guo
2012-01-01
Silver (Ag) nanoparticles with different average sizes are prepared,and the nonlinear absorption and refraction of these nanoparticles are investigated with femtosecond laser pulses at 800 nm.The smallest Ag nanoparticles show insignificant nonlinear absorption,whereas the larger ones show saturable absorption.By considering the previously reported positive nonlinear absorption of 9 nm Ag nanoparticles,the nonlinear absorptions of Ag nanoparticles are found to be size-dependent.All these nonlinear absorptions can be compatibly explained from the viewpoints of electronic transitions,energy bands and electronic structures in the conduction band of Ag nanoparticles.The nonlinear refraction is attributed to the effect of hot electrons arising from the intraband transition in the s-p conduction band of Ag nanoparticles.
Nonlinear excitation of low-n harmonics in reduced MHD simulations of edge-localized modes
Krebs, Isabel; Lackner, Karl; Guenter, Sibylle
2013-01-01
Nonlinear simulations of the early ELMphase based on a typical type-I ELMy ASDEX Upgrade discharge have been carried out using the reduced MHD code JOREK. The analysis is focused on the evolution of the toroidal Fourier spectrum. It is found that during the nonlinear evolution, linearly subdominant low-n Fourier components, in particular the n = 1, grow to energies comparable with linearly dominant harmonics. A simple model is developed, based on the idea that energy is transferred among the toroidal harmonics via second order nonlinear interaction. The simple model reproduces and explains very well the early nonlinear evolution of the toroidal spectrum in the JOREK simulations. Furthermore, it is shown for the n = 1 harmonic, that its spatial structure changes significantly during the transition from linear to nonlinearly driven growth. The rigidly growing structure of the linearly barely unstable n = 1 reaches far into the plasma core. In contrast, the nonlinearly driven n = 1 has a rigidly growing structur...
A quadratic-shaped-finger comb parametric resonator
Guo, Congzhong; Fedder, Gary K.
2013-09-01
A large-stroke (8 µm) parametric resonator excited by an in-plane ‘shaped-finger’ electrostatic comb drive is fabricated using a 15 µm thick silicon-on-insulator microelectromechanical systems (SOI-MEMS) process. A quadratic capacitance-engagement response is synthesized by engineering a custom-shaped comb finger profile. A folded-flexure suspension allows lateral motion while constraining rotational modes. The excitation of the nonlinear parametric resonance is realized by selecting an appropriate combination of the linear and cubic electrostatic stiffness coefficients through a specific varying-gap comb-finger design. The large-amplitude parametric resonance promotes high signal-to-noise ratio for potential use in sensitive chemical gravimetric sensors, strain gauges, and mode-matched gyroscope applications.
DEFF Research Database (Denmark)
Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.
Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....
Analysis of Synchronization Phenomena in Broadband Signals with Nonlinear Excitable Media
Directory of Open Access Journals (Sweden)
Klaus Lehnertz
2009-01-01
Full Text Available We apply the method of frequency-selective excitation waves in excitable media to characterize synchronization phenomena in interacting complex dynamical systems by measuring coincidence rates of induced excitations. We relax the frequency-selectivity of excitable media and demonstrate two applications of the method to signals with broadband spectra. Findings obtained from analyzing time series of coupled chaotic oscillators as well as electroencephalographic (EEG recordings from an epilepsy patient indicate that this method can provide an alternative and complementary way to estimate the degree of phase synchronization in noisy signals.
Remick, Kevin; Dane Quinn, D.; Michael McFarland, D.; Bergman, Lawrence; Vakakis, Alexander
2016-05-01
The authors investigate a vibration-based energy harvesting system utilizing essential (nonlinearizable) nonlinearities and electromagnetic coupling elements. The system consists of a grounded, weakly damped linear oscillator (primary system) subjected to a single impulsive load. This primary system is coupled to a lightweight, damped oscillating attachment (denoted as nonlinear energy sink, NES) via a neodymium magnet and an inductance coil, and a piano wire, which generates an essential geometric cubic stiffness nonlinearity. Under impulsive input, the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing intentional large-amplitude and high-frequency instabilities in the response of the NES. These TRCs result in strong energy transfer from the directly excited primary system to the light-weight attachment. The energy is harvested by the electromagnetic elements in the coupling and, in the present case, dissipated in a resistive element in the electrical circuit. The primary goal of this work is to numerically, analytically, and experimentally demonstrate the efficacy of employing this type of intentional high-frequency dynamic instability to achieve enhanced vibration energy harvesting under impulsive excitation.
Energy Technology Data Exchange (ETDEWEB)
Zhu, Z. W., E-mail: zhuzhiwen@tju.edu.cn [Department of Mechanics, Tianjin University, 300072, Tianjin (China); Tianjin Key Laboratory of Non-linear Dynamics and Chaos Control, 300072, Tianjin (China); Zhang, W. D., E-mail: zhangwenditju@126.com; Xu, J., E-mail: xujia-ld@163.com [Department of Mechanics, Tianjin University, 300072, Tianjin (China)
2014-03-15
The non-linear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF) subjected to in-plane stochastic excitation were studied. Non-linear differential items were introduced to interpret the hysteretic phenomena of the GMF, and the non-linear dynamic model of the GMF subjected to in-plane stochastic excitation was developed. The stochastic stability was analysed, and the probability density function was obtained. The condition of stochastic Hopf bifurcation and noise-induced chaotic response were determined, and the fractal boundary of the system's safe basin was provided. The reliability function was solved from the backward Kolmogorov equation, and an optimal control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that the system stability varies with the parameters, and stochastic Hopf bifurcation and chaos appear in the process; the area of the safe basin decreases when the noise intensifies, and the boundary of the safe basin becomes fractal; the system reliability improved through stochastic optimal control. Finally, the theoretical and numerical results were proved by experiments. The results are helpful in the engineering applications of GMF.
Fu, F.
2010-01-01
A 3-dimensional finite element model built by the author was used in this paper to analyze the progressive collapse of a multi-storey steel composite frame building. The proposed model can represent the global 3-D behavior of the multi-storey building under the sudden column removal scenarios. Based on this model, parametric studies were carried out to investigate the structural behavior with variations in: strength of structural steel, strength of concrete and reinforcement mesh size. Throug...
Steady states of the parametric rotator and pendulum
Energy Technology Data Exchange (ETDEWEB)
Bouzas, Antonio O, E-mail: abouzas@fis.mda.cinvestav.m [Departamento de Fisica Aplicada, CINVESTAV-IPN, Carretera Antigua a Progreso Km. 6, Apdo Postal 73 ' Cordemex' , Merida 97310, Yucatan (Mexico)
2010-11-15
We discuss several steady-state rotation and oscillation modes of the planar parametric rotator and pendulum with damping. We consider a general elliptic trajectory of the suspension point for both rotator and pendulum, for the latter at an arbitrary angle with gravity, with linear and circular trajectories as particular cases. We treat the damped, nonlinear equation of motion of the parametric rotator and pendulum perturbatively for small parametric excitation and damping, although our perturbative approach can be extended to other regimes as well. Our treatment involves only ordinary second-order differential equations with constant coefficients, and provides numerically accurate perturbative solutions in terms of elementary functions. Some of the steady-state rotation and oscillation modes studied here have not been discussed in the previous literature. Other well-known ones, such as parametric resonance and the inverted pendulum, are extended to elliptic parametric excitation tilted with respect to gravity. The results presented here should be accessible to advanced undergraduates, and of interest to graduate students and specialists in the field of nonlinear mechanics.
Constant, Thomas J; Hendry, Euan; Chang, Darrick E
2016-01-01
It has recently been demonstrated that difference frequency mixing (DFM) can generate surface plasmons in graphene [1]. Here, we present detailed calculations comparing the contributions to this effect from substrate and from graphene nonlinearities. Our calculations show that the substrate (quartz) nonlinearity gives rise to a surface plasmon intensity that is around twelve orders of magnitude smaller than that arising from the intrinsic graphene response. This surprisingly efficient intrinsic process, given the centrosymmetric structure of graphene, arises almost entirely due to non-local contributions to the second order optical nonlinearity of graphene.
Xu, Zhi-Jie
2015-01-01
We first propose fundamental solutions of wave propagation in dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain using stationary phase approximation. Solution is also compared with numerical results from molecular dynamics (MD) simulations. Locally dominant phonon modes (k-space) are introduced based on these solutions. These locally defined spatially and temporally varying phonon modes k(x, t) are critical to the concept of the local thermodynamic equilibrium (LTE). Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It is found that the system energy is gradually redistributed among these excited phonons modes (k-space). This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution. This time scale is dependent on the spatial distribution (or frequency content) of the initial perturbation and the dispersion relation. Sharper and more concentrated perturbation leads to a faster energy redistribution and dissipation. This energy redistribution generates localized phonons with various frequencies that can be important for phonon-phonon interaction and energy dissipation in nonlinear systems. Depending on the initial perturbation and temperature, the time scale associated with this energy distribution can be critical for energy dissipation compared to the Umklapp scattering process. Ballistic type of heat transport along the harmonic chain reveals that at any given position, the lowest mode (k = 0) is excited first and gradually expanding to the highest mode (kmax(x,t)), where kmax(x,t) can only asymptotically approach the maximum mode kB of the first Brillouin zone (kmax(x,t) → kB). No energy distributed into modes with kmax(x,t) proportional to the sound speed
DEFF Research Database (Denmark)
Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.
there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte Carlo......A method for computing the lower-order moments of randomly-excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random...
Kim, Kihong
2015-12-01
The Goos-Hänchen shift of p wave beams incident on a metal-nonlinear dielectric bilayer in the Kretschmann configuration is studied theoretically. The reflectance, the phase of the reflection coefficient and the Goos-Hänchen shift are calculated in a numerically precise manner by using the invariant imbedding method. The Goos-Hänchen shift has been found to be able to take both extremely large positive and negative values due to surface plasmon excitations and very strong bistability and unique hysteresis phenomena appear. In addition, several previous results on the intensity dependence of the Goos-Hänchen shift are pointed out to be erroneous.
Katsouleas, Thomas; Sahai, Aakash
2015-11-01
The excitation of a non-linear ion-wake by a train of non-linear electron wake of an electron and a positron beam is modeled and its use for positron acceleration is explored. The ion-wake is shown to be a driven non-linear ion-acoustic wave in the form of a cylindrical ion-soliton similar to the solution of the cKdV equation. The phases of the oscillating radial electric fields of the slowly-propagating electron wake are asymmetric in time and excite time-averaged inertial ion motion radially. The radial field of the electron compression region sucks-in the ions and the field of space-charge region of the wake expels them, driving a cylindrical ion-soliton structure with on-axis and bubble-edge density-spikes. Once formed, the channel-edge density-spike is driven radially outwards by the thermal pressure of the thermalized wake energy. Its channel-like structure due to the flat-residue left behind by the propagating ion-soliton, is independent of the energy-source driving the non-linear electron wake. We explore the use of the partially-filled channel formed by the cylindrical ion-soliton for a novel regime of positron acceleration. PIC simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration (arXiv:1504.03735). Work supported by the US Department of Energy under DE-SC0010012 and the National Science Foundation under NSF-PHY-0936278.
Coordinated nonlinear robust control of TCSC and excitation for multi-machine systems
Institute of Scientific and Technical Information of China (English)
Shengwei MEI; Juming CHEN; Qiang LU; Akihiko YOKOYAMA; Masuo GOTO
2004-01-01
An advanced nonlinear robust control scheme is proposed for multi-machine power systems equipped with thyristor-controlled series compensation (TCSC). First, a decentralized nonlinear robust control approach based on the feedback linearization and H∞ theory is introduced to eliminate the nonlinearities and interconnections of the studied system, and to attenuate the exogenous disturbances that enter the system. Then, a system model uilt up, which has considered all the generators' and TCSC's dynamics, and the effects of uncertainties such as disturbances. Next, a decentralized nonlinear robust coordinated control law is developed based on this model. Simulation results on a six-machine power system show that the transient stability of the power system is obviously improved and the power transfer capacity of long distance transmission lines is enhanced regardless of fault locahons and system operation points. In addition, the control law has engineering practicality since all the variables in the expression of he control strategy can be measured locally.
Energy Technology Data Exchange (ETDEWEB)
Sayyar-Rodsari, Bijan; Schweiger, Carl; Hartman, Eric
2007-10-07
The difficult problems being tackled in the accelerator community are those that are nonlinear, substantially unmodeled, and vary over time. Such problems are ideal candidates for model-based optimization and control if representative models of the problem can be developed that capture the necessary mathematical relations and remain valid throughout the operation region of the system, and through variations in system dynamics. The goal of this proposal is to develop the methodology and the algorithms for building high-fidelity mathematical representations of complex nonlinear systems via constrained training of combined first-principles and neural network models.
DEFF Research Database (Denmark)
Thomsen, Jon Juel
2006-01-01
Effects of strong high-frequency excitation at multiple frequencies (multi-HFE) are analyzed for a class of generally nonlinear systems. The effects are illustrated for a simple pendulum system with a vibrating support, and for a parametrically excited flexible beam. For the latter, theoretical...
DEFF Research Database (Denmark)
Peucheret, Christophe; Da Ros, Francesco; Vukovic, Dragana;
- compatible fabrication process, degrees of freedom in dispersion engineering, and high nonlinear coecient. However, the detrimental eect of free-carrier absorption induced by two-photon absorp- tion has so far prevented them from being used for the demonstration of phase-sensitive processing. Thanks...
A novel order reduction method for nonlinear dynamical system under external periodic excitations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The concept of approximate inertial manifold (AIM) is extended to develop a kind of nonlinear order reduction technique for non-autonomous nonlinear systems in second-order form in this paper.Using the modal transformation,a large nonlinear dynamical system is split into a ’master’ subsystem,a ’slave’ subsystem,and a ’negligible’ subsystem.Accordingly,a novel order reduction method (Method I) is developed to construct a low order subsystem by neglecting the ’negligible’ subsystem and slaving the ’slave’ subsystem into the ’master’ subsystem using the extended AIM.As a comparison,Method II accounting for the effects of both ’slave’ subsystem and the ’negligible’ subsystem is also applied to obtain the reduced order subsystem.Then,a typical 5-degree-of-freedom nonlinear dynamical system is given to compare the accuracy and efficiency of the traditional Galerkin truncation (ignoring the contributions of the slave and negligible subsystems),Method I and Method II.It is shown that Method I gives a considerable increase in accuracy for little computational cost in comparison with the standard Galerkin method,and produces almost the same accuracy as Method II.Finally,a 3-degree-of-freedom nonlinear dynamical system is analyzed by using the analytic method for showing predominance and convenience of Method I to obtain the analytically reduced order system.
Institute of Scientific and Technical Information of China (English)
杜正东
2004-01-01
The author considered the heteroclinic bifurcations and subharmonic orbits of parametrically excited Duffing system with quadratic damping using Melnikov method. And discussed the effect of the quadratic damping to the bifurcations.%利用Melnikov方法,讨论了带二次阻尼的参数激励Duffing系统的异宿分岔及次谐和轨道,以及二次阻尼项对分岔的影响.
DEFF Research Database (Denmark)
Rasmussen, Kim; Christiansen, Peter Leth; Johansson, Magnus
1998-01-01
A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech-like are exp......A one-dimensional discrete nonlinear Schrodinger (DNLS) model with the power dependence, r(-s) on the distance r, of dispersive interactions is proposed. The stationary states of the system are studied both analytically and numerically. Two kinds of trial functions, exp-like and sech...
Directory of Open Access Journals (Sweden)
H. M. Abdelhafez
2016-03-01
Full Text Available The modified differential transform method (MDTM, Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.
Directory of Open Access Journals (Sweden)
H. Bayıroğlu
2012-01-01
Full Text Available Vibrational conveyers with a centrifugal vibration exciter transmit their load based on the jumping method. Common unbalanced-mass driver oscillates the trough. The motion is strictly related to the vibrational parameters. The transition over resonance of a vibratory system, excited by rotating unbalances, is important in terms of the maximum vibrational amplitude produced and the power demand on the drive for the crossover. The mechanical system is driven by the DC motor. In this study, the working ranges of oscillating shaking conveyers with nonideal vibration exciter have been analyzed analytically for superharmonic and subharmonic resonances by the method of multiple scales and numerically. The analytical results obtained in this study agree well with the numerical results.
Passivity-Based Nonlinear Excitation Control of Power Systems with Structure Matrix Reassignment
Directory of Open Access Journals (Sweden)
Bing Chu
2013-08-01
Full Text Available Passivity-based control is widely used in electronic circuit systems because it can utilize their internal structures to facilitate the controller design. In this paper, we first propose a dissipative Hamiltonian realization of power systems and discuss the disadvantages of the traditional passivity-based excitation controller. Then, a novel excitation controller is put forward to reassign the interconnection and dissipative matrix, and the corresponding Hamiltonian function. Simulation results verify that the proposed controller can effectively improve the transient stability of the power system.
TBA equations for excited states in the O(3) and O(4) nonlinear $\\sigma$-model
Balog, J.; Hegedus, A
2003-01-01
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $\\sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $\\sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
Non-linear Springing Excitation Due to a Bidirectional Wave Field
DEFF Research Database (Denmark)
Vidic-Perunovic, Jelena; Jensen, Jørgen Juncher
2005-01-01
Significant springing vibrations in ships have recently been measured in a large ocean-going bulk carrier. So far calculations using various linear and non-linear hydrodynamic procedures have not been able to predict the measured responses. In the present paper it is shown that the springing...
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...
Yamaguchi, Maiku; Nobusada, Katsuyuki; Yatsui, Takashi
2015-10-01
Electron dynamics excited by an optical near field (ONF) in a two-dimensional quantum dot model was investigated by solving a time-dependent Schrödinger equation. It was found that the ONF excitation of the electron caused two characteristic phenomena: a two-photon absorption and an induction of a magnetic dipole moment with a strong third-harmonic component. By analyzing the interaction dynamics of the ONF and the electron, we explained that the physical mechanism underlying these phenomena was the second-harmonic electric-field component concomitant with the near-field excitation originating from the nonuniformity of the ONF. Despite a y -polarized ONF source, the second-harmonic component of an x -polarized electric field was inherently generated. The effect of the second-harmonic electric-field component is not due to usual second-order nonlinear response but appears only when we explicitly consider the electron dynamics interacting with the ONF beyond the conventional optical response assuming the dipole approximation.
Linear and nonlinear excitations in two stacks of parallel arrays of long Josephson junctions
DEFF Research Database (Denmark)
Carapella, G.; Constabile, Giovanni; Latempa, R.;
2000-01-01
We investigate a structure consisting of two parallel arrays of long Josephson junctions sharing a common electrode that allows inductive coupling between the arrays. A model for this structure is derived starting from the description of its continuous limit. The excitation of linear cavity modes...
Nonlinear Response of Localized Excitons: Effects of the Excitation-Induced Dephasing
DEFF Research Database (Denmark)
Borri, Paola; Langbein, Wolfgang Werner; Birkedal, Dan;
1997-01-01
. In particular, we show experimentally that the excitation-induced dephasing gives rise to a photon echo in inhomogeneous systems. We develop a simple analytical model for the delay dependence of the signal, which enables us to deduce the dephasing time from the four-wave mixing decay....
Intensity dependences of the nonlinear optical excitation of plasmons in graphene.
Constant, T J; Hornett, S M; Chang, D E; Hendry, E
2017-03-28
Recently, we demonstrated an all-optical coupling scheme for plasmons, which takes advantage of the intrinsic nonlinear optical response of graphene. Frequency mixing using free-space, visible light pulses generates surface plasmons in a planar graphene sample, where the phase matching condition can define both the wavevector and energy of surface waves and intraband transitions. Here, we also show that the plasmon generation process is strongly intensity-dependent, with resonance features washed out for absorbed pulse fluences greater than 0.1 J m(-2) This implies a subtle interplay between the nonlinear generation process and sample heating. We discuss these effects in terms of a non-equilibrium charge distribution using a two-temperature model.This article is part of the themed issue 'New horizons for nanophotonics'.
Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field
Institute of Scientific and Technical Information of China (English)
胡宇达; 张金志
2013-01-01
Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid-ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para-metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.
Saha, Asit
2017-03-01
Positron acoustic shock waves (PASHWs) in unmagnetized electron-positron-ion (e-p-i) plasmas consisting of mobile cold positrons, immobile positive ions, q-nonextensive distributed electrons, and hot positrons are studied. The cold positron kinematic viscosity is considered and the reductive perturbation technique is used to derive the Burgers equation. Applying traveling wave transformation, the Burgers equation is transformed to a one dimensional dynamical system. All possible vector fields corresponding to the dynamical system are presented. We have analyzed the dynamical system with the help of potential energy, which helps to identify the stability and instability of the equilibrium points. It is found that the viscous force acting on cold mobile positron fluid is a source of dissipation and is responsible for the formation of the PASHWs. Furthermore, fully nonlinear arbitrary amplitude positron acoustic waves are also studied applying the theory of planar dynamical systems. It is also observed that the fundamental features of the small amplitude and arbitrary amplitude PASHWs are significantly affected by the effect of the physical parameters q e , q h , μ e , μ h , σ , η , and U. This work can be useful to understand the qualitative changes in the dynamics of nonlinear small amplitude and fully nonlinear arbitrary amplitude PASHWs in solar wind, ionosphere, lower part of magnetosphere, and auroral acceleration regions.
Phase-locking phenomena and excitation of damped and driven nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Shagalov, A G [Institute of Metal Physics, Ekaterinburg 620041 (Russian Federation); Rasmussen, J Juul; Naulin, V [Risoe-DTU, Building 128, PO Box 49, DK-4000 Roskilde (Denmark)], E-mail: shagalov@imp.uran.ru, E-mail: jens.juul.rasmussen@risoe.dk, E-mail: volker.naulin@risoe.dk
2009-01-30
Resonant phase-locking phenomena ('autoresonance') in the van der Pol-Duffing oscillator forced by a small amplitude periodic driving with slowly varying frequency have been studied. We show that autoresonance occurs for oscillators with sufficiently small damping, when the system may have bi-stable states. We find the range of parameters of the oscillator, the thresholds and the appropriate control paths where autoresonant excitation of high amplitude oscillations is possible.
Phase-locking phenomena and excitation of damped and driven nonlinear oscillators
DEFF Research Database (Denmark)
Shagalov, A.G.; Juul Rasmussen, Jens; Naulin, Volker
2009-01-01
Resonant phase-locking phenomena ('autoresonance') in the van der Pol Duffing oscillator forced by a small amplitude periodic driving with slowly varying frequency have been studied. We show that autoresonance occurs for oscillators with sufficiently small damping, when the system may have bi......-stable states. We find the range of parameters of the oscillator, the thresholds and the appropriate control paths where autoresonant excitation of high amplitude oscillations is possible....
DEFF Research Database (Denmark)
Micaletti, R. C.; Cakmak, A. S.; Nielsen, Søren R. K.;
A method for computing the lower-order moments of randomly-excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random...... structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficient and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random...... initial conditions. This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases...
Tabi, C. B.; Motsumi, T. G.; Bansi Kamdem, C. D.; Mohamadou, A.
2017-08-01
A nonlinear model of blood flow in large vessels is addressed. The influence of radiations, viscosity and uniform magnetic fields on velocity and temperature distribution waveforms is studied. Exact solutions for the studied model are investigated through the F - expansion method. Based on the choice of parameter values, single-, multi-soliton and Jacobi elliptic function solutions are obtained. Viscosity and permanent magnetic field bring about wave spreading and reduce the velocity of blood, while radiations have reversed effects with strong impact on the waveform frequency of both the velocity and temperature distribution.
Multiple Frequency Parametric Sonar
2015-09-28
300003 1 MULTIPLE FREQUENCY PARAMETRIC SONAR STATEMENT OF GOVERNMENT INTEREST [0001] The invention described herein may be manufactured and...beams. However, the multiple nonlinear interactions are not taken advantage of in order to generate additional efficiencies, bandwidth, and SNR...array. [0050] It will be understood that many additional changes in details, materials , steps, and arrangements of parts which have been described
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Ali [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); Masood, W. [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad (Pakistan)
2016-05-15
Linear and nonlinear electrostatic ion acoustic waves in a weakly relativistic magnetorotating plasma in the presence of non-Maxwellian electrons and warm ions have been examined. The system under consideration has yielded two solutions, namely, the fast and slow acoustic modes which have been observed to depend on the streaming velocity, ion to electron temperature ratio, and the nonthermality parameter of the non-Maxwellian electrons. Using the multiple time scale analysis, we have derived the three dimensional nonlinear Zakharov–Kuznetsov equation and also presented its solution. Both compressive and rarefactive solitary structures have been found in consonance with the satellite observations. It has been observed that although the linear dispersion relation gives both fast and slow ion acoustic waves, the solitary structures form only for the fast acoustic mode. The dependence of the characteristics of the solitary structures on several plasma parameters has also been explored. The present investigation may be beneficial to understanding the rotating plasma environments such as those found in the planetary magnetospheres of Saturn and Jupiter.
Non-Linear Integral Equation and excited-states scaling functions in the sine-Gordon model
Destri, C
1997-01-01
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length L using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large L (perturbative) and small L (conformal) regimes as well as numerically. We derive the conformal weights of the Bethe states with holes and non-string complex roots (close and wide roots) in the UV limit. These weights agree with the Coulomb gas description, yielding a UV conformal spectrum related by duality to the IR conformal spectrum of the six vertex model.
Directory of Open Access Journals (Sweden)
Julie Vercelloni
Full Text Available Recently, attempts to improve decision making in species management have focussed on uncertainties associated with modelling temporal fluctuations in populations. Reducing model uncertainty is challenging; while larger samples improve estimation of species trajectories and reduce statistical errors, they typically amplify variability in observed trajectories. In particular, traditional modelling approaches aimed at estimating population trajectories usually do not account well for nonlinearities and uncertainties associated with multi-scale observations characteristic of large spatio-temporal surveys. We present a Bayesian semi-parametric hierarchical model for simultaneously quantifying uncertainties associated with model structure and parameters, and scale-specific variability over time. We estimate uncertainty across a four-tiered spatial hierarchy of coral cover from the Great Barrier Reef. Coral variability is well described; however, our results show that, in the absence of additional model specifications, conclusions regarding coral trajectories become highly uncertain when considering multiple reefs, suggesting that management should focus more at the scale of individual reefs. The approach presented facilitates the description and estimation of population trajectories and associated uncertainties when variability cannot be attributed to specific causes and origins. We argue that our model can unlock value contained in large-scale datasets, provide guidance for understanding sources of uncertainty, and support better informed decision making.
Vercelloni, Julie; Caley, M Julian; Kayal, Mohsen; Low-Choy, Samantha; Mengersen, Kerrie
2014-01-01
Recently, attempts to improve decision making in species management have focussed on uncertainties associated with modelling temporal fluctuations in populations. Reducing model uncertainty is challenging; while larger samples improve estimation of species trajectories and reduce statistical errors, they typically amplify variability in observed trajectories. In particular, traditional modelling approaches aimed at estimating population trajectories usually do not account well for nonlinearities and uncertainties associated with multi-scale observations characteristic of large spatio-temporal surveys. We present a Bayesian semi-parametric hierarchical model for simultaneously quantifying uncertainties associated with model structure and parameters, and scale-specific variability over time. We estimate uncertainty across a four-tiered spatial hierarchy of coral cover from the Great Barrier Reef. Coral variability is well described; however, our results show that, in the absence of additional model specifications, conclusions regarding coral trajectories become highly uncertain when considering multiple reefs, suggesting that management should focus more at the scale of individual reefs. The approach presented facilitates the description and estimation of population trajectories and associated uncertainties when variability cannot be attributed to specific causes and origins. We argue that our model can unlock value contained in large-scale datasets, provide guidance for understanding sources of uncertainty, and support better informed decision making.
Hide, Raymond
1997-02-01
This paper discusses the derivation of the autonomous sets of dimensionless nonlinear ordinary differential equations (ODE's) that govern the behaviour of a hierarchy of related electro-mechanical self-exciting Faraday-disk homopolar dynamo systems driven by steady mechanical couples. Each system comprises N interacting units which could be arranged in a ring or lattice. Within each unit and connected in parallel or in series with the coil are electric motors driven into motion by the dynamo, all having linear characteristics, so that nonlinearity arises entirely through the coupling between components. By introducing simple extra terms into the equations it is possible to represent biasing effects arising from impressed electromotive forces due to thermoelectric or chemical processes and from the presence of ambient magnetic fields. Dissipation in the system is due not only to ohmic heating but also to mechanical friction in the disk and the motors, with the latter agency, no matter how weak, playing an unexpectedly crucial rôle in the production of régimes of chaotic behaviour. This has already been demonstrated in recent work on a case of a single unit incorporating just one series motor, which is governed by a novel autonomous set of nonlinear ODE's with three time-dependent variables and four control parameters. It will be of mathematical as well as geophysical and astrophysical interest to investigate systematically phase and amplitude locking and other types of behaviour in the more complicated cases that arise when N > 1, which can typically involve up to 6 N dependent variables and 19 N-5 control parameters. Even the simplest members of the hierarchy, with N as low as 1, 2 or 3, could prove useful as physically-realistic low-dimensional models in theoretical studies of fluctuating stellar and planetary magnetic fields. Geomagnetic polarity reversals could be affected by the presence of the Earth's solid metallic inner core, driven like an electric motor
Small-amplitude excitations in a deformable discrete nonlinear Schrödinger equation
Konotop, V V
1996-01-01
A detailed analysis of the small-amplitude solutions of a deformed discrete nonlinear Schrödinger equation is performed. For generic deformations the system possesses "singular" points which split the infinite chain in a number of independent segments. We show that small-amplitude dark solitons in the vicinity of the singular points are described by the Toda-lattice equation while away from the singular points are described by the Korteweg-de Vries equation. Depending on the value of the deformation parameter and of the background level several kinds of solutions are possible. In particular we delimit the regions in the parameter space in which dark solitons are stable in contrast with regions in which bright pulses on nonzero background are possible. On the boundaries of these regions we find that shock waves and rapidly spreading solutions may exist.
Institute of Scientific and Technical Information of China (English)
陈予恕; 徐鉴
1996-01-01
The bifurcation of the second-order approximate solutions of nonlinear parametrically excited systems possessing generalized van der Pol’s dampings and quintic Duffing’s nonlinearities subjected to a primary parametric resonance is investigated. Using singularity theory with Z2-symmetry, bifurcations of the solutions are universally classified in a topologically equivalent sense for Z2-codimension>3. The question of whether the approximate solutions from the classical perturbation methods can be topologically equivalent in describing the periodic responses and the bifurcations of the original systems is made clear. The numerical results indicate that the vibration characteristic may suddenly disappear in the range of Z2-codimension>4.
Tongal, Hakan; Booij, Martijn J.
2016-01-01
A nonlinear stochastic self-exciting threshold autoregressive (SETAR) model and a chaotic k-nearest neighbour (k-nn) model, for the first time, were compared in one and multi-step ahead daily flow forecasting for nine rivers with low, medium, and high flows in the western United States. The
Kondrashov, A. V.; Ustinov, A. B.; Kalinikos, B. A.; Demokritov, S. O.
2016-11-01
This paper reports the first experimental study of broadband chaotic nonlinear spin- wave excitations which is formed through development of four-wave parametric processes in active ring oscillator based on metallized ferrite film. We find that an increase in the oscillation power leads to Hopf bifurcations sequence. Monochromatic, periodic quasi-periodic and chaotic excitations are observed. Spectra of the chaotic excitations consist of series of chaotic bands separated well in frequency. Parameters of the chaotic attractors are discussed.
Nonlinear Vibration Analysis for a Jeffcott Rotor with Seal and Air-Film Bearing Excitations
Directory of Open Access Journals (Sweden)
Yuefang Wang
2010-01-01
Full Text Available The nonlinear coupling vibration and bifurcation of a high-speed centrifugal compressor with a labyrinth seal and two air-film journal bearings are presented in this paper. The rotary shaft and disk are modeled as a rigid Jeffcott rotor. Muszynska's model is used to express the seal force with multiple parameters. For air-film journal bearings, the model proposed by Zhang et al. is adopted to express unsteady bearing forces. The Runge-Kutta method is used to numerically determine the vibration responses of the disk center and the bearings. Bifurcation diagrams for transverse motion of the rotor are presented with parameters of rotation speed and pressure drop of the seal. Multiple subharmonic, periodic, and quasiperiodic motions are presented with two seal-pressure drops. The bifurcation characteristics show inherent interactions between forces of the air-film bearings and the seal, presenting more complicated rotor dynamics than the one with either of the forces alone. Bifurcation diagrams are obtained with parameters of pressure drop and seal length determined for the sake of operation safety.
Nonlinear excitations for the positron acoustic waves in auroral acceleration regions
Saha, Asit; Ali, Rustam; Chatterjee, Prasanta
2017-09-01
Positron acoustic waves (PAWs) in an unmagnetized electron-positron-ion (e-p-i) plasma consisting of mobile cold positrons, immobile positive ions, q-nonextensive distributed electrons and hot positrons are studied. The standard reductive perturbation technique (RPT) is applied to derive the Kurteweg-de Vries (KdV) and modified Kurteweg-de Vries (mKdV) equations for PAWs. Variations of the total energy of the conservative systems corresponding to the KdV and mKdV equations are presented. Using numerical simulations, effect of the nonextensive parameter (q), temperature ratio (σ) of electrons to hot positrons and speed (U) of the traveling wave are discussed on the positron acoustic solitary wave solutions of the KdV and mKdV equations. Considering an external periodic perturbation, the perturbed dynamical systems corresponding to the KdV and mKdV equations are analyzed by employing phase orbit analysis, Poincare section and Lyapunov exponent. The frequency (ω) of the external periodic perturbation plays the role of the switching parameter in chaotic motions of the perturbed PAWs through quasiperiodic route to chaos. This work may be useful to understand the qualitative changes in the dynamics of nonlinear perturbations in auroral acceleration regions.
Yan, Guiyun; Chen, Fuquan; Wu, Yingxiong
2016-01-01
Different from previous researches which mostly focused on linear response control of seismically excited high-rise buildings, this study aims to control nonlinear seismic response of high-rise buildings. To this end, a semi-active control strategy, in which H∞ control algorithm is used and magneto-rheological dampers are employed for an actuator, is presented to suppress the nonlinear vibration. In this strategy, a modified Kalman-Bucy observer which is suitable for the proposed semi-active strategy is developed to obtain the state vector from the measured semi-active control force and acceleration feedback, taking into account of the effects of nonlinearity, disturbance and uncertainty of controlled system parameters by the observed nonlinear accelerations. Then, the proposed semi-active H∞ control strategy is applied to the ASCE 20-story benchmark building when subjected to earthquake excitation and compared with the other control approaches by some control criteria. It is indicated that the proposed semi-active H∞ control strategy provides much better control performances by comparison with the semi-active MPC and Clipped-LQG control approaches, and can reduce nonlinear seismic response and minimize the damage in the buildings. Besides, it enhances the reliability of the control performance when compared with the active control strategy. Thus, the proposed semi-active H∞ control strategy is suitable for suppressing the nonlinear vibration of high-rise buildings.
Nonlinear saturation of wave packets excited by low-energy electron horseshoe distributions.
Krafft, C; Volokitin, A
2013-05-01
Horseshoe distributions are shell-like particle distributions that can arise in space and laboratory plasmas when particle beams propagate into increasing magnetic fields. The present paper studies the stability and the dynamics of wave packets interacting resonantly with electrons presenting low-energy horseshoe or shell-type velocity distributions in a magnetized plasma. The linear instability growth rates are determined as a function of the ratio of the plasma to the cyclotron frequencies, of the velocity and the opening angle of the horseshoe, and of the relative thickness of the shell. The nonlinear stage of the instability is investigated numerically using a symplectic code based on a three-dimensional Hamiltonian model. Simulation results show that the dynamics of the system is mainly governed by wave-particle interactions at Landau and normal cyclotron resonances and that the high-order normal cyclotron resonances play an essential role. Specific features of the dynamics of particles interacting simultaneously with two or more waves at resonances of different natures and orders are discussed, showing that such complex processes determine the main characteristics of the wave spectrum's evolution. Simulations with wave packets presenting quasicontinuous spectra provide a full picture of the relaxation of the horseshoe distribution, revealing two main phases of the evolution: an initial stage of wave energy growth, characterized by a fast filling of the shell, and a second phase of slow damping of the wave energy, accompanied by final adjustments of the electron distribution. The influence of the density inhomogeneity along the horseshoe on the wave-particle dynamics is also discussed.
Energy Technology Data Exchange (ETDEWEB)
Sahai, A. A.; Katsouleas, T. C.; Gessner, S.; Hogan, M.; Joshi, C.; Mori, W. B. [Electrical and Computer Engineering, Duke University, Durham, NC 27708 (United States); SLAC National Accelerator Laboratory, Menlo Park, CA 90309 (United States); University of California Los Angeles, Los Angeles, CA 90095 (United States)
2012-12-21
We study the various physical processes and their timescales involved in the excitation of wakefields in relativistically hot plasma. This has relevance to the design of a high repetition-rate plasma wakefield collider in which the plasma has not had time to cool between bunches in addition to understanding the physics of cosmic jets in relativistically hot astrophysical plasmas. When the plasma is relativistically hot (plasma temperature near m{sub e}c{sup 2}), the thermal pressure competes with the restoring force of ion space charge and can reduce or even eliminate the accelerating field of a wake. We will investigate explicitly the case where the hot plasma is created by a preceding Wakefield drive bunch 10's of picoseconds to many nanoseconds ahead of the next drive bunch. The relativistically hot plasma is created when the excess energy (not coupled to the driven e{sup -} bunch) in the wake driven by the drive e{sup -} bunch is eventually converted into thermal energy on 10's of picosecond timescale. We will investigate the thermalization and diffusion processes of this non-equilibrium plasma on longer time scales, including the effects of ambi-polar diffusion of ions driven by hot electron expansion, possible Columbic explosion of ions producing higher ionization states and ionization of surrounding neutral atoms via collisions with hot electrons. Preliminary results of the transverse and longitudinal wakefields at different timescales of separation between a first and second bunch are presented and a possible experiment to study this topic at the FACET facility is described.
Directory of Open Access Journals (Sweden)
Syed Hamad
2015-12-01
Full Text Available We report results from our studies on the fabrication and characterization of silicon (Si nanoparticles (NPs and nanostructures (NSs achieved through the ablation of Si target in four different liquids using ∼2 picosecond (ps pulses. The consequence of using different liquid media on the ablation of Si target was investigated by studying the surface morphology along with material composition of Si based NPs. The recorded mean sizes of these NPs were ∼9.5 nm, ∼37 nm, ∼45 nm and ∼42 nm obtained in acetone, water, dichloromethane (DCM and chloroform, respectively. The generated NPs were characterized by selected area electron diffraction (SAED, high resolution transmission microscopy (HRTEM, Raman spectroscopic techniques and Photoluminescence (PL studies. SAED, HRTEM and Raman spectroscopy data confirmed that the material composition was Si NPs in acetone, Si/SiO2 NPs in water, Si-C NPs in DCM and Si-C NPs in chloroform and all of them were confirmed to be polycrystalline in nature. Surface morphological information of the fabricated Si substrates was obtained using the field emission scanning electron microscopic (FESEM technique. FESEM data revealed the formation of laser induced periodic surface structures (LIPSS for the case of ablation in acetone and water while random NSs were observed for the case of ablation in DCM and chloroform. Femtosecond (fs nonlinear optical properties and excited state dynamics of these colloidal Si NPs were investigated using the Z-scan and pump-probe techniques with ∼150 fs (100 MHz and ∼70 fs (1 kHz laser pulses, respectively. The fs pump-probe data obtained at 600 nm consisted of single and double exponential decays which were tentatively assigned to electron-electron collisional relaxation (1 ps. Large third order optical nonlinearities (∼10−14 e.s.u. for these colloids have been estimated from Z-scan data at an excitation wavelength of 680 nm suggesting that the colloidal Si NPs find
Energy Technology Data Exchange (ETDEWEB)
Hamad, Syed; Nageswara Rao, S. V. S.; Pathak, A. P. [School of Physics, University of Hyderabad, Hyderabad 500046, Telangana (India); Krishna Podagatlapalli, G.; Mounika, R.; Venugopal Rao, S., E-mail: soma-venu@yahoo.com, E-mail: soma-venu@uohyd.ac.in [Advanced Center of Research in High Energy Materials (ACRHEM), University of Hyderabad, Hyderabad 500046, Telangana (India)
2015-12-15
We report results from our studies on the fabrication and characterization of silicon (Si) nanoparticles (NPs) and nanostructures (NSs) achieved through the ablation of Si target in four different liquids using ∼2 picosecond (ps) pulses. The consequence of using different liquid media on the ablation of Si target was investigated by studying the surface morphology along with material composition of Si based NPs. The recorded mean sizes of these NPs were ∼9.5 nm, ∼37 nm, ∼45 nm and ∼42 nm obtained in acetone, water, dichloromethane (DCM) and chloroform, respectively. The generated NPs were characterized by selected area electron diffraction (SAED), high resolution transmission microscopy (HRTEM), Raman spectroscopic techniques and Photoluminescence (PL) studies. SAED, HRTEM and Raman spectroscopy data confirmed that the material composition was Si NPs in acetone, Si/SiO{sub 2} NPs in water, Si-C NPs in DCM and Si-C NPs in chloroform and all of them were confirmed to be polycrystalline in nature. Surface morphological information of the fabricated Si substrates was obtained using the field emission scanning electron microscopic (FESEM) technique. FESEM data revealed the formation of laser induced periodic surface structures (LIPSS) for the case of ablation in acetone and water while random NSs were observed for the case of ablation in DCM and chloroform. Femtosecond (fs) nonlinear optical properties and excited state dynamics of these colloidal Si NPs were investigated using the Z-scan and pump-probe techniques with ∼150 fs (100 MHz) and ∼70 fs (1 kHz) laser pulses, respectively. The fs pump-probe data obtained at 600 nm consisted of single and double exponential decays which were tentatively assigned to electron-electron collisional relaxation (<1 ps) and non-radiative transitions (>1 ps). Large third order optical nonlinearities (∼10{sup −14} e.s.u.) for these colloids have been estimated from Z-scan data at an excitation wavelength of 680 nm
Hamad, Syed; Krishna Podagatlapalli, G.; Mounika, R.; Nageswara Rao, S. V. S.; Pathak, A. P.; Venugopal Rao, S.
2015-12-01
We report results from our studies on the fabrication and characterization of silicon (Si) nanoparticles (NPs) and nanostructures (NSs) achieved through the ablation of Si target in four different liquids using ˜2 picosecond (ps) pulses. The consequence of using different liquid media on the ablation of Si target was investigated by studying the surface morphology along with material composition of Si based NPs. The recorded mean sizes of these NPs were ˜9.5 nm, ˜37 nm, ˜45 nm and ˜42 nm obtained in acetone, water, dichloromethane (DCM) and chloroform, respectively. The generated NPs were characterized by selected area electron diffraction (SAED), high resolution transmission microscopy (HRTEM), Raman spectroscopic techniques and Photoluminescence (PL) studies. SAED, HRTEM and Raman spectroscopy data confirmed that the material composition was Si NPs in acetone, Si/SiO2 NPs in water, Si-C NPs in DCM and Si-C NPs in chloroform and all of them were confirmed to be polycrystalline in nature. Surface morphological information of the fabricated Si substrates was obtained using the field emission scanning electron microscopic (FESEM) technique. FESEM data revealed the formation of laser induced periodic surface structures (LIPSS) for the case of ablation in acetone and water while random NSs were observed for the case of ablation in DCM and chloroform. Femtosecond (fs) nonlinear optical properties and excited state dynamics of these colloidal Si NPs were investigated using the Z-scan and pump-probe techniques with ˜150 fs (100 MHz) and ˜70 fs (1 kHz) laser pulses, respectively. The fs pump-probe data obtained at 600 nm consisted of single and double exponential decays which were tentatively assigned to electron-electron collisional relaxation (1 ps). Large third order optical nonlinearities (˜10-14 e.s.u.) for these colloids have been estimated from Z-scan data at an excitation wavelength of 680 nm suggesting that the colloidal Si NPs find potential applications
Li, Wei; Tang, Yougang; Liu, Liqin; Liu, Shuxiao; Cai, Runbo
2017-04-01
Many studies have been done on the heave-pitch unstable coupling response for a spar platform by a 2-DOF model. In fact, in addition to the heave and pitch which are in one plane, the nonlinear unstable motion will also occur in roll. From the results of the experiments, the unstable roll motion plays a dominant role in the motion of a spar platform which is much stronger than that of pitch. The objective of this paper is to study 3-DOF coupling response performance of spar platform under wave and vortex-induced force. The nonlinear coupled equations in heave, roll and pitch are established by considering time-varying wet surface and coupling. The first order steady-state response is solved by multi-scales method when the incident wave frequency approaches the heave natural frequency. Numerical integration of the motion equations has been performed to verify the first-order perturbation solution. The results are confirmed by model test. There is a saturation phenomenon associated with heave mode in 3-DOF systems and all extra energy is transferred to roll and pitch. It is observed that sub-harmonic response occurs in roll and pitch when the wave force exceeds a certain value. The energy distribution in roll and pitch is determined by the initial value and damping characteristics of roll and pitch. The energy transfers from heave to pitch and then transfers from pitch to roll. Due to the influence of the low-frequency vortex-excited force, the response of roll is more complicated than that of pitch.
Shortell, Matthew P; Jaatinen, Esa A; Chang, Jin; Waclawik, Eric R
2014-03-24
We report a new approach that uses the single beam Z-scan technique, to discriminate between excited state absorption (ESA) and two and three photon nonlinear absorption. By measuring the apparent delay or advance of the pulse in reaching the detector, the nonlinear absorption can be unambiguously identified as either instantaneous or transient. The simple method does not require a large range of input fluences or sophisticated pulse-probe experimental apparatus. The technique is easily extended to any absorption process dependent on pulse width and to nonlinear refraction measurements. We demonstrate in particular, that the large nonlinear absorption in ZnO nanocones when exposed to nanosecond 532 nm pulses, is due mostly to ESA, not pure two-photon absorption.
Energy Technology Data Exchange (ETDEWEB)
Debut, V.; Antunes, J. [ITN, ADL, P-2686 Sacavem Codex (Portugal); Delaune, X. [CEA Saclay, DEN, DM2S, SEMT, Lab Etud Dynam, F-01101 Gif Sur Yvette (France)
2010-07-01
For achieving realistic numerical simulations of bowed string instruments, based on physical modeling, a good understanding of the actual friction interaction phenomena is of great importance. Most work published in the field including our own has assumed that bow/string frictional forces behave according to the classical Coulomb stick-slip model, with an empirical velocity-dependent sliding friction coefficient. Indeed, the basic self-excited string motions (such as the Helmholtz regime) are well captured using such friction model. However, recent work has shown that the tribological behavior of the bow/string rosin interface is rather complex, therefore the basic velocity-dependent Coulomb model may be an over-simplistic representation of the friction force. More specifically, it was suggested that a more accurate model of the interaction force can be achieved by coupling the system dynamical equations with a thermal model which encapsulates the complex interface phenomena. In spite of the interesting work performed by Askenfelt, a direct measurement of the actual dynamical friction forces without disturbing the string motion is quite difficult. Therefore, in this work we develop a modal-based identification technique making use of inverse methods and optimization techniques, which enables the identification of the interface force, as well as the string self-excited motion, from the dynamical reactions measured at the string end supports. The method gives convincing results using simulated data originated from nonlinear computations of a bowed string. Furthermore, in cases where the force identifications are very sensitive to errors in the transfer function modal parameters, we suggest a method to improve the modal frequencies used for the identifications. Preliminary experimental results obtained using a basic bowing device, by which the string is excited with the stick of the bow, are then presented. Our identifications, from the two dynamical string reactions
Haiwu, Rong; Wang, Xiangdong; Xu, Wei; Fang, Tong
2009-08-01
The subharmonic response of single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to narrow-band random excitation is investigated. The narrow-band random excitation used here is a filtered Gaussian white noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of asymptotic averaging over the "fast" variables. The averaged stochastic equations are solved exactly by the method of moments for the mean-square response amplitude for the case of linear system with zero offset. A perturbation-based moment closure scheme is proposed and the formula of the mean-square amplitude is obtained approximately for the case of linear system with nonzero offset. The perturbation-based moment closure scheme is used once again to obtain the algebra equation of the mean-square amplitude of the response for the case of nonlinear system. The effects of damping, detuning, nonlinear intensity, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detunings or large nonlinear intensity.
Nonlinear Response Analysis of Bridges Under Multi-support Excitation%桥梁在多点激振下的非线性响应
Institute of Scientific and Technical Information of China (English)
郭咏辉; 贺国京
2000-01-01
In the nonlinear respondense analysis of bridges under multi-support excitation ,theeffect matrix and Wilson-θ method are used. A corresponding program is given,which cananalyze the nonlinear or linear respondense under multi-support excitation and the nonlinearor linear respondence under consistent excitation. The results of.numerical test compares thefour cases. It can be concluded that the nonlinear and multi-support excitation affect greatlyon the respondense of bridge. This can't be ignored%用影响矩阵考虑了桥梁在多点激振下的非线性地震响应，并利用Wilsom-θ法编制了相应的程序．该程序可用来计算非一致输入下的线性或非线性响应和一致输入下的线性或非线性响应．通过算例对以上四种情况进行了比较，结果表明多点激振效应和非线性作用对结构动力响应均有较大影响，不容忽视
Third Conference on nonlinear science and complexity (NSC)
Machado, José; Baleanu, Dumitru; Dynamical Systems and Methods
2012-01-01
Nonlinear Systems and Methods For Mechanical, Electrical and Biosystems presents topics observed at the 3rd Conference on Nonlinear Science and Complexity(NSC), focusing on energy transfer and synchronization in hybrid nonlinear systems. The studies focus on fundamental theories and principles,analytical and symbolic approaches, computational techniques in nonlinear physical science and mathematics. Broken into three parts, the text covers:\\ Parametrical excited pendulum, nonlinear dynamics in hybrid systems, dynamical system synchronization and (N+1) body dynamics as well as new views different from the existing results in nonlinear dynamics. Mathematical methods for dynamical systems including conservation laws, dynamical symmetry in nonlinear differential equations and invex energies. Nonlinear phenomena in physical problems such as solutions, complex flows, chemical kinetics, Toda lattices and parallel manipulator. This book is useful to scholars, researchers and advanced technical members of industrial l...
Parametric dispersion and amplification of acoustohelicon waves in piezoelectric semiconductors
Neogi, A.; Ghosh, S.
1991-01-01
Assuming that the origin of the nonlinear interaction lies in the second-order optical susceptibility arising from the nonlinear induced current density and using the coupled-mode theory, the parametric dispersion and amplification of acoustohelicon waves is analytically investigated in a longitudinally magnetized piezoelectric semiconductor of noncentrosymmetric nature. The relevant experiments have not been reported. The threshold value of the pump electric field E0th and its corresponding excitation intensity is obtained. The longitudinal magnetic field decreases the required magnitude of E0th for the excitation of parametric amplification. The phenomenon of self-defocusing of the signal in the prevailing case is found to be a consequence of the negative dispersive characteristics exhibited by the acoustohelicon waves. Numerical analyses are performed for an InSb crystal at 77 K, duly irradiated by frequency-doubled pulsed 10.6-μm CO2 lasers. The parametric gain constant is observed to be maximum when the cyclotron frequency ωc attains the magnitude equal to that of ω0, the incident laser frequency (=1.78×1014 s-1 ).
Chen, G; Chen, J; Zhuo, S; Xiong, S; Zeng, H; Jiang, X; Chen, R; Xie, S
2009-07-01
A noninvasive method using microscopy and spectroscopy for analysing the morphology of collagen and elastin and their biochemical variations in skin tissue will enable better understanding of the pathophysiology of hypertrophic scars and facilitate improved clinical management and treatment of this disease. To obtain simultaneously microscopic images and spectra of collagen and elastin fibres in ex vivo skin tissues (normal skin and hypertrophic scar) using a nonlinear spectral imaging method, and to compare the morphological structure and spectral characteristics of collagen and elastin fibres in hypertrophic scar tissues with those of normal skin, to determine whether this approach has potential for in vivo assessment of the pathophysiology of human hypertrophic scars and for monitoring treatment responses as well as for tracking the process of development of hypertrophic scars in clinic. Ex vivo human skin specimens obtained from six patients aged from 10 to 50 years old who were undergoing skin plastic surgery were examined. Five patients had hypertrophic scar lesions and one patient had no scar lesion before we obtained his skin specimen. A total of 30 tissue section samples of 30 mum thickness were analysed by the use of a nonlinear spectral imaging system consisting of a femtosecond excitation light source, a high-throughput scanning inverted microscope, and a spectral imaging detection system. The high-contrast and high-resolution second harmonic generation (SHG) images of collagen and two-photon excited fluorescence (TPEF) images of elastin fibres in hypertrophic scar tissues and normal skin were acquired using the extracting channel tool of the system. The emission spectra were analysed using the image-guided spectral analysis method. The depth-dependent decay constant of the SHG signal and the image texture characteristics of hypertrophic scar tissue and normal skin were used to quantitatively assess the amount, distribution and orientation of their
The influence of and the identification of nonlinearity in flexible structures
Zavodney, Lawrence D.
1988-01-01
Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.
Energy Technology Data Exchange (ETDEWEB)
Goto, T. [Tohoku University, Sendai (Japan)
1996-08-20
Investigations were given on nanocrystals of CuCl and CdTe with regard to their nonlinear optical mechanism. The experiment used a femto-second pump probe spectroscope. The experiment on CuCl nanocrystals revealed the following facts: in the case where one photon is absorbed into one nanocrystal, cascade mitigation occurs to the pair of electrons and holes, and exciters; and in the case where two photons are absorbed into one nanocrystal, exciter molecules are made via the pair of electrons and holes and the exciters. Thus, it was found that the optical nonlinearity occurs when more than two photons are absorbed into one nanocrystal, and inter-exciter interactions and formation of the exciter molecules are the physical causes thereof. The experiment on CdTe nanocrystals indicated that electrons and holes produced by laser beam are distributed instantaneously between the size-quantized discrete levels, and that temperature in the electron system drops with lapse of time. 9 refs., 6 figs.
Braun, David J.; Sutas, Andrius; Vijayakumar, Sethu
2017-01-01
Theory predicts that parametrically excited oscillators, tuned to operate under resonant condition, are capable of large-amplitude oscillation useful in diverse applications, such as signal amplification, communication, and analog computation. However, due to amplitude saturation caused by nonlinearity, lack of robustness to model uncertainty, and limited sensitivity to parameter modulation, these oscillators require fine-tuning and strong modulation to generate robust large-amplitude oscillation. Here we present a principle of self-tuning parametric feedback excitation that alleviates the above-mentioned limitations. This is achieved using a minimalistic control implementation that performs (i) self-tuning (slow parameter adaptation) and (ii) feedback pumping (fast parameter modulation), without sophisticated signal processing past observations. The proposed approach provides near-optimal amplitude maximization without requiring model-based control computation, previously perceived inevitable to implement optimal control principles in practical application. Experimental implementation of the theory shows that the oscillator self-tunes itself near to the onset of dynamic bifurcation to achieve extreme sensitivity to small resonant parametric perturbations. As a result, it achieves large-amplitude oscillations by capitalizing on the effect of nonlinearity, despite substantial model uncertainties and strong unforeseen external perturbations. We envision the present finding to provide an effective and robust approach to parametric excitation when it comes to real-world application.
Energy Technology Data Exchange (ETDEWEB)
Maxein, Karl Dominik
2009-12-15
Lithium niobate (LiNbO{sub 3}) is a widely employed material in nonlinear optics and photonics. Its usage is hampered by the photorefractive effect, which can destroy beam profiles and phase matching conditions. Existing methods to suppress photorefraction fail for the interesting regime of very high intensities and short pulses. Therefore, the photorefractive effect is investigated using femtosecond laser pulses: By utilizing so-called 2K holography, the occupation of energetically shallow traps is observed to occur in less than 100 fs after a two-photon excitation. Writing of photorefractive gratings into oxidized iron-doped LiNbO{sub 3} is much faster with pulses than with cw light. This is explained by the sensitization of the crystal due to charge trapping in photorefractive centers after nonlinear excitations. Finally, light-induced scattering of pulse light is suppressed compared to the scattering of cw light due to the small coherence length of pulses. (orig.)
Quantum nonlinear optics without photons
Stassi, Roberto; Macrı, Vincenzo; Kockum, Anton Frisk; Di Stefano, Omar; Miranowicz, Adam; Savasta, Salvatore; Nori, Franco
2017-08-01
Spontaneous parametric down-conversion is a well-known process in quantum nonlinear optics in which a photon incident on a nonlinear crystal spontaneously splits into two photons. Here we propose an analogous physical process where one excited atom directly transfers its excitation to a pair of spatially separated atoms with probability approaching 1. The interaction is mediated by the exchange of virtual rather than real photons. This nonlinear atomic process is coherent and reversible, so the pair of excited atoms can transfer the excitation back to the first one: the atomic analog of sum-frequency generation of light. The parameters used to investigate this process correspond to experimentally demonstrated values in ultrastrong circuit quantum electrodynamics. This approach can be extended to realize other nonlinear interatomic processes, such as four-atom mixing, and is an attractive architecture for the realization of quantum devices on a chip. We show that four-qubit mixing can efficiently implement quantum repetition codes and, thus, can be used for error-correction codes.
Excitation of kinetic geodesic acoustic modes by drift waves in nonuniform plasmas
Energy Technology Data Exchange (ETDEWEB)
Qiu, Z. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Chen, L. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Dept. Physics and Astronomy, Univ. of California, Irvine, California 92697-4575 (United States); Zonca, F. [Inst. Fusion Theory and Simulation, Zhejiang Univ., Hangzhou 310027 (China); Associazione Euratom-ENEA sulla Fusione, C.P. 65 - I-00044 - Frascati (Italy)
2014-02-15
Effects of system nonuniformities and kinetic dispersiveness on the spontaneous excitation of Geodesic Acoustic Mode (GAM) by Drift Wave (DW) turbulence are investigated based on nonlinear gyrokinetic theory. The coupled nonlinear equations describing parametric decay of DW into GAM and DW lower sideband are derived and then solved both analytically and numerically to investigate the effects on the parametric decay process due to system nonuniformities, such as nonuniform diamagnetic frequency, finite radial envelope of DW pump, and kinetic dispersiveness. It is found that the parametric decay process is a convective instability for typical tokamak parameters when finite group velocities of DW and GAM associated with kinetic dispersiveness and finite radial envelope are taken into account. When, however, nonuniformity of diamagnetic frequency is taken into account, the parametric decay process becomes, time asymptotically, a quasi-exponentially growing absolute instability.
Institute of Scientific and Technical Information of China (English)
张瑞成; 王佩佩
2013-01-01
在考虑轧机电气系统谐波转矩及机械摩擦因数的基础上，建立直流电动机-轧机主传动机电耦合系统的模型。采用多尺度法求解该机电耦合模型在主参数共振情况下的一阶近似解，给出了振子的频率响应方程，用数值方法研究了定常解的稳定性，并应用Poincare映射方法和最大Lyapunov指数分析了谐波角频率对轧机主传动机电耦合系统非线性参激共振的影响。%The electromechanical coupling model of a rolling mill and DC motor system is established based on the mechanical friction factor and the harmonic torque of the rolling mill electrical system .By means of a multiple-scales method,the existence and stability of periodic solutions in a first order approximation close to the main parametric resonance are investigated ,and the frequency-response equation is provided .Bifurcations of the system and regions of chaotic solutions are found .And the impacts of the harmonic angular frequency on the rolling mill electromechanical coupling nonlinear parametric excitation resonance are ana -lyzed by the Poincare mapping method and the maximum Lyapunov exponent .
Biggs, Jason D
2009-01-01
The preceding paper describes a strategy for externally influencing the course of short-time electronic excitation transfer (EET) in molecular dimers and observing the process by nonlinear wave-packet interferometry (nl-WPI). Within a sample of isotropically oriented dimers having a specified internal geometry, a vibrational mode internal to the acceptor chromophore can be preferentially driven by electronically nonresonant impulsive stimulated Raman (or resonant infrared) excitation with a short polarized control pulse. A subsequent electronically resonant polarized pump then preferentially excites the donor, and EET ensues. Here we test both the control strategy and its spectroscopic investigation-with some sacrifice of amplitude-level detail-by calculating the pump-probe difference signal. That signal is the limiting case of the control-influenced nl-WPI signal in which the two pulses in the pump pulse-pair coincide, as do the two pulses in the probe pulse-pair. We present calculated pump-probe difference ...
Design of a nonlinear torsional vibration absorber
Tahir, Ammaar Bin
larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.
Song, Dong; Wang, Zhuo; Marmarelis, Vasilis Z; Berger, Theodore W
2009-02-01
This paper presents a synergistic parametric and non-parametric modeling study of short-term plasticity (STP) in the Schaffer collateral to hippocampal CA1 pyramidal neuron (SC) synapse. Parametric models in the form of sets of differential and algebraic equations have been proposed on the basis of the current understanding of biological mechanisms active within the system. Non-parametric Poisson-Volterra models are obtained herein from broadband experimental input-output data. The non-parametric model is shown to provide better prediction of the experimental output than a parametric model with a single set of facilitation/depression (FD) process. The parametric model is then validated in terms of its input-output transformational properties using the non-parametric model since the latter constitutes a canonical and more complete representation of the synaptic nonlinear dynamics. Furthermore, discrepancies between the experimentally-derived non-parametric model and the equivalent non-parametric model of the parametric model suggest the presence of multiple FD processes in the SC synapses. Inclusion of an additional set of FD process in the parametric model makes it replicate better the characteristics of the experimentally-derived non-parametric model. This improved parametric model in turn provides the requisite biological interpretability that the non-parametric model lacks.
Jacobi elliptic functions: A review of nonlinear oscillatory application problems
Kovacic, Ivana; Cveticanin, Livija; Zukovic, Miodrag; Rakaric, Zvonko
2016-10-01
This review paper is concerned with the applications of Jacobi elliptic functions to nonlinear oscillators whose restoring force has a monomial or binomial form that involves cubic and/or quadratic nonlinearity. First, geometric interpretations of three basic Jacobi elliptic functions are given and their characteristics are discussed. It is shown then how their different forms can be utilized to express exact solutions for the response of certain free conservative oscillators. These forms are subsequently used as a starting point for a presentation of different quantitative techniques for obtaining an approximate response for free perturbed nonlinear oscillators. An illustrative example is provided. Further, two types of externally forced nonlinear oscillators are reviewed: (i) those that are excited by elliptic-type excitations with different exact and approximate solutions; (ii) those that are damped and excited by harmonic excitations, but their approximate response is expressed in terms of Jacobi elliptic functions. Characteristics of the steady-state response are discussed and certain qualitative differences with respect to the classical Duffing oscillator excited harmonically are pointed out. Parametric oscillations of the oscillators excited by an elliptic-type forcing are considered as well, and the differences with respect to the stability chart of the classical Mathieu equation are emphasized. The adjustment of the Melnikov method to derive the general condition for the onset of homoclinic bifurcations in a system parametrically excited by an elliptic-type forcing is provided and compared with those corresponding to harmonic excitations. Advantages and disadvantages of the use of Jacobi elliptic functions in nonlinear oscillatory application problems are discussed and some suggestions for future work are given.
Enhanced parametric processes in binary metamaterials
Gorkunov, Maxim V.; Shadrivov, Ilya V.; Kivshar, Yuri S.
2005-01-01
We suggest double-resonant (binary) metamaterials composed of two types of magnetic resonant elements, and demonstrate that in the nonlinear regime such metamaterials provide unique possibilities for phase-matched parametric interaction and enhanced second-harmonic generation.
Parametric form of QCD travelling waves
Peschanski, R.
2005-01-01
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a solvable hierarchy of differential equations. A universal parametric form of travelling waves emerges from the first two orders of the expansion.
Parametric form of QCD travelling waves
Peschanski, R.
2005-01-01
We derive parametric travelling-wave solutions of non-linear QCD equations. They describe the evolution towards saturation in the geometric scaling region. The method, based on an expansion in the inverse of the wave velocity, leads to a solvable hierarchy of differential equations. A universal parametric form of travelling waves emerges from the first two orders of the expansion.
Energy Technology Data Exchange (ETDEWEB)
Molli, Muralikrishna; Bhat Kademane, Abhijit; Pradhan, Prabin; Sai Muthukumar, V. [Sri Sathya Sai Institute of Higher Learning, Department of Physics, Puttaparthi, Andhra Pradesh (India)
2016-08-15
In this work, we report for the first time, the nonlinear optical absorption properties of vanadium pentoxide (V{sub 2}O{sub 5}) nanoparticles in the femtosecond excitation regime. V{sub 2}O{sub 5} nanoparticles were synthesized through solution combustion technique. The as-synthesized samples were further characterized using XRD, FESEM, EDAX, TEM and UV-visible spectroscopy. X-ray diffraction results revealed the crystalline nature of the nanoparticles. Electron microscopy studies showed the size of the nanoparticles to be ∝200 nm. Open-aperture z-scan technique was employed to study the nonlinear optical absorption behavior of the synthesized samples using a 100-fs laser pulses at 800 nm from a regeneratively amplified Ti: sapphire laser. The mechanism of nonlinear absorption was found to be a three-photon absorption process which was explained using the density of states of V{sub 2}O{sub 5} obtained using density functional theory. These nanoparticles exhibit strong intensity-dependent nonlinear optical absorption and hence could be considered for optical-power-limiting applications. (orig.)
Auzinsh, M.; Berzins, A.; Ferber, R.; Gahbauer, F.; Kalvans, L.; Mozers, A.; Spiss, A.
2015-05-01
We studied alignment-to-orientation conversion caused by excited-state level crossings in a nonzero magnetic field of both atomic rubidium isotopes. Experimental measurements were performed on the transitions of the D2 line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. In the experiments, laser-induced fluorescence components were observed at linearly polarized excitation and their difference was taken afterwards. By observing the two oppositely circularly polarized components, we were able to see structures not visible in the difference graphs, which give deeper insight into the processes responsible for these signals. We studied how these signals are dependent on intensity and how they are affected when the exciting laser is tuned to different hyperfine transitions. The comparison between experiment and theory was carried out fulfilling the nonlinear absorption conditions. The theoretical curves described the experimental measurements satisfactorily, reproducing even small features in the shapes of the curves.
Plekhanov, A. I.; Basova, T. V.; Parkhomenko, R. G.; Gürek, A. G.
2017-02-01
In this work, the nonlinear optical properties of unsubstituted lutetium (LuPc2) and dysprosium (DyPc2) bisphthalocyanines as well as octasubstituted Lu(PcR8)2 derivative with R=-S(C6H13) were studied at a wavelength of 1550 nm with 10 ns and 300 fs pulses. Based on Z-scan measurements the nonlinear absorption and refraction coefficient as well as the nature of nonlinear optical properties were analyzed for these materials. Open aperture Z-scan indicates strong two-photon absorption in all three bisphthalocyanines in nano- and femtosecond regimes. With good nonlinear optical coefficients, bisphthalocyanines of rare earth elements are expected to be promising materials for the creation of optical limiters.
Planar Parametrization in Isogeometric Analysis
DEFF Research Database (Denmark)
Gravesen, Jens; Evgrafov, Anton; Nguyen, Dang-Manh
2012-01-01
Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing...... and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape...... are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysis-oriented methods. Their performance is illustrated through a few numerical examples....
Planar Parametrization in Isogeometric Analysis
DEFF Research Database (Denmark)
Gravesen, Jens; Evgrafov, Anton; Nguyen, Dang-Manh;
2012-01-01
Before isogeometric analysis can be applied to solving a partial differential equation posed over some physical domain, one needs to construct a valid parametrization of the geometry. The accuracy of the analysis is affected by the quality of the parametrization. The challenge of computing...... and maintaining a valid geometry parametrization is particularly relevant in applications of isogemetric analysis to shape optimization, where the geometry varies from one optimization iteration to another. We propose a general framework for handling the geometry parametrization in isogeometric analysis and shape...... are suitable for our framework. The non-linear methods we consider are based on solving a constrained optimization problem numerically, and are divided into two classes, geometry-oriented methods and analysis-oriented methods. Their performance is illustrated through a few numerical examples....
Hide, Raymond; Moroz, Irene M.
1999-10-01
The elucidation of the behaviour of physically realistic self-exciting Faraday-disk dynamos bears inter alia on attempts by theoretical geophysicists to interpret observations of geomagnetic polarity reversals. Hide [The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos, Phys. Earth Planet. Interiors 103 (1997) 281-291; Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo, Nonlinear Processes in Geophysics 4 (1998) 201-205] has introduced a novel 4-mode set of nonlinear ordinary differential equations to describe such a dynamo in which a nonlinear electric motor is connected in series with the coil. The applied couple, α, driving the disk is steady and the Lorentz couple driving the motor is a quadratic function, x(1-ɛ)+ɛσx 2, of the dynamo-generated current x, with 0≤ɛ≤1. When there are no additional biasing effects due to background magnetic fields etc., the behaviour of the dynamo is determined by eight independent non-negative control parameters. These include ρ, proportional to the resistance of the disk to azimuthal eddy currents, and β, an inverse measure of the moment of inertia of the armature of the motor. When β=0 (the case when the motor is absent and ɛ and σ are redundant) and ρ -1≠0 , the 4-mode dynamo equations reduce to the 3-mode Lorenz equations, which can behave chaotically [E. Knobloch, Chaos in the segmented disc dynamo, Phys. Lett. A 82 (1981) 439-440]. When β≠0 but ρ -1=0 , the 4-mode set of equations reduces to a 3-mode dynamo [R. Hide (1997), see above], which can also behave chaotically when ɛ=0 [R. Hide, A.C. Skeldon, D.J. Acheson, A study of two novel self-exciting single-disk homopolar dynamos: theory, Proc. R. Soc. Lond. A 452 (1996) 1369-1395] but not when ɛ=1 [R. Hide (1998), see above]. In the latter case, however, all persistent fluctuations are completely quenched [R. Hide (1998), see above]. In this paper we investigate
Vendrell, Oriol; Brill, Michael; Gatti, Fabien; Lauvergnat, David; Meyer, Hans-Dieter
2009-06-21
Quantum dynamical calculations are reported for the zero point energy, several low-lying vibrational states, and the infrared spectrum of the H(5)O(2)(+) cation. The calculations are performed by the multiconfiguration time-dependent Hartree (MCTDH) method. A new vector parametrization based on a mixed Jacobi-valence description of the system is presented. With this parametrization the potential energy surface coupling is reduced with respect to a full Jacobi description, providing a better convergence of the n-mode representation of the potential. However, new coupling terms appear in the kinetic energy operator. These terms are derived and discussed. A mode-combination scheme based on six combined coordinates is used, and the representation of the 15-dimensional potential in terms of a six-combined mode cluster expansion including up to some 7-dimensional grids is discussed. A statistical analysis of the accuracy of the n-mode representation of the potential at all orders is performed. Benchmark, fully converged results are reported for the zero point energy, which lie within the statistical uncertainty of the reference diffusion Monte Carlo result for this system. Some low-lying vibrationally excited eigenstates are computed by block improved relaxation, illustrating the applicability of the approach to large systems. Benchmark calculations of the linear infrared spectrum are provided, and convergence with increasing size of the time-dependent basis and as a function of the order of the n-mode representation is studied. The calculations presented here make use of recent developments in the parallel version of the MCTDH code, which are briefly discussed. We also show that the infrared spectrum can be computed, to a very good approximation, within D(2d) symmetry, instead of the G(16) symmetry used before, in which the complete rotation of one water molecule with respect to the other is allowed, thus simplifying the dynamical problem.
Institute of Scientific and Technical Information of China (English)
章扬忠; 谢涛
2014-01-01
The axisymmetric toroidal electrostatic mode discussed in this paper refers collectively to the nearly ideal electro-static fluid mode with zero toroidal mode number in magnetically confined toroidal plasmas like tokamak, including geodesic acoustic mode, sound waves and the so-called nearly zero-frequency zonal flow. Use is made of cold ion fluid model in the toroidal coordinate system with a circular cross section to develop the theory of parametric excitation for the three above mentioned modes systematically to the first order of inverse large aspect ratio, which ends up with the four following observations: (1) The density zonal flow is only associated with the excitation of the first harmonic cosine sound wave and is independent of the potential zonal flow. (2) The geodesic acoustic mode is the high frequency branch of the dispersion in the form of coupling between the first harmonic sine sound wave and the nearly zero-frequency zonal flow due to geodesic curvature, while the low frequency branch of the same dispersion is identified to be the ‘toroidally modified nearly zero-frequency zonal flow’. (3) Only a weak coupling exists between the second harmonic sine sound wave and the nearly zero-frequency zonal flow. (4) All cosine sound waves and sine sound waves beyond the second harmonic are decoupled to the nearly zero-frequency zonal flow. A Gaussian type of drift wave energy spectrum with only a few parameters is introduced for calculation. Emphasis is laid on the effects resulting from the finite radial spectrum width such as double Landau-singularity, which reveal a significant modification to the δ-spectrum, thus resulting in serious restriction to the parametric excitation of geodesic acoustic mode and nearly zero-frequency zonal flow. Also discussed is the possibility of excitation of density zonal flow in the high q region. Numerical results are presented graphically and discussed in the reasonable physical regime. It is indicated that the
Energy Technology Data Exchange (ETDEWEB)
Ataei, Nader
2006-05-09
Different types of exciter are used for voltage supply to the synchronous generators of power stations depending on the required power and design. The exciter system of the generator, which as a rule consists syncronous motors and commutators, is commonly modeled in conventional models by control units with nonlinear characteristics which do not give an accurate picture of the dynamic processes inside the exciter motor. It was not possible to assess the component loads of the exciter components and the physical characteristics within the exciter system. In this study, a brushless exciter for the grid-connected synchronous generator was investigated which consists of two synchronous motors as primary and secondary exciter and two commutator bridges. A dynamic simulation model was developed for calculating the interactions between the grid, generator and exciter unit in consideration of electromagnetic and galvanic coupling. For this, the normal control units were replaced by physical components of the exciter system, i.e. electric exciter motors and commutators. The study was carried out using an enhanced version of the Siemens NETOMAC software, which provided information on the loads on the exciter components in case of internal and external failures. In particular, loads in coils and commutators were calculated that could not be measured before. The findings enable more accurate dimensioning of the exciter unit making it more fail-safe, and the protective systems can be adjusted more accurately. One important result of the investigation was the identification of all dynamic processes going on between the exciter motors, commutators, generator and grid induced by external and internal failures. (orig.) [German] Zur Spannungsversorgung der Synchrongeneratoren in Kraftwerken werden je nach Leistungsanforderung und Baukonzept unterschiedliche Erregereinrichtungen verwendet. Das Erregersystem des Generators, das in der Regel aus Erregersynchronmaschinen und
Batsikadze, G; Moliadze, V; Paulus, W; Kuo, M-F; Nitsche, M A
2013-04-01
Transcranial direct current stimulation (tDCS) of the human motor cortex at an intensity of 1 mA with an electrode size of 35 cm(2) has been shown to induce shifts of cortical excitability during and after stimulation. These shifts are polarity-specific with cathodal tDCS resulting in a decrease and anodal stimulation in an increase of cortical excitability. In clinical and cognitive studies, stronger stimulation intensities are used frequently, but their physiological effects on cortical excitability have not yet been explored. Therefore, here we aimed to explore the effects of 2 mA tDCS on cortical excitability. We applied 2 mA anodal or cathodal tDCS for 20 min on the left primary motor cortex of 14 healthy subjects. Cathodal tDCS at 1 mA and sham tDCS for 20 min was administered as control session in nine and eight healthy subjects, respectively. Motor cortical excitability was monitored by transcranial magnetic stimulation (TMS)-elicited motor-evoked potentials (MEPs) from the right first dorsal interosseous muscle. Global corticospinal excitability was explored via single TMS pulse-elicited MEP amplitudes, and motor thresholds. Intracortical effects of stimulation were obtained by cortical silent period (CSP), short latency intracortical inhibition (SICI) and facilitation (ICF), and I wave facilitation. The above-mentioned protocols were recorded both before and immediately after tDCS in randomized order. Additionally, single-pulse MEPs, motor thresholds, SICI and ICF were recorded every 30 min up to 2 h after stimulation end, evening of the same day, next morning, next noon and next evening. Anodal as well as cathodal tDCS at 2 mA resulted in a significant increase of MEP amplitudes, whereas 1 mA cathodal tDCS decreased corticospinal excitability. A significant shift of SICI and ICF towards excitability enhancement after both 2 mA cathodal and anodal tDCS was observed. At 1 mA, cathodal tDCS reduced single-pulse TMS-elicited MEP amplitudes and shifted SICI
Wierschem, Nicholas E.; Hubbard, Sean A.; Luo, Jie; Fahnestock, Larry A.; Spencer, Billie F.; McFarland, D. Michael; Quinn, D. Dane; Vakakis, Alexander F.; Bergman, Lawrence A.
2017-02-01
Limiting peak stresses and strains in a structure subjected to high-energy, short-duration transient loadings, such as blasts, is a challenging problem, largely due to the well-known insensitivity of the first few cycles of the structural response to damping. Linear isolation, while a potential solution, requires a very low fundamental natural frequency to be effective, resulting in large nearly-rigid body displacement of the structure, while linear vibration absorbers have little or no effect on the early-time response where relative motions, and thus stresses and strains, are at their highest levels. The problem has become increasingly important in recent years with the expectation of blast-resistance as a design requirement in new construction. In this paper, the problem is examined experimentally and computationally in the context of offset-blast loading applied to a custom-built nine story steel frame structure. A fully-passive response mitigation system consisting of six lightweight, essentially nonlinear vibration absorbers (termed nonlinear energy sinks - NESs) is optimized and deployed on the upper two floors of this structure. Two NESs have vibro-impact nonlinearities and the other four possess smooth but essentially nonlinear stiffnesses. Results of the computational and experimental study demonstrate the efficacy of the proposed passive nonlinear mitigation system to rapidly and efficiently attenuate the global structural response, even at early time (i.e., starting at the first response cycle), thus minimizing the peak demand on the structure. This is achieved by nonlinear redistribution of the blast energy within the modal space through low-to-high energy scattering due to the action of the NESs. The experimental results validate the theoretical predictions.
Angle-Resolved Spectroscopy of Parametric Fluorescence
Hsu, Feng-kuo
2013-01-01
The parametric fluorescence from a nonlinear crystal forms a conical radiation pattern. We measure the angular and spectral distributions of parametric fluorescence in a beta-barium borate crystal pumped by a 405-nm diode laser employing angle-resolved imaging spectroscopy. The experimental angle-resolved spectra and the generation efficiency of parametric down conversion are compared with a plane-wave theoretical analysis. The parametric fluorescence is used as a broadband light source for the calibration of the instrument spectral response function in the wavelength range from 450 to 1000 nm.
Nonlinear models for autoregressive conditional heteroskedasticity
DEFF Research Database (Denmark)
Teräsvirta, Timo
This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation...... are discussed. Forecasting volatility with nonlinear models is considered. Finally, parametric nonlinear models based on multi- plicative decomposition of the variance receive attention....
The effect of nonlinearities on the response of a single-machine- quasi-infinite busbar system
Energy Technology Data Exchange (ETDEWEB)
Hamdan, A.M.A.; Nayfeh, A.H.
1989-08-01
A single machine quasi-infinite busbar system is formulated taking into consideration quadratic and cubic nonlinearities. The model equation contains parametric (time-varying coefficients) and external (inhomogeneous terms) excitations. The method of multiple scales is used to determine approximations to the responses of the system to simultaneous principal parametric resonances and subharmonic resonances of order one-half. In contrast with the linear analysis, the non-linear analysis shows that the response may exhibit (a) limit cycles instead of infinite motions, (b) multivaluedness that may lead to jumps, (c) subcritical instabilities, and (d) constructive and destructive interferenced of resonances.
Indian Academy of Sciences (India)
VENKATESH P R; VENKATESAN A
2016-07-01
Additional sinusoidal and different non-sinusoidal periodic perturbations applied to the periodically forced nonlinear oscillators decide the maintainance or inhibitance of chaos. It is observed that the weak amplitude of the sinusoidal force without phase is sufficient to inhibit chaos rather than the other non-sinusoidal forces and sinusoidal force with phase. Apart from sinusoidal force without phase, i.e., from various non-sinusoidal forces and sinusoidal force with phase, square force seems to be an effective weak perturbation to suppress chaos. The effectiveness of weak perturbation for suppressing chaos is understood with the total power average of the external forces applied to the system. In any chaotic system, the total power average of the external forces isconstant and is different for different nonlinear systems. This total power average decides the nature of the force to suppress chaos in the sense of weak perturbation. This has been a universal phenomenon for all the chaoticnon-autonomous systems. The results are confirmed by Melnikov method and numerical analysis. With the help of the total power average technique, one can say whether the chaos in that nonlinear system is to be supppressed or not.
Martynovich, E. F.; Glazunov, D. S.; Grigorova, A. A.; Starchenko, A. A.; Kirpichnikov, A. V.; Trunov, V. I.; Merzlyakov, M. A.; Petrov, V. V.; Pestryakov, E. V.
2008-09-01
Analysis of the spatial distribution of the color centers formed in wide-gap LiF and MgF2 crystals in a laser beam channel has shown that these centers are formed in numerous longitudinal filaments into which a laser beam splits when propagating in a medium. The luminescence of the produced color centers is photoluminescence, which is excited by the supercontinuum radiation in the filaments.
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Merging Nonlinear Optics and Negative-Index Metamaterials
Popov, Alexander K
2011-01-01
The extraordinary properties of nonlinear optical propagation processes in double-domain positive/negative index metamaterials are reviewed. These processes include second harmonic generation, three- and four-wave frequency mixing, and optical parametric amplification. Striking contrasts with the properties of the counterparts in ordinary materials are shown. We also discuss the possibilities for compensating strong losses inherent to plasmonic metamaterials, which present a major obstacle in numerous exciting applications, and the possibilities for creation of unique ultracompact photonic devices such as data processing chips and nonlinear-optical sensors. Finally, we propose similar extraordinary three-wave mixing processes in crystals based on optical phonons with negative dispersion.
High-codimensional static bifurcations of strongly nonlinear oscillator
Institute of Scientific and Technical Information of China (English)
Zhang Qi-Chang; Wang Wei; Liu Fu-Hao
2008-01-01
The static bifurcation of the parametrically excited strongly nonlinear oscillator is studied.We consider the averaged equations of a system subject to Duffing-van der Pol and quintic strong nonlinearity by introducing the undetermined fundamental frequency into the computation in the complex normal form.To discuss the static bifurcation,the bifurcation problem is described as a 3-codimensional unfolding with Z2 symmetry on the basis of singularity theory.The transition set and bifurcation diagrams for the singularity are presented,while the stability of the zero solution is studied by using the eigenvalues in various parameter regions.
Xiong, S. Y.; Yang, J. G.; Zhuang, J.
2011-10-01
In this work, we use nonlinear spectral imaging based on two-photon excited fluorescence (TPEF) and second harmonic generation (SHG) for analyzing the morphology of collagen and elastin and their biochemical variations in basal cell carcinoma (BCC), squamous cell carcinoma (SCC) and normal skin tissue. It was found in this work that there existed apparent differences among BCC, SCC and normal skin in terms of their thickness of the keratin and epithelial layers, their size of elastic fibers, as well as their distribution and spectral characteristics of collagen. These differences can potentially be used to distinguish BCC and SCC from normal skin, and to discriminate between BCC and SCC, as well as to evaluate treatment responses.
A NOVEL NONLINEAR ADAPTIVE OPTIMAL EXCITATION CONTROLLER%一种非线性自适应最优励磁控制器的设计
Institute of Scientific and Technical Information of China (English)
谢小荣; 崔文进; 唐义良; 韩英铎
2001-01-01
The paper presents a novel nonlinear adaptive optimal excitation controller. The design is based on a 3rd-order double-axis dynamic model of synchronous machine. Satisfactory performance of transient stability control and steady-state voltage regulation has been achieved, under variation of operating conditions, using nonlinear feedback compensation which is implemented by algebraic calculation. A simple adaptive gain-tuning algorithm is embedded in the controller to optimise, at different operating point, the preset LQ performance index and guidance is provided to determine the weighting matrix. Simulation results demonstrate the superiority of the proposed method in comparison with conventional linear optimal excitation controller.%提出了一种非线性自适应最优励磁控制器。新的控制设计方法基于同步发电机的三阶双轴数学模型，其仅由代数运算实现的分散非线性反馈补偿律保证了系统在各种运行方式下具有足够的稳态调节精度。控制算法内置一个简单的在线自适应变增益策略以达到在各种工况下动态最优化控制的目的，通过求解闭环特征值优化问题来选取权矩阵的方法改善了系统受扰后的暂态响应性能。仿真计算结果表明，与传统的线性最优控制器相比，新的励磁控制器具有多方面优点。
Puķīte, Jānis; Wagner, Thomas
2016-05-01
We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer-Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, for scenarios with strong absorptions non-linear effects cannot always be neglected. This is especially the case for observation geometries, for which the light contributing to the measurement is crossing the atmosphere under spatially well-separated paths differing strongly in length and location, like in limb geometry. In these cases, often full retrieval algorithms are applied to address the non-linearities, requiring iterative forward modelling of absorption spectra involving time-consuming wavelength-by-wavelength radiative transfer modelling. In this study, we propose to describe the non-linear effects by additional sensitivity parameters that can be used e.g. to build up a lookup table. Together with widely used box air mass factors (effective light paths) describing the linear response to the increase in the trace gas amount, the higher-order sensitivity parameters eliminate the need for repeating the radiative transfer modelling when modifying the absorption scenario even in the presence of a strong absorption background. While the higher-order absorption structures can be described as separate fit parameters in the spectral analysis (so-called DOAS fit), in practice their quantitative evaluation requires good measurement quality (typically better than that available from current measurements). Therefore, we introduce an iterative retrieval algorithm correcting for the higher-order absorption structures not yet considered in the DOAS fit as well as the absorption dependence on
J. Puķīte; T. Wagner
2016-01-01
We address the application of differential optical absorption spectroscopy (DOAS) of scattered light observations in the presence of strong absorbers (in particular ozone), for which the absorption optical depth is a non-linear function of the trace gas concentration. This is the case because Beer–Lambert law generally does not hold for scattered light measurements due to many light paths contributing to the measurement. While in many cases linear approximation can be made, ...
Messina, Francesco; Nagar, Alessandro
2017-06-01
By post-Newtonian (PN) expanding the well-known, factorized and resummed, effective-one-body energy flux for circularized binaries, we show that (i) because of the presence of the resummed tail factor, the 4.5PN-accurate tails-of-tails-of-tails contribution to the energy flux recently computed by Marchand et al. [Classical Quantum Gravity 33, 244003 (2016), 10.1088/0264-9381/33/24/244003] is actually contained in the resummed expression; this is also the case of the next-to-leading-order tail-induced spin-orbit term of Marsat et al. [Classical Quantum Gravity 31, 025023 (2014), 10.1088/0264-9381/31/2/025023]; (ii) in performing this expansion, we also obtain, for the first time, the explicit 3.5PN leading-order tail-induced spin-spin flux term; and (iii) pushing the PN expansion of the (nonspinning) EOB flux up to 5.5PN order, we compute 4PN, 5PN, and 5.5PN contributions to the energy flux, though in a form that explicitly depends on, currently unknown, 4PN and 5PN non-test-mass corrections to the factorized waveform amplitudes. Within this (parametrized) 4.5PN accuracy, we calculate the Taylor F2 approximant. Focusing for simplicity on the nonspinning case and using the numerical-relativity calibrated IMRPhenomD waveform model as a benchmark, we demonstrate that it is possible to reproduce the derivative of the IMRPhenomD phase (say up to the frequency of the Schwarzschild last-stable-orbit) by flexing only a 4PN "effective" waveform amplitude parameter. A preliminary analysis also illustrates that similar results can be obtained for the spin-aligned case provided only the leading-order spin-orbit and spin-spin terms are kept. Our findings suggest that these types of EOB-derived, parametrized, higher-order, PN approximants may serve as promising tools to construct inspiral-merger-ringdown phenomenological models or even to replace the standardly used 3.5PN-accurate TaylorF2 approximant in searches of small-mass binaries.
Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances
Directory of Open Access Journals (Sweden)
Ali H. Nayfeh
1998-01-01
Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.
Radu, A.; Duque, C. A.
2015-08-01
The conduction subband structure of a triangular cross-section GaAs/AlGaAs quantum well wire under intense laser field is theoretically investigated by taking into account a finite confining potential. The calculation of the subband energy levels is based on a two-dimensional finite element method within the effective mass approximation. It is shown that a transversally polarized laser field non-uniformly shifts the subband energy levels and could be used for tuning the intersubband transitions and altering the related optical susceptibilities. We found that the non-resonant laser field allows the magnification and the red- or blueshift of the third-order non-linear susceptibility peaks for particular polarizations of the pump light and proper laser parameter values. The effects of the laser dressing field on the intersubband third harmonic generation and quadratic electro-optical process are discussed.
Intrator, T.; Hershkowitz, N.; Chan, C.
1984-01-01
Counterstreaming large-diameter electron beams in a steady-state laboratory experiment are observed to generate transverse radiation at twice the upper-hybrid frequency (2omega-UH) with a quadrupole radiation pattern. The electromagnetic wave power density is nonlinearly enhanced over the power density obtained from a single beam-plasma system. Electromagnetic power density scales exponentially with beam energy and increases with ion mass. Weak turbulence theory can predict similar (but weaker) beam energy scaling but not the high power density, or the predominance of the 2omega-UH radiation peak over the omega-UH peak. Significant noise near the upper-hybrid and ion plasma frequencies is also measured, with normalized electrostatic wave energy density W(ES)/n(e)T(e) approximately 0.01.
Institute of Scientific and Technical Information of China (English)
Yan Wang; Qing Wang; Wei Zhang; Xiaoming Liu; Jiangde Peng
2005-01-01
@@ A broadband multiwavelength Raman fiber ring laser (RFRL) covering the whole C-band at room temperature are presented. The effect of the intracavity highly nonlinear dispersion-shifted fiber on broadening and flattening the output spectrum envelope is discussed and experimentally demonstrated. More than 45-dB extinction-ratio multiwavelength output from 1527.76 to 1566.86 nm with 100-GHz channel spacing and 2.1-dB power ripple has been achieved by carefully controlling the individual powers of three pump lasers.
Couplings in parametrically excited inclined cables systems
Michon, Guilhem; Berlioz, Alain; Lamarque, Claude-Henri
2008-01-01
Cables in stayed bridges are subjected to important dynamic solicitations for which dynamic model are now well established. Due to their design, such structures highlight resonance phenomena and instabilities frequently observed. Nevertheless, some structures exhibit important vibration amplitudes that can not be explained simply. Measurement recently performed on a bridge point a coupling of the cable with the deck or the pillar. The present paper suggests to consider the deck flexibility co...
Chaos control of parametric driven Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Jin, Leisheng; Mei, Jie; Li, Lijie, E-mail: L.Li@swansea.ac.uk [College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom)
2014-03-31
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Parametric resonance in concrete beam-columns
Sharma,Mamta R.; Singh,Arbind K; Benipal,Gurmail S
2014-01-01
A dynamic instability, called parametric resonance, is exhibited by undampedelastic beam-columns when under the action of pulsating axial force. The scope of the existing theory of parametric resonance is restricted to physically linear beam-columns undergoing finite lateral displacements. In this Paper, the dynamic behaviour of physically nonlinear elastic cracked concrete beam-columns under pulsating axial force and constant lateral force is investigated. The constitutive equations derived ...
Chaos control of parametric driven Duffing oscillators
Jin, Leisheng; Mei, Jie; Li, Lijie
2014-03-01
Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.
Energy Technology Data Exchange (ETDEWEB)
YATES,GEORGE J.; MCDONALD,THOMAS E. JR.; BLISS,DAVID E.; CAMERON,STEWART M.; GREIVES,KENNETH H.; ZUTAVERN,FRED J.
2000-12-20
Laboratory experiments utilizing different near-infrared (NIR) sensitive imaging techniques for LADAR range gated imaging at eye-safe wavelengths are presented. An OPO/OPA configuration incorporating a nonlinear crystal for wavelength conversion of 1.56 micron probe or broadcast laser light to 807 nm light by utilizing a second pump laser at 532 nm for gating and gain, was evaluated for sensitivity, resolution, and general image quality. These data are presented with similar test results obtained from an image intensifier based upon a transferred electron (TE) photocathode with high quantum efficiency (QE) in the 1-2 micron range, with a P-20 phosphor output screen. Data presented include range-gated imaging performance in a cloud chamber with varying optical attenuation of laser reflectance images.
Coupled mode parametric resonance in a vibrating screen model
Slepyan, Leonid I
2013-01-01
We consider a simple dynamic model of the vibrating screen operating in the parametric resonance (PR) mode. This model was used in the course of designing and setting of such a screen in LPMC. The PR-based screen compares favorably with conventional types of such machines, where the transverse oscillations are excited directly. It is characterized by larger values of the amplitude and by insensitivity to damping in a rather wide range. The model represents an initially strained system of two equal masses connected by a linearly elastic string. Self-equilibrated, longitudinal, harmonic forces act on the masses. Under certain conditions this results in transverse, finite-amplitude oscillations of the string. The problem is reduced to a system of two ordinary differential equations coupled by the geometric nonlinearity. Damping in both the transverse and longitudinal oscillations is taken into account. Free and forced oscillations of this mass-string system are examined analytically and numerically. The energy e...
Institute of Scientific and Technical Information of China (English)
林作铨; 李未
1995-01-01
Parametric logic is introduced. The language, semantics and axiom system of parametric logic are defined. Completeness theorem of parametric logic is provided. Parametric logic has formal ability powerful enough to capture a wide class of logic as its special cases, and therefore can be viewed as a uniform basis for modern logics.
Transverse nonlinear vibrations of a circular spinning disk with a varying rotating speed
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We analyze the transverse nonlinear vibrations of a rotating flexible disk subjected to a rotating point force with a periodically varying rotating speed. Based on Hamilton’s principle, the nonlinear governing equations of motion (coupled equations among the radial, tangential and transverse displacements) are derived for the rotating flexible disk. When the in-plane inertia is ignored and a stress function is introduced, the three nonlinearly coupled partial differential equations are reduced to two nonlinearly coupled partial differential equations. According to Galerkin’s approach, a four-degree-of-freedom nonlinear system governing the weakly split resonant modes is derived. The resonant case considered here is 1:1:2:2 internal resonance and a critical speed resonance. The primary parametric resonance for the first-order sin and cos modes and the fundamental parametric resonance for the second-order sin and cos modes are also considered. The method of multiple scales is used to obtain a set of eight-dimensional nonlinear averaged equations. Based on the averaged equations, using numerical simulations, the influence of different parameters on the nonlinear vibrations of the spinning disk is detected. It is concluded that there exist complicated nonlinear behaviors including the periodic, period-n and multi-pulse type chaotic motions for the spinning disk with a varying rotating speed. It is also found that among all parameters, the damping and excitation have great influence on the nonlinear responses of the spinning disk with a varying rotating speed.
Energy Technology Data Exchange (ETDEWEB)
Guo, Kong-Ming, E-mail: kmguo@xidian.edu.cn [School of Electromechanical Engineering, Xidian University, P.O. Box 187, Xi' an 710071 (China); Jiang, Jun, E-mail: jun.jiang@mail.xjtu.edu.cn [State Key Laboratory for Strength and Vibration, Xi' an Jiaotong University, Xi' an 710049 (China)
2014-07-04
To apply stochastic sensitivity function method, which can estimate the probabilistic distribution of stochastic attractors, to non-autonomous dynamical systems, a 1/N-period stroboscopic map for a periodic motion is constructed in order to discretize the continuous cycle into a discrete one. In this way, the sensitivity analysis of a cycle for discrete map can be utilized and a numerical algorithm for the stochastic sensitivity analysis of periodic solutions of non-autonomous nonlinear dynamical systems under stochastic disturbances is devised. An external excited Duffing oscillator and a parametric excited laser system are studied as examples to show the validity of the proposed method. - Highlights: • A method to analyze sensitivity of stochastic periodic attractors in non-autonomous dynamical systems is proposed. • Probabilistic distribution around periodic attractors in an external excited Φ{sup 6} Duffing system is obtained. • Probabilistic distribution around a periodic attractor in a parametric excited laser system is determined.
Why preferring parametric forecasting to nonparametric methods?
Jabot, Franck
2015-05-07
A recent series of papers by Charles T. Perretti and collaborators have shown that nonparametric forecasting methods can outperform parametric methods in noisy nonlinear systems. Such a situation can arise because of two main reasons: the instability of parametric inference procedures in chaotic systems which can lead to biased parameter estimates, and the discrepancy between the real system dynamics and the modeled one, a problem that Perretti and collaborators call "the true model myth". Should ecologists go on using the demanding parametric machinery when trying to forecast the dynamics of complex ecosystems? Or should they rely on the elegant nonparametric approach that appears so promising? It will be here argued that ecological forecasting based on parametric models presents two key comparative advantages over nonparametric approaches. First, the likelihood of parametric forecasting failure can be diagnosed thanks to simple Bayesian model checking procedures. Second, when parametric forecasting is diagnosed to be reliable, forecasting uncertainty can be estimated on virtual data generated with the fitted to data parametric model. In contrast, nonparametric techniques provide forecasts with unknown reliability. This argumentation is illustrated with the simple theta-logistic model that was previously used by Perretti and collaborators to make their point. It should convince ecologists to stick to standard parametric approaches, until methods have been developed to assess the reliability of nonparametric forecasting. Copyright © 2015 Elsevier Ltd. All rights reserved.
Adur, J.; Pelegati, V. B.; de Thomaz, A. A.; Bottcher-Luiz, F.; Andrade, L. A. L. A.; Almeida, D. B.; Carvalho, H. F.; Cesar, C. L.
2012-03-01
We applied Two-photon Excited Fluorescence (TPEF), Second/Third Harmonic Generation (SHG and THG) and Fluorescence Lifetime Imaging (FLIM) Non Linear Optics (NLO) Laser-Scanning Microscopy within the same imaging platform to evaluate their use as a diagnostic tool in ovarian tumors. We assess of applicability of this multimodal approach to perform a pathological evaluation of serous and mucinous tumors in human samples. The combination of TPEF-SHG-THG imaging provided complementary information about the interface epithelium/stromal, such as the transformation of epithelium surface (THG) and the overall fibrillar tissue architecture (SHG). The fact that H&E staining is the standard method used in clinical pathology and that the stored samples are usually fixed makes it important a re-evaluation of these samples with NLO microscopy to compare new results with a library of already existing samples. FLIM, however, depends on the chemical environment around the fluorophors that was completely changed after fixation; therefore it only makes sense in unstained samples. Our FLIM results in unstained samples demonstrate that it is possible to discriminate healthy epithelia from serous or mucinous epithelia. Qualitative and quantitative analysis of the different imaging modalities used showed that multimodal nonlinear microscopy has the potential to differentiate between cancerous and healthy ovarian tissue.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Nonlinear physics of shear Alfvén waves
Energy Technology Data Exchange (ETDEWEB)
Zonca, Fulvio [Associazione EURATOM-ENEA sulla Fusione, C.P. 65-00044 Frascati, Italy and Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007 (China); Chen, Liu [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007, P.R.C. and Department of Physics and Astronomy, University of California, Irvine, CA 92697 (United States)
2014-02-12
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Observation of non-degenerate photorefractive parametric amplification
DEFF Research Database (Denmark)
Pedersen, H.C.; Johansen, P.M.
1996-01-01
We report on the first experimental observation of so-called nondegenerate photorefractive parametric amplification. We show that due to this effect it is possible for a weakly modulated photoinduced grating to be parametrically amplified via nonlinear interaction with a strongly modulated...
Fiber-optic parametric amplifier and oscillator based on intracavity parametric pump technique.
Luo, Zhengqian; Zhong, Wen-De; Tang, Ming; Cai, Zhiping; Ye, Chenchun; Xiao, Xiaosheng
2009-01-15
A cost-effective fiber optical parametric amplifier (FOPA) based on the laser intracavity pump technique has been proposed and demonstrated experimentally. The parametric process is realized by inserting a 1 km highly nonlinear dispersion-shifted fiber (HNL-DSF) into a fiber ring-laser cavity that consists of a high-power erbium-doped fiber (EDF) amplifier and two highly reflective fiber Bragg gratings. Compared with the conventional parametric pump schemes, the proposed pumping technique is free from a tunable semiconductor laser as the pump source and also the pump phase modulation. When the oscillating power of 530 mW in the EDF laser cavity is achieved to pump the HNL-DSF, a peak parametric gain of 27.5 dB and a net gain over 45 nm are obtained. Moreover, a widely tunable fiber-optic parametric oscillator is further developed using the FOPA as a gain medium.
分子高激发振动态的经典非线性性质%The classical nonlinear properties of molecular highly excited vibration
Institute of Scientific and Technical Information of China (English)
吴国祯
2011-01-01
The concepts of classical nonlinear dynamics are employed to interpret the spectroscopic properties of the molecular highly excited vibration. These concepts include the Morse oscillator, the pendulum dynamics, chaos and the overlapping of resonances leading to chaos. The relations of resonance, constant of motion and the basic dynamical unit to the pendulum dynamics are stressed. An algebraic Hamiltonian in the coset space is employed for the dynamical analysis from which the dynamical potential can be easily obtained. The dynamical potential is closely related to the classical fixed points in which the quantized levels are embedded in various quantal environments.Localized modes are easily identified in various systems which share similar dynamical potentials. The dissociation of DCO radical is finally interpreted by these concepts from the classical nonlinear dynamics.%该文阐述如何运用经典非线性力学的概念,来理解分子高激发振动态的谱学性质.内容包括:莫尔斯振子,单摆的动力学和共振的关系,力学体系的构成单元是单摆,一个共振对应于一个守恒量,混沌,共振的重叠导致混沌的产生等.我们的出发点是运用二次量子化算子构成的代数哈密顿量,经由海森伯对应而得到的陪集空间上的动力学体系.从此哈密顿量,可以得到动力学势.而动力学势和经典的不动点关系密切,并且量子态就处在由动力学势所包围,分成的几个量子环境中.从动力学势,可以依据它的对称性,方便推得局域模式的存在,最后我们利用这些非线性力学的概念,来分析DCO分子高激发振动态的解离问题.
Theoretical and algorithmic advances in multi-parametric programming and control
Pistikopoulos, Efstratios N.
2012-04-21
This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.
Zero-voltage nondegenerate parametric mode in Josephson tunnel junctions
DEFF Research Database (Denmark)
Pedersen, Niels Falsig
1976-01-01
A new parametric mode in a Josephson tunnel junction biased in the zero-voltage mode is suggested. It is a nondegenerate parametric excitation where the junction plasma resonance represents the input circuit, and a junction geometrical resonance represents the idler circuit. This nondegenerate mo...... for such a coupling. Journal of Applied Physics is copyrighted by The American Institute of Physics....
Parametrizing Algebraic Curves
Lemmermeyer, Franz
2011-01-01
We present the technique of parametrization of plane algebraic curves from a number theorist's point of view and present Kapferer's simple and beautiful (but little known) proof that nonsingular curves of degree > 2 cannot be parametrized by rational functions.
Nonlinear Light-Matter Interactions in Metamaterials
O'Brien, Kevin Patrick
Metamaterials possess extraordinary linear optical properties never observed in natural materials such as a negative refractive index, enabling exciting applications such as super resolution imaging and cloaking. In this thesis, we explore the equally extraordinary nonlinear properties of metamaterials. Nonlinear optics, the study of light-matter interactions where the optical fields are strong enough to change material properties, has fundamental importance to physics, chemistry, and material science as a non-destructive probe of material properties and has important technological applications such as entangled photon generation and frequency conversion. Due to their ability to manipulate both linear and nonlinear light matter interactions through sub-wavelength structuring, metamaterials are a promising direction for both fundamental and applied nonlinear optics research. We perform the first experiments on nonlinear propagation in bulk zero and negative index optical metamaterials and demonstrate that a zero index material can phase match four wave mixing processes in ways not possible in finite index materials. In addition, we demonstrate the ability of nonlinear scattering theory to describe the geometry dependence of second and third harmonic generation in plasmonic nanostructures. As an application of nonlinear metamaterials, we propose a phase matching technique called "resonant phase matching" to increase the gain and bandwidth of Josephson junction traveling wave parametric amplifiers. With collaborators, we demonstrate a best in class amplifier for superconducting qubit readout--over 20 dB gain with near quantum limited noise performance with a bandwidth and dynamic range an order of magnitude larger than alternative devices. In conclusion, we have demonstrated several ways in which nonlinear metamaterials surpass their natural counterparts. We look forward to the future of the field where nonlinear and quantum metamaterials will enable further new
Detection of Parametric Roll on Ships
DEFF Research Database (Denmark)
Galeazzi, Roberto; Blanke, Mogens; Poulsen, Niels Kjølstad
2012-01-01
Recent years have shown several incidents with dramatic damage on container vessels caused by parametric resonance. When the resonance starts, the roll oscillation at a sub-harmonic frequency of the wave excitation may be completely unexpected. Timely warning about the onset of the resonance phen...
Parametric resonance in ideal magnetohydrodynamics
Zaqarashvili
2000-08-01
We show that an external nonelectromagnetic periodic inhomogeneous force sets up a parametric resonance in an ideal magnetohydrodynamics. Alfven waves with certain wavelengths grow exponentially in amplitude. Nonlinear interaction between the resonant harmonics produces the long-term modulation of amplitudes. The mechanism of the energy transformation from an external nonelectromagnetic force to magnetic oscillations of the system presented here can be used in understanding the physical background of the gravitational action on the magnetized medium. Future application of this theory to several astrophysical problems is briefly discussed.
Non-linear dynamic response of a wind turbine blade
Chopra, I.; Dugundji, J.
1979-01-01
The paper outlines the nonlinear dynamic analysis of an isolated three-degree flap-lag-feather wind turbine blade under a gravity field and with shear flow. Lagrangian equations are used to derive the nonlinear equations of motion of blade for arbitrarily large angular deflections. The limit cycle analysis for forced oscillations and the determination of the principal parametric resonance of the blade due to periodic forces from the gravity field and wind shear are performed using the harmonic balance method. Results are obtained first for a two-degree flap-lag blade, then the effect of the third degree of freedom (feather) is studied. The self-excited flutter solutions are obtained for a uniform wind and with gravity forces neglected. The effects of several parameters on the blade stability are examined, including coning angle, structural damping, Lock number, and feather frequency. The limit cycle flutter solution of a typical configuration shows a substantial nonlinear softening spring behavior.
Institute of Scientific and Technical Information of China (English)
钟艳春; 杨庆俊; 包钢
2011-01-01
The nonlinear dynamics characteristic of pneumatic vibration isolation system with a multi-frequency excitation was studied with the method of nonlinear dynamics. First, relative load curve of an air spring under a certain initial pressure was obtained by test, and based on the test data, a cube polynomial equation was obtained by means of nonlinear polynomial curve fitting according to the equilibrium heights of the air spring. Then, the nonlinear model of pneumatic vibration isolation system with a multi-frequency excitation was built and nonlinear dynamics equation was obtained according to nonlinear restoring force of the air spring. Next, the method of multiple scales was used to solve the nonlinear dynamics equation. Finally, combination resonance of pneumatic vibration isolation system with a multi-frequency excitation was analyzed and influences of the nonlinear parameter to the system were discussed. The results show that when combination frequencies are near the linearized natural frequency, combination resonance becomes strong. Cube nonlinear parameter directly influences nonlinear characteristic of the system, the greater the excitation amplitude, the more obvious of the nonlinear characteristic.%运用非线性动力学的方法研究气动隔振系统在多个频率激励下的非线性动力学特性.通过试验的方法得到空气弹簧在一定初始压力下的相对载荷曲线,以空气弹簧工作高度为自变量,用三次多项式对该曲线进行非线性拟合,得到弹簧非线性恢复力与工作高度的三次多项式表达式.建立气动隔振系统在3个激励频率下的非线性模型,根据弹簧的非线性恢复力,得到系统的非线性动力学方程.运用多尺度法对该非线性动力学方程进行求解,分析3个频率共同作用下的组合共振,讨论各非线性参数对系统的影响.研究结果表明:当组合频率接近系统线性化固有频率时,系统具有很强的组合共振;三次非线性
On Parametric (and Non-Parametric Variation
Directory of Open Access Journals (Sweden)
Neil Smith
2009-11-01
Full Text Available This article raises the issue of the correct characterization of ‘Parametric Variation’ in syntax and phonology. After specifying their theoretical commitments, the authors outline the relevant parts of the Principles–and–Parameters framework, and draw a three-way distinction among Universal Principles, Parameters, and Accidents. The core of the contribution then consists of an attempt to provide identity criteria for parametric, as opposed to non-parametric, variation. Parametric choices must be antecedently known, and it is suggested that they must also satisfy seven individually necessary and jointly sufficient criteria. These are that they be cognitively represented, systematic, dependent on the input, deterministic, discrete, mutually exclusive, and irreversible.
Nonlinear optical properties of atomic vapor and semiconductors
Energy Technology Data Exchange (ETDEWEB)
Kim, Doseok [Univ. of California, Berkeley, CA (United States). Dept. of Physics
1997-05-01
This thesis contains the study of highly forbidden resonant second harmonic generation (SHG) in atomic potassium vapor using tunable picosecond pulses. Various output characteristics of vapor SHG have been investigated including the input intensity dependence, potassium vapor density dependence, buffer gas pressure dependence, and spatial profile. Recently, the discovery of new nonlinear optical crystals such as barium borate (β-BaB_{2}O_{4}, BBO) and lithium borate (LiB_{3}O_{5}, LBO) has greatly improved the performance of a tunable coherent optical devices based on optical parametric generation and amplification. In the second part of this thesis, a homebuilt picosecond optical parametric generator/amplifier (OPG/OPA) system is described in detail, including its construction details and output characteristics. This laser device has found many useful applications in spectroscopic studies including surface nonlinear optical spectroscopy via sum-frequency generation (SFG). The last part of this thesis reports studies on multiphoton-excited photoluminescence from porous silicon and GaN. Multiphoton excitation and photoluminescence can give numerous complementary information about semiconductors not obtainable with one-photon, above-bandgap excitation.
Westra, H.J.R.; Karabacak, D.M.; Brongersma, S.H.; Crego-Calama, M.; Van der Zant, H.S.J.; Venstra, W.J.
2011-01-01
The interactions between parametrically- and directly-driven vibration modes of a clamped-clamped beam resonator are studied. An integrated piezoelectric transducer is used for direct and parametric excitation. First, the parametric amplification and oscillation of a single mode are analyzed by the
Westra, H.J.R.; Karabacak, D.M.; Brongersma, S.H.; Crego-Calama, M.; Van der Zant, H.S.J.; Venstra, W.J.
2011-01-01
The interactions between parametrically- and directly-driven vibration modes of a clamped-clamped beam resonator are studied. An integrated piezoelectric transducer is used for direct and parametric excitation. First, the parametric amplification and oscillation of a single mode are analyzed by the
Galaĭchuk, Yu A.; Kudryashov, V. A.; Strizhevskiĭ, V. L.; Fontaniĭ, V. A.; Yashkir, Yu N.
1985-07-01
A systematic analysis was made of the spectral characteristics of resonance four-photon parametric conversion of infrared radiation as a result of two-photon resonance pumping of the 3S-3D and 3S-5S transitions in sodium and the influence of these characteristics on the threshold sensitivity of a parametric conversion detector was investigated. An experimental study was made of the characteristics of the noise radiation generated as a result of hyperparametric scattering. The results obtained can be used to select the optimal parameters of high-sensitivity detectors of weak infrared signals by parametric conversion in alkali metal vapors.
Energy harvesting using parametric resonant system due to time-varying damping
Scapolan, Matteo; Tehrani, Maryam Ghandchi; Bonisoli, Elvio
2016-10-01
In this paper, the problem of energy harvesting is considered using an electromechanical oscillator. The energy harvester is modelled as a spring-mass-damper, in which the dissipated energy in the damper can be stored rather than wasted. Previous research provided the optimum damping parameter, to harvest maximum amount of energy, taking into account the stroke limit of the device. However, the amount of the maximum harvested energy is limited to a single frequency in which the device is tuned. Active and semi-active strategies have been suggested, which increases the performance of the harvester. Recently, nonlinear damping in the form of cubic damping has been proposed to extend the dynamic range of the harvester. In this paper, a periodic time-varying damper is introduced, which results in a parametrically excited system. When the frequency of the periodic time-varying damper is twice the excitation frequency, the system internal energy increases proportionally to the energy already stored in the system. Thus, for certain parametric damping values, the system can become unstable. This phenomenon can be exploited for energy harvesting. The transition curves, which separate the stable and unstable dynamics are derived, both analytically using harmonic balance method, and numerically using time simulations. The design of the harvester is such that its response is close to the transition curves of the Floquet diagram, leading to stable but resonant system. The performance of the parametric harvester is compared with the non-parametric one. It is demonstrated that performances and the frequency bandwidth in which the energy can be harvested can be both increased using time-varying damping.
Directory of Open Access Journals (Sweden)
J. Ju
2017-07-01
Full Text Available The flexible Cartesian robotic manipulator (FCRM is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.
Parametric Methods for Order Tracking Analysis
DEFF Research Database (Denmark)
Jensen, Tobias Lindstrøm; Nielsen, Jesper Kjær
2017-01-01
Order tracking analysis is often used to find the critical speeds at which structural resonances are excited by a rotating machine. Typically, order tracking analysis is performed via non-parametric methods. In this report, however, we demonstrate some of the advantages of using a parametric method...... for order tracking analysis. Specifically, we show that we get a much better time and frequency resolution, obtain a much more robust and accurate estimate of the RPM profile, and are able to perform accurate order tracking analysis even without the tachometer signal....
The closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for nonlinear systems
Chen, Lincong; Sun, Jian-Qiao
2016-12-01
In this paper, we propose a new method to obtain the closed-form solution of the reduced Fokker-Planck-Kolmogorov equation for single degree of freedom nonlinear systems under external and parametric Gaussian white noise excitations. The assumed stationary probability density function consists of an exponential polynomial with a logarithmic term to account for parametric excitations. The undetermined coefficients in the assumed solution are computed with the help of an iterative method of weighted residue. We have found that the iterative process generates a sequence of solutions that converge to the exact solutions if they exist. Three examples with known exact steady-state probability density functions are used to demonstrate the convergence of the proposed method.
Klimentov, Sergei M.; Garnov, Serge V.; Epifanov, Alexander S.; Manenkov, Alexander A.
1994-06-01
For application of optical parametric oscillator (OPO) to investigation of nonlinear interaction of laser radiation with matter the factor of importance is stability of light spatial distribution and spotsize position on a target through a tuning range. Collinear temperature tunable schemes show an advantage for these purposes, in particular, for small pump beam diameters. A simple and efficient visible range parametric converter can be realized using two-pass configuration, where parametric luminescence is excited on the first pass through a nonlinear crystal and amplified on the second pass after spatial filtering. Lack of resonator simplifies high power UV pumping and getting of relatively narrow emission spectrum. Using such an approach, we have made the oscillator-amplifier system temperature tunable in the range of 440 to 670 nm employing 4-cm-length ADP crystal pumped by 266 nm radiation from the single-mode YAG:Nd laser. The output energy of 3 mJ in about 1-ns pulsewidth has been achieved with total conversion efficiency of 10%. A spatial profile of the output beam kept its shape within the branch of the tuning curve. This allowed us to use the device as a proper tool for investigation of two-photon excitation in undoped CsI and KI single crystals. The OPO signal output was used to record photoconductivity spectra in these materials.
On the Nonlinear Structural Analysis of Wind Turbine Blades using Reduced Degree-of-Freedom Models
DEFF Research Database (Denmark)
Holm-Jørgensen, Kristian; Larsen, Jesper Winther; Nielsen, Søren R.K.
2008-01-01
, modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based...... on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response...... representing the case of infinitely many included modes, is shown to predict stable and ordered response for all considered parameters. Further, the analysis shows that the reduced-degree-of-freedom model of relatively low order overestimates the response near resonance peaks, which is a consequence...
Parametric instabilities in magnetized bi-ion and dusty plasmas
Indian Academy of Sciences (India)
N F Cramer; M P Hertzberg; S V Vladimirov
2003-12-01
The excitation of low frequency modes of oscillations in a magnetized bi-ion or dusty plasma with parametric pumping of the magnetic ﬁeld is analysed. The equation of motion governing the perturbed plasma is derived and parametrically excited transverse modes propagating along the magnetic ﬁeld are found. With multiple ion species or charged dust present, a number of different circularly polarized modes can be excited. The stability of these modes is investigated as a function of the plasma parameters. The modulational instabilities of large amplitude normal modes, modiﬁed by the extra ion species or dust and propagating along the magnetic ﬁeld, are also investigated.
Energy Technology Data Exchange (ETDEWEB)
Frommen, C. [Marburg Univ. (Germany). Fachbereich Chemie; Pebler, J. [Marburg Univ. (Germany). Fachbereich Chemie
1995-05-01
Measurements of the {sup 57}Fe Moessbauer effect and of the magnetic susceptibilities on a single crystal have been performed on the quasi-1-d antiferromagnetic chain of (NH{sub 4}){sub 2}Mn{sub 0.98}Fe{sub 0.02}F{sub 5} as a function of temperature. Particular attention was paid to the region very near the Neel point. The Moessbauer spectra fitted by the Blume-Tjon model show definite relaxation effects, which are attributed to short-range order with temperature-dependent relaxation times. The soliton model of nonlinear excitations was applied. Experimental data confirm the predicted exponential temperature dependence of the thermal excitation of moving domain walls. From the activation energy a local anisotropy energy D/k of -3.9 K was derived. (orig.)
Simulations of Non-Linear Resistance De-Excitation of Synchronous Generators%同步发电机非线性电阻灭磁仿真研究
Institute of Scientific and Technical Information of China (English)
张扬
2011-01-01
De -excitation with non -linear resistance is usually adopted in large synchronous generators. This paper describes the Matlab Mathematical simulation models of the de -excitation with non -linear resistance with consideration given to the nonlinearity of no-load characteristic of generator and the induction effect of rotor damper winding. The de -excitation simulation of a 667 MW hydro-turbine generator in the Pubugou Hydropower Station is conducted with curves of the field current and voltage and the damping winding current on the d-axis obtained. At the same time, the magnetic energy absorbed by de-excitation resistor, field winding and damping winding on d-axis, the de-excitation time are also obtained, so a true and visual observation of the de-excitation process is provided.%同步发电机通常采用非线性电阻灭磁方式,建立了非线性电阻(包括碳化硅和氧化锌)灭磁的Matlab仿真模型.其中考虑了空载特性的非线性和转子阻尼绕组的效应.通过对某水电站的667 MW水轮发电机进行灭磁仿真,最终得出了磁场电流、电压、d轴阻尼绕组电流的变化情况,以及非线性电阻等各部分吸收的磁能和灭磁时间,从而更真实直观地展示了非线性电阻灭磁过程.
Theory and design of nonlinear metamaterials
Rose, Alec Daniel
If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers
Institute of Scientific and Technical Information of China (English)
谢建军; 吴晓
2012-01-01
研究碳纤维材料矩形单层索网在基础位移激励下的非线性振动问题,是索网抗震防震设计的基础.在考虑温度变化的基础上,建立了碳纤维矩形索网在基础位移激励下的非线性振动方程,采用Galerkin原理及KBM法求得了碳纤维材料矩形单层索网非线性振动的近似解.在把碳纤维索网与钢丝索网比较的基础上,讨论分析了温度、位移激励、振幅、阻尼等因素对矩形单层索网非线性振动的影响,得到了碳纤维索网振动特性优于钢丝索网振动特性的结论.%It was studied that the nonlinear vibration of rectangular cable net using carbon fiber cables under foundation displacement excitation,and it is the base of earthquake prevention design of cable net. Meanwhile its nonlinear vibration equation was presented on the basis of considering temperature changing. And the approximate solution of nonlinear vibration of rectangular cable mesh was given used Galerkin principle and KBM method. Then something that affects its nonlinear vibration, such as the amount of temperature changing, foundation displacement excitation, amplitude as well as damping was discussed with the comparison between steel cable and carbon fiber cable. At last the conclusions was got that the vibration characteristics of cable net using carbon fiber cables is superior to cable net using steel.
Institute of Scientific and Technical Information of China (English)
刘少斌
2011-01-01
研究碳纤维材料索桁架在主体结构位移激励下的非线性振动问题,是空间索结构抗震防震设计的基础.在考虑温度变化的基础上,建立碳纤维索桁架在主体结构位移激励下的非线性振动方程,采用Galerkin原理及Krylov-Bogo1iulov-Mitropolsky法求得碳纤维材料索桁架非线性振动的近似解.在将碳纤维索网与钢丝索网比较的基础上,讨论分析温度、位移激励、振幅、阻尼等因素对索桁架非线性振动的影响,得到碳纤维索桁架振动特性优于钢丝索桁架振动特性的结论.%It was studied that the nonlinear vibration of cable truss using carbon fiber cables under main structure displacement excitation, and it is the base of earthquake prevention design of cable net.Meanwhile its nonlinear vibration equation was presented on the basis of considering temperature changing.And the approximate solution of nonlinear vibration of cable truss was given used Galerkin principle and Krylov-Bogoliulov-Mitropolsky method.Then something that affects its nonlinear vibration, such as the amount of temperature changing, main structure displacement excitation, amplitude as well as damping was discussed with the comparison between steel cable and carbon fiber cable.At last the conclusions was got that the vibration characteristics of cable net using carbon fiber cables is superior to cable net using steel.
Maitra, Rahul; Akinaga, Yoshinobu; Nakajima, Takahito
2017-08-01
A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.
Nonlinear optical interactions in silicon waveguides
Kuyken, B.; Leo, F.; Clemmen, S.; Dave, U.; Van Laer, R.; Ideguchi, T.; Zhao, H.; Liu, X.; Safioui, J.; Coen, S.; Gorza, S. P.; Selvaraja, S. K.; Massar, S.; Osgood, R. M.; Verheyen, P.; Van Campenhout, J.; Baets, R.; Green, W. M. J.; Roelkens, G.
2017-03-01
The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.
Controlling Parametric Resonance
DEFF Research Database (Denmark)
Galeazzi, Roberto; Pettersen, Kristin Ytterstad
2012-01-01
Parametric resonance is a resonant phenomenon which takes place in systems characterized by periodic variations of some parameters. While seen as a threatening condition, whose onset can drive a system into instability, this chapter advocates that parametric resonance may become an advantage if t...
Auzinsh, M; Ferber, R; Gahbauer, F; Kalvans, L; Mozers, A; Spiss, A
2015-01-01
We studied alignment-to-orientation conversion caused by excited-state level crossings in a nonzero magnetic field of both atomic rubidium isotopes. Experimental measurements were performed on the transitions of the $D_2$ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. In the experiments laser induced fluorescence (LIF) components were observed at linearly polarized excitation and their difference was taken afterwards. By observing the two oppositely circularly polarized components we were able to see structures not visible in the difference graphs, which yields deeper insight into the processes responsible for these signals. We studied how these signals are dependent on laser power density and how they are affected when the exciting laser is tuned to different hyperfine tr...
Mishima, A.; Nasu, K.
1989-03-01
The one-dimensional extended Peierls-Hubbard model with half-filled-band electrons is studied in order to clarify the lattice relaxation path of the photogenerated charge-transfer excitation in halogen-bridged mixed-valence metal complexes. The ground and excited states are calculated within mean-field theory for electrons and the adiabatic approximation for phonons. It is concluded that the main origin of the photoinduced absorption is a distant pair of the hole-polaron and the electron-polaron. This distant pair is created not from the ground state of the self-trapped exciton (STE), but from the excited states of the STE through their autodissociation. This is consistent with the experiment on the excitation energy dependence of the photoinduced absorption yield.
Rayleigh-type parametric chemical oscillation.
Ghosh, Shyamolina; Ray, Deb Shankar
2015-09-28
We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.
Rayleigh-type parametric chemical oscillation
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Shyamolina; Ray, Deb Shankar, E-mail: pcdsr@iacs.res.in [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032 (India)
2015-09-28
We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.
Airy beam optical parametric oscillator.
Aadhi, A; Chaitanya, N Apurv; Jabir, M V; Vaity, Pravin; Singh, R P; Samanta, G K
2016-05-04
Airy beam, a non-diffracting waveform, has peculiar properties of self-healing and self-acceleration. Due to such unique properties, the Airy beam finds many applications including curved plasma wave-guiding, micro-particle manipulation, optically mediated particle clearing, long distance communication, and nonlinear frequency conversion. However, many of these applications including laser machining of curved structures, generation of curved plasma channels, guiding of electric discharges in a curved path, study of nonlinear propagation dynamics, and nonlinear interaction demand Airy beam with high power, energy, and wavelength tunability. Till date, none of the Airy beam sources have all these features in a single device. Here, we report a new class of coherent sources based on cubic phase modulation of a singly-resonant optical parametric oscillator (OPO), producing high-power, continuous-wave (cw), tunable radiation in 2-D Airy intensity profile existing over a length >2 m. Based on a MgO-doped periodically poled LiNbO3 crystal pumped at 1064 nm, the Airy beam OPO produces output power more than 8 W, and wavelength tunability across 1.51-1.97 μm. This demonstration gives new direction for the development of sources of arbitrary structured beams at any wavelength, power, and energy in all time scales (cw to femtosecond).
A quantum parametric oscillator with trapped ions
Ding, Shiqian; Hablutzel, Roland; Loh, Huanqian; Matsukevich, Dzmitry
2015-01-01
A system of harmonic oscillators coupled via nonlinear interaction is a fundamental model in many branches of physics, from biophysics to electronics and condensed matter physics. In quantum optics, weak nonlinear interaction between light modes has enabled, for example, the preparation of squeezed states of light and generation of entangled photon pairs. While strong nonlinear interaction between the modes has been realized in circuit QED systems, achieving significant interaction strength on the level of single quanta in other physical systems remains a challenge. Here we experimentally demonstrate such interaction that is equivalent to photon up- and down-conversion using normal modes of motion in a system of two Yb ions. The nonlinearity is induced by the intrinsic anharmonicity of the Coulomb interaction between the ions and can be used to simulate fully quantum operation of a degenerate optical parametric oscillator. We exploit this interaction to directly measure the parity and Wigner functions of ion ...
Silva, Clodoaldo J.; Daqaq, Mohammed F.
2017-02-01
Despite the shear amount of research studies on nonlinear flexural dynamics of cantilever beams, very few efforts address the practical geometry involving a constant thickness and linearly-varying width. This stems from the nature of the associated linear eigenvalue problem which cannot be easily solved in closed form. In this paper, we present a closed-form solution to this particular linear eigenvalue problem in the form of a general Meijer-G differential equation for which a solution is readily available in the shape of the Meijer-G functions. Using this approach, the exact linear modal frequencies and shapes are obtained and used in the discretization of the nonlinear partial-differential equation describing the dynamics of the system. The discretized system of ordinary-differential equations is then solved using the method of multiple scales to obtain an approximate analytical solution describing the primary resonance behavior of a given vibration mode. An analytical expression for the modal effective nonlinearity is obtained and used to analyze the influence of the beam's tapering on the nonlinear primary resonance behavior of the response (softening/hardening). Results are then compared to a finite element (FE) solution of the linear eigenvalue problem in which the modal shapes obtained using the FE method are fit into a set of orthogonal polynomial functions and used to discretize the nonlinear problem. It is shown that, while the modal frequencies obtained using the FE method approximate those obtained analytically with negligible error (less than 1%), there is a substantial error in the resulting estimates of the modal effective nonlinearity. This indicates that, even negligible errors in the approximate solution of the linear problem, can propagate to become significant when analyzing the nonlinear problem further reinforcing the importance of the exact solution.
Institute of Scientific and Technical Information of China (English)
王俭臣; 齐晓慧; 单甘霖
2015-01-01
飞行器在全包络上表现出明显的气动参数不确定性，以某无人机纵向模型为研究对象，提出一种不确定参数在线估计的自适应观测器故障重构方法。首先，将系统状态方程描述为一类带时变参数的仿射非线性结构，在参数增广系统能观性分析基础上，采用增广容积卡尔曼滤波（augmented cubature Kalman filter，ACKF）算法实现气动参数在线估计，以克服鲁棒性死区故障检测方法的保守性，提高检测灵敏度。其次，将所估计参数用于自适应观测器设计，由于 Lie 导数分析方法保证了对象系统的能观性，故系统不必满足文献方法中的特定规范形式；在此基础上，给出了故障检测自适应阈值和故障参数调节律，并分析了估计误差的收敛性。仿真实验表明了所提方法的有效性。%Aiming at the obvious aerodynamic parametric uncertainties of aircraft in the full flight envelope, a fault reconstruction method based on a modified adaptive observer is proposed.The adaptive observer is im-proved by the uncertain parameter estimation process and validated on the longitudinal model of some unmanned vehicle.According to this method,the longitudinal model is described as an affine nonlinear structure with time variant parameters,and the observability of its parameter-augmented model is analyzed.On this basis,to deal with conservatism of the robustness dead zone technique in fault detection and refine the detection sensitivity, aerodynamic parameters are identified on line by the augmented cubature Kalman filter (ACKF)algorithm. Then the parameter estimations are adopted in adaptive observer design.As the Lie derivative based criterion guarantees observability of the object system,the literature restriction that the object system must be within some particular structure is avoided.Based on this,the adaptive fault detection threshold and the fault parame-ter regulation law are derived
Parametrizing arbitrary galaxy morphologies: potentials and pitfalls
Andrae, René; Jahnke, Knud; Melchior, Peter
2011-02-01
Given the enormous galaxy data bases of modern sky surveys, parametrizing galaxy morphologies is a very challenging task due to the huge number and variety of objects. We assess the different problems faced by existing parametrization schemes (CAS, Gini, M20, Sérsic profile, shapelets) in an attempt to understand why parametrization is so difficult and in order to suggest improvements for future parametrization schemes. We demonstrate that morphological observables (e.g. steepness of the radial light profile, ellipticity, asymmetry) are intertwined and cannot be measured independently of each other. We present strong arguments in favour of model-based parametrization schemes, namely reliability assessment, disentanglement of morphological observables and point spread function modelling. Furthermore, we demonstrate that estimates of the concentration and Sérsic index obtained from the Zurich Structure & Morphology catalogue are in excellent agreement with theoretical predictions. We also demonstrate that the incautious use of the concentration index for classification purposes can cause a severe loss of the discriminative information contained in a given data sample. Moreover, we show that, for poorly resolved galaxies, concentration index and M20 suffer from strong discontinuities, i.e. similar morphologies are not necessarily mapped to neighbouring points in the parameter space. This limits the reliability of these parameters for classification purposes. Two-dimensional Sérsic profiles accounting for centroid and ellipticity are identified as the currently most reliable parametrization scheme in the regime of intermediate signal-to-noise ratios and resolutions, where asymmetries and substructures do not play an important role. We argue that basis functions provide good parametrization schemes in the regimes of high signal-to-noise ratios and resolutions. Concerning Sérsic profiles, we show that scale radii cannot be compared directly for profiles of different
On optimal performance of nonlinear energy sinks in multiple-degree-of-freedom systems
Tripathi, Astitva; Grover, Piyush; Kalmár-Nagy, Tamás
2017-02-01
We study the problem of optimizing the performance of a nonlinear spring-mass-damper attached to a class of multiple-degree-of-freedom systems. We aim to maximize the rate of one-way energy transfer from primary system to the attachment, and focus on impulsive excitation of a two-degree-of-freedom primary system with an essentially nonlinear attachment. The nonlinear attachment is shown to be able to perform as a 'nonlinear energy sink' (NES) by taking away energy from the primary system irreversibly for some types of impulsive excitations. Using perturbation analysis and exploiting separation of time scales, we perform dimensionality reduction of this strongly nonlinear system. Our analysis shows that efficient energy transfer to nonlinear attachment in this system occurs for initial conditions close to homoclinic orbit of the slow time-scale undamped system, a phenomenon that has been previously observed for the case of single-degree-of-freedom primary systems. Analytical formulae for optimal parameters for given impulsive excitation input are derived. Generalization of this framework to systems with arbitrary number of degrees-of-freedom of the primary system is also discussed. The performance of both linear and nonlinear optimally tuned attachments is compared. While NES performance is sensitive to magnitude of the initial impulse, our results show that NES performance is more robust than linear tuned mass damper to several parametric perturbations. Hence, our work provides evidence that homoclinic orbits of the underlying Hamiltonian system play a crucial role in efficient nonlinear energy transfers, even in high dimensional systems, and gives new insight into robustness of systems with essential nonlinearity.
Semiactive variable stiffness control for parametric vibration of cables
Institute of Scientific and Technical Information of China (English)
Li Hui; Chen Wenli; Ou Jinping
2006-01-01
In this paper, a semiactive variable stiffness (SVS) device is used to decrease cable oscillations caused by parametric excitation, and the equation of motion of the parametric vibration of the cable with this SVS device is presented.The ON/OFF control algorithm is used to operate the SVS control device. The vibration response of the cable with the SVS device is numerically studied for a variety of additional stiffness combinations in both the frequency and time domains and for both parametric and classical resonance vibration conditions. The numerical studies further consider the cable sag effect.From the numerical results, it is shown that the SVS device effectively suppresses the cable resonance vibration response, and as the stiffness of the device increases, the device achieves greater suppression of vibration. Moreover, it was shown that the SVS device increases the critical axial displacement of the excitation under cable parametric vibration conditions.
Decomposing a pulsed optical parametric amplifier into independent squeezers
Lvovsky, A I; Banaszek, K
2006-01-01
We discuss the concept of characteristic squeezing modes applied to a travelling-wave optical parametric amplifier pumped by an ultrashort pulse. The characteristic modes undergo decoupled single-mode squeezing transformations, and therefore they form a useful basis to describe the evolution of the entire multimode system. This provides an elegant and intuitive picture of quantum statistical properties of parametric fluorescence. We analyse the efficiency of detecting quadrature squeezing, and present results of numerical calculations for a realistic nonlinear medium.
Institute of Scientific and Technical Information of China (English)
赵洪山; 兰晓明; 周雪青
2013-01-01
This paper presented a multi-machine power system nonlinear excitation predictive control method which combined model predictive control and model reduction technology in order to tackle the problem that the optimal excitation control and the traditional proportional-integral-derivative (PID) excitation control could not consider the constraint of states and input of the system, and to reduce the complexity of the numerical calculation of high order dynamic model in nonlinear excitation predictive control. First, The theory of empirical Gramians balanced reduction was used to reduce the orders of power system nonlinear dynamic model to save the computing time of open-loop optimization of model predictive control. Then, it used the least-square residual of system input and output as the objection function, using reduced dynamic model as equivalent constraint and the change limits of system output and control input as unequivalent constrain to establish the excitation predictive control model based on reduced model. Next, the interior-point method was used to solve the optimal problem meanwhile to realize multi-step prediction. Finally, we took advantage of a four-machine power system to verify the effectiveness of the predictive control method. The simulation results show that nonlinear excitation predictive control method based on balanced reduced model for the multi-machine power systems can greatly shorten the optimization time, meanwhile maintain the voltage of generator terminals within the set points and improve the stability of power system.% 将预测控制与模型降阶技术相结合提出一种基于平衡降阶模型的多机电力系统非线性励磁预测控制方法，以解决最优励磁控制和传统比例积分微分励磁控制无法考虑系统复杂状态和控制输入约束的问题，并且降低非线性励磁预测控制高阶动态模型数值计算的复杂性。首先，利用经验Gramians 平衡降阶原理，对电力系统
Resource Letter NO-1: Nonlinear Optics
Garmire, Elsa
2011-03-01
This Resource Letter provides a guide to the literature on nonlinear optics. Books, journals, and websites are introduced that cover the general subject. Journal articles and websites are cited covering the following topics: second-order nonlinearities in transparent media including second-harmonic generation and optical parametric oscillation, third-order and higher nonlinearities, nonlinear refractive index, absorptive nonlinearities such as saturable absorption and multiphoton absorption, and scattering nonlinearities such as stimulated Raman scattering and stimulated Brillouin scattering. Steady-state and transient phenomena, fiber optics, solitons, nonlinear wave mixing, optical phase conjugation, nonlinear spectroscopy, and multiphoton microscopy are all outlined.
Yang, Tianqi; Huang, Xiaoting; Zhou, Hong; Wu, Guangheng; Lai, Tianshu
2016-05-30
MoS2 films are grown on SiO2/Si substrates by chemical vapor deposition. The vibrational properties of optical phonons of mono-, bi- and multilayer MoS2 are studied by Raman scattering spectroscopy over temperature range from 90 to 540 K with 514.5 nm and 785 nm lasers. The Raman peaks of E2g1 and A1g modes are observed simultaneously for mono-, bi- and multilayer MoS2 with 514.5 nm laser, but only the Raman peak of E2g1 mode is seen for monolayer MoS2 as 785 nm laser is used, revealing electron-phonon exchange excitation mechanism of A1g mode for the first time. The Raman shifts of E2g1 and A1g modes present obvious nonlinear temperature dependence. A semi-quantitative model is used to fit the nonlinear temperature dependence of Raman shifts which matches well to experimental data. Meanwhile, the fitting results reveal that the nonlinear temperature dependence of Raman shifts of E2g1 mode mainly originates from three-phonon anharmonic effect, while one of A1g mode is contributed by stronger three- and weaker four-phonon anharmonic effects cooperatively but two contributions are comparable in intensity.
Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A
2017-04-28
Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Current-driven non-linear magnetodynamics in exchange-biased spin valves
Energy Technology Data Exchange (ETDEWEB)
Seinige, Heidi; Wang, Cheng; Tsoi, Maxim, E-mail: tsoi@physics.utexas.edu [Physics Department, University of Texas at Austin, Austin, Texas 78712 (United States)
2015-05-07
This work investigates the excitation of parametric resonance in exchange-biased spin valves (EBSVs). Using a mechanical point contact, high density dc and microwave currents were injected into the EBSV sample. Observing the reflected microwave power and the small rectification voltage that develops across the contact allows detecting the current-driven magnetodynamics not only in the bulk sample but originating exclusively from the small contact region. In addition to ferromagnetic resonance (FMR), parametric resonance at twice the natural FMR frequency was observed. In contrast to FMR, this non-linear resonance was excited only in the vicinity of the point contact where current densities are high. Power-dependent measurements displayed a typical threshold-like behavior of parametric resonance and a broadening of the instability region with increasing power. Parametric resonance showed a linear shift as a function of applied dc bias which is consistent with the field-like spin-transfer torque induced by current on magnetic moments in EBSV.
Sato, Shunsuke A.; Taniguchi, Yasutaka; Shinohara, Yasushi; Yabana, Kazuhiro
2015-12-01
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
Energy Technology Data Exchange (ETDEWEB)
Sato, Shunsuke A. [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Taniguchi, Yasutaka [Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan); Department of Medical and General Sciences, Nihon Institute of Medical Science, 1276 Shimogawara, Moroyama-Machi, Iruma-Gun, Saitama 350-0435 (Japan); Shinohara, Yasushi [Max Planck Institute of Microstructure Physics, 06120 Halle (Germany); Yabana, Kazuhiro [Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8571 (Japan); Center for Computational Science, University of Tsukuba, Tsukuba 305-8571 (Japan)
2015-12-14
We develop methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta-generalized gradient approximation was proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional was proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt the predictor-corrector step for a stable time evolution. We have developed a method to evaluate electronic excitation energy without referring to the energy functional which is unknown for the TB-mBJ potential. For the HSE functional, we have developed a method for the operation of the Fock-like term in Fourier space to facilitate efficient use of massive parallel computers equipped with graphic processing units. We compare electronic excitations in silicon and germanium induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: they are close to each other using TB-mBJ and HSE and are much smaller in LDA. At high laser intensities close to the damage threshold, electronic excitation energies do not differ much among the three cases.
Parametric decay of parallel and oblique Alfven waves in the expanding solar wind
Del Zanna, L; Landi, S; Verdini, A; Velli, M
2014-01-01
The long-term evolution of large-amplitude Alfven waves propagating in the solar wind is investigated by performing two-dimensional MHD simulations within the expanding box model. The linear and nonlinear phases of the parametric decay instability are studied for both circularly polarized waves in parallel propagation and for arc-polarized waves in oblique propagation. The non-monochromatic case is also considered. In the oblique case, the direct excitation of daughter modes transverse to the local background field is found for the first time in an expanding environment, and this transverse cascade seems to be favored for monochromatic mother waves. The expansion effect reduces the instability growth rate, and it can even suppress its onset for the lowest frequency modes considered here, possibly explaining the persistence of these outgoing waves in the solar wind.
Intramolecular and nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Davis, M.J. [Argonne National Laboratory, IL (United States)
1993-12-01
Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.
A bifurcation analysis of boiling water reactor on large domain of parametric spaces
Pandey, Vikas; Singh, Suneet
2016-09-01
The boiling water reactors (BWRs) are inherently nonlinear physical system, as any other physical system. The reactivity feedback, which is caused by both moderator density and temperature, allows several effects reflecting the nonlinear behavior of the system. Stability analyses of BWR is done with a simplified, reduced order model, which couples point reactor kinetics with thermal hydraulics of the reactor core. The linear stability analysis of the BWR for steady states shows that at a critical value of bifurcation parameter (i.e. feedback gain), Hopf bifurcation occurs. These stable and unstable domains of parametric spaces cannot be predicted by linear stability analysis because the stability of system does not include only stability of the steady states. The stability of other dynamics of the system such as limit cycles must be included in study of stability. The nonlinear stability analysis (i.e. bifurcation analysis) becomes an indispensable component of stability analysis in this scenario. Hopf bifurcation, which occur with one free parameter, is studied here and it formulates birth of limit cycles. The excitation of these limit cycles makes the system bistable in the case of subcritical bifurcation whereas stable limit cycles continues in an unstable region for supercritical bifurcation. The distinction between subcritical and supercritical Hopf is done by two parameter analysis (i.e. codimension-2 bifurcation). In this scenario, Generalized Hopf bifurcation (GH) takes place, which separates sub and supercritical Hopf bifurcation. The various types of bifurcation such as limit point bifurcation of limit cycle (LPC), period doubling bifurcation of limit cycles (PD) and Neimark-Sacker bifurcation of limit cycles (NS) have been identified with the Floquet multipliers. The LPC manifests itself as the region of bistability whereas chaotic region exist because of cascading of PD. This region of bistability and chaotic solutions are drawn on the various
Institute of Scientific and Technical Information of China (English)
王波; 薛纭
2012-01-01
The motion stability of axially moving viscoelastic beams subjected to the parametrically excited tension is presented. The parametric vibration of axially moving beams is studied in this paper. The axial tension is characterized as a simple harmonic variation about the initial tension. The material time derivative is used in the viscoelastic constitutive relation. Asymptotic analysis is proposed to investigate the governing equation of an axially accelerating viscoelastic beam via the method of multiple scales. Beams are always fastened up by elastic joints at both ends. The supporting conditions may be formulated as simple supports with torsion springs. If the axial speed variation frequency approaches the sum of arbitrary two natural frequencies or the twice arbitrary natural frequency, the combined resonance or principal parametric resonance may occur. Analytical expressions of the instability boundary are obtained for summation and principal parametric resonance. Numerical examples show the effects of the viscous damping: whenever the instability regions for either the combined or the principal parametric resonance occcur, they will both decras while the viscous damping is increasing.%研究了轴向匀速运动黏弹性梁的运动稳定性.考察轴向拉力在初始拉力的基础上做微小简谐变化的参激振动.建立了受轴向拉力参数激励时轴向运动梁的控制微分方程,黏弹性本构关系引入了物质时间导数.轴向运动梁两端的边界受由带有扭转弹簧的套筒铰支约束的混杂边界条件.应用多尺度法直接求解轴向运动梁参激振动的控制方程,并导出了当扰动拉力的频率接近未扰系统任意两个固有频率之和及任一固有频率2倍时所发生的组合共振和主共振的稳定边界方程.数值例子给出了黏弹阻尼对轴向运动黏弹性梁参激振动发生组合共振和主共振的影响,结果显示:不论组合共振还是主共振发生时,失稳区域均