Nonlinearity induced synchronization enhancement in mechanical oscillators
Czaplewski, David A.; Lopez, Omar; Guest, Jeffrey R.; Antonio, Dario; Arroyo, Sebastian I.; Zanette, Damian H.
2018-05-08
An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.
Single-ion nonlinear mechanical oscillator
International Nuclear Information System (INIS)
Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.
2010-01-01
We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.
Computing with networks of nonlinear mechanical oscillators.
Directory of Open Access Journals (Sweden)
Jean C Coulombe
Full Text Available As it is getting increasingly difficult to achieve gains in the density and power efficiency of microelectronic computing devices because of lithographic techniques reaching fundamental physical limits, new approaches are required to maximize the benefits of distributed sensors, micro-robots or smart materials. Biologically-inspired devices, such as artificial neural networks, can process information with a high level of parallelism to efficiently solve difficult problems, even when implemented using conventional microelectronic technologies. We describe a mechanical device, which operates in a manner similar to artificial neural networks, to solve efficiently two difficult benchmark problems (computing the parity of a bit stream, and classifying spoken words. The device consists in a network of masses coupled by linear springs and attached to a substrate by non-linear springs, thus forming a network of anharmonic oscillators. As the masses can directly couple to forces applied on the device, this approach combines sensing and computing functions in a single power-efficient device with compact dimensions.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Shocks, singularities and oscillations in nonlinear optics and fluid mechanics
Santo, Daniele; Lannes, David
2017-01-01
The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .
Analytical Solutions to Non-linear Mechanical Oscillation Problems
DEFF Research Database (Denmark)
Kaliji, H. D.; Ghadimi, M.; Barari, Amin
2011-01-01
In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...
Classical Yang-Mills mechanics. Nonlinear colour oscillations
International Nuclear Information System (INIS)
Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.
1981-01-01
A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru
Energy Technology Data Exchange (ETDEWEB)
Chandra, J; Scott, A C
1983-01-01
Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.
Modeling nonlinearities in MEMS oscillators.
Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A
2013-08-01
We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.
Oscillators from nonlinear realizations
Kozyrev, N.; Krivonos, S.
2018-02-01
We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.
Oscillations in nonlinear systems
Hale, Jack K
2015-01-01
By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa
Nonlinear (Anharmonic Casimir Oscillator
Directory of Open Access Journals (Sweden)
Habibollah Razmi
2011-01-01
Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.
International Nuclear Information System (INIS)
Macias-Diaz, J.E.; Puri, A.
2007-01-01
In the present Letter, we simulate the propagation of binary signals in semi-infinite, mechanical chains of coupled oscillators harmonically driven at the end, by making use of the recently discovered process of nonlinear supratransmission. Our numerical results-which are based on a brand-new computational technique with energy-invariant properties-show an efficient and reliable transmission of information
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
... are derived, and the relevant properties and features of oscillating solitons are illustrated. Oscillating solitons are controlled by the reciprocal of the group velocity and Kerr nonlinearity. Results of this paper will be valuable to the study of dispersion-managed optical communication system and mode-locked fibre lasers.
Cubication of conservative nonlinear oscillators
International Nuclear Information System (INIS)
Belendez, Augusto; Alvarez, Mariela L; Fernandez, Elena; Pascual, Inmaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show that at resona......We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Nonlinearity in oscillating bridges
Directory of Open Access Journals (Sweden)
Filippo Gazzola
2013-09-01
Full Text Available We first recall several historical oscillating bridges that, in some cases, led to collapses. Some of them are quite recent and show that, nowadays, oscillations in suspension bridges are not yet well understood. Next, we survey some attempts to model bridges with differential equations. Although these equations arise from quite different scientific communities, they display some common features. One of them, which we believe to be incorrect, is the acceptance of the linear Hooke law in elasticity. This law should be used only in presence of small deviations from equilibrium, a situation which does not occur in widely oscillating bridges. Then we discuss a couple of recent models whose solutions exhibit self-excited oscillations, the phenomenon visible in real bridges. This suggests a different point of view in modeling equations and gives a strong hint how to modify the existing models in order to obtain a reliable theory. The purpose of this paper is precisely to highlight the necessity of revisiting the classical models, to introduce reliable models, and to indicate the steps we believe necessary to reach this target.
Oscillating solitons in nonlinear optics
Indian Academy of Sciences (India)
The study of solitons in those physical systems reveals some exciting .... With the following power series expansions for g(z,t) and f(z,t): g(z,t) = εg1(z,t) + ... If nonlinearity γ (z) is also taken as a function in figure 1b, the periodic and oscillation.
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.
2009-06-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.; Salama, Khaled N.
2009-01-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
Directory of Open Access Journals (Sweden)
Paulius Palevicius
2014-01-01
Full Text Available Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.
Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas
2014-01-01
Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms. PMID:24451467
Palevicius, Paulius; Ragulskis, Minvydas; Palevicius, Arvydas; Ostasevicius, Vytautas
2014-01-21
Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.
A simple approach to nonlinear oscillators
International Nuclear Information System (INIS)
Ren Zhongfu; He Jihuan
2009-01-01
A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.
Qualitative analysis of nonlinear power oscillation in NSRR
International Nuclear Information System (INIS)
Suzudo, T.; Shinohara, Y.
1994-01-01
The performance of the automatic control system of NSRR is investigated experimentally and theoretically in connection with the power oscillation. A subsystem in the automatic control system relevant to the onset of the power oscillation is determined, and it is found that the subsystem possesses nonlinearity. Although the detailed mechanism of the nonlinearity cannot be identified because of lack of signals measured inside the subsystem, the input and output signals imply that the nonlinearity is a sort of backlash. A simplified reactor dynamic model with backlash simulates the dynamics of the NSRR power oscillation. (Author)
Nonlinear analysis of ring oscillator circuits
Ge, Xiaoqing
2010-06-01
Using nonlinear systems techniques, we analyze the stability properties and synchronization conditions for ring oscillator circuits, which are essential building blocks in digital systems. By making use of its cyclic structure, we investigate local and global stability properties of an n-stage ring oscillator. We present a sufficient condition for global asymptotic stability of the origin and obtain necessity if the ring oscillator consists of identical inverter elements. We then give a synchronization condition for identical interconnected ring oscillators.
Nonlinear analysis of ring oscillator circuits
Ge, Xiaoqing; Arcak, Murat; Salama, Khaled N.
2010-01-01
Using nonlinear systems techniques, we analyze the stability properties and synchronization conditions for ring oscillator circuits, which are essential building blocks in digital systems. By making use of its cyclic structure, we investigate local and global stability properties of an n-stage ring oscillator. We present a sufficient condition for global asymptotic stability of the origin and obtain necessity if the ring oscillator consists of identical inverter elements. We then give a synchronization condition for identical interconnected ring oscillators.
PT -symmetric dimer of coupled nonlinear oscillators
Indian Academy of Sciences (India)
We provide a systematic analysis of a prototypical nonlinear oscillator ... recently, a number of nonlinear variants have been explored, like split-ring resonator chain .... Note that these solutions are valid for any value of ǫ (and hence δ) including ǫ ..... [16] M Abramowitz and I A Stegun, Handbook of mathematical functions ...
Momeni, F.; Naderi, M. H.
2018-05-01
In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.
Analytical solution of strongly nonlinear Duffing oscillators
El-Naggar, A.M.; Ismail, G.M.
2016-01-01
In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε)α=α(ε) is defined such that the value of α is always small regardless of the magnitude of the original parameter εε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to αα. Approximate solution obtained by the present method is compared with the solution of energy balance m...
Three-dimensional analysis of nonlinear plasma oscillation
International Nuclear Information System (INIS)
Miano, G.
1990-01-01
In an underdense plasma a large-amplitude plasma oscillation may be produced by the beating of two external and colinear electromagnetic waves with a frequency difference approximately equal to the plasma frequency - plasma beat wave (PBW) resonant mechanism. The plasma oscillations are driven by the ponderomotive force arising from the beating of the two imposed electromagnetic waves. In this paper two pump electromagnetic waves with arbitrary transverse profiles have been considered. The plasma is described by using the three dimensinal weakly relativistic fluid equations. The nonlinear plasma oscillation dynamics is studied by using the eulerian description, the averaging and the multiple time scale methods. Unlike the linear theory a strong cross field coupling between longitudinal ans transverse electric field components of the plasma oscillation comes out, resulting in a nonlinear phase change and energy transfer between the two components. Unlike the one-dimensional nonlinear theory, the nonlinear frequency shift is caused by relativistic effects as well as by convective effects and electromagnetic field generated from the three dimensional plasma oscillation. The large amplitude plasma oscillation dynamics produced by a bunched relativistic electron beam with arbitrary transverse profile - plasma wave field (PWF) - or by a high power single frequency short electromagnetic pulse with arbitrary transverse profile - electromagnetic plasma wake field (EPWF) - may be described by means of the present theory. (orig.)
Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.
Chen, Changyao; Zanette, Damián H; Czaplewski, David A; Shaw, Steven; López, Daniel
2017-05-26
Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.
Chaotic synchronization of two complex nonlinear oscillators
International Nuclear Information System (INIS)
Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.
2009-01-01
Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
Detecting Nonlinear Oscillations in Broadband Signals
Czech Academy of Sciences Publication Activity Database
Vejmelka, Martin; Paluš, Milan
2009-01-01
Roč. 19, - (2009), 1015114-1-1015114-7 ISSN 1054-1500 R&D Projects: GA MŠk 7E08027 EU Projects: European Commission(XE) 200728 - BRAINSYNC Institutional research plan: CEZ:AV0Z10300504 Keywords : nonlinear dynamical systems * oscillations * random processes * time series analysis * EEG Subject RIV: FH - Neurology Impact factor: 1.795, year: 2009
Analytical solution of strongly nonlinear Duffing oscillators
Directory of Open Access Journals (Sweden)
A.M. El-Naggar
2016-06-01
Full Text Available In this paper, a new perturbation technique is employed to solve strongly nonlinear Duffing oscillators, in which a new parameter α=α(ε is defined such that the value of α is always small regardless of the magnitude of the original parameter ε. Therefore, the strongly nonlinear Duffing oscillators with large parameter ε are transformed into a small parameter system with respect to α. Approximate solution obtained by the present method is compared with the solution of energy balance method, homotopy perturbation method, global error minimization method and lastly numerical solution. We observe from the results that this method is very simple, easy to apply, and gives a very good accuracy not only for small parameter εbut also for large values of ε.
Nonlinear oscillations in coriolis based gyroscopes
Directory of Open Access Journals (Sweden)
Dag Kristiansen
1999-01-01
Full Text Available In this paper we model and analyze nonlinear oscillations which are known to exist in some Coriolis based gyroscopes due to large amplitude excitation in the drive loop. A detailed derivation of a dynamic model for a cylinder gyroscope which includes geometric nonlinearities is given, and energy transfer between the system's modes are analyzed using perturbation theory and by proposing a simplified model. The model is also simulated, and the results are shown to give an accurate description of the experimental results. This work is done in order to gain a better understanding of the gyroscope's dynamics, and is intended to be a starting point for designing nonlinear observers and vibration controllers for the gyroscope in order to increase the performance.
Energy Technology Data Exchange (ETDEWEB)
Blaquiere, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1961-07-01
The author completes the two-parameter diagram theory which he has previously explained, by giving a geometric criterion of stability for a non-linear system under forced conditions. After two simple geometric transformations of the diagram he obtains the separators which are the boundary conditions for the zones of stability. (author) [French] L'auteur complete la theorie du diagramme a deux parametres, qu'il a anterieurement exposee, par l'enonce d'un critere geometrique de stabilite, relatif aux regimes forces d'un systeme non lineaire. Il obtient, par deux transformations geometriques simples du diagramme, les separatrices qui delimitent les zones de stabilite. (auteur)
International Nuclear Information System (INIS)
Khoroshun, L.P.
1995-01-01
The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero
Sensitivity and Nonlinearity of Thermoacoustic Oscillations
Juniper, Matthew P.; Sujith, R. I.
2018-01-01
Nine decades of rocket engine and gas turbine development have shown that thermoacoustic oscillations are difficult to predict but can usually be eliminated with relatively small ad hoc design changes. These changes can, however, be ruinously expensive to devise. This review explains why linear and nonlinear thermoacoustic behavior is so sensitive to parameters such as operating point, fuel composition, and injector geometry. It shows how nonperiodic behavior arises in experiments and simulations and discusses how fluctuations in thermoacoustic systems with turbulent reacting flow, which are usually filtered or averaged out as noise, can reveal useful information. Finally, it proposes tools to exploit this sensitivity in the future: adjoint-based sensitivity analysis to optimize passive control designs and complex systems theory to warn of impending thermoacoustic oscillations and to identify the most sensitive elements of a thermoacoustic system.
Complex behavior in chains of nonlinear oscillators.
Alonso, Leandro M
2017-06-01
This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.
Breaking of ensembles of linear and nonlinear oscillators
International Nuclear Information System (INIS)
Buts, V.A.
2016-01-01
Some results concerning the study of the dynamics of ensembles of linear and nonlinear oscillators are stated. It is shown that, in general, a stable ensemble of linear oscillator has a limited number of oscillators. This number has been defined for some simple models. It is shown that the features of the dynamics of linear oscillators can be used for conversion of the low-frequency energy oscillations into high frequency oscillations. The dynamics of coupled nonlinear oscillators in most cases is chaotic. For such a case, it is shown that the statistical characteristics (moments) of chaotic motion can significantly reduce potential barriers that keep the particles in the capture region
Nonlinear resonance in Duffing oscillator with fixed and integrative ...
Indian Academy of Sciences (India)
We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Dufﬁng oscillator with two types of time-delayed feedbacks, namely, ﬁxed and integrative. Particularly, we analyse the effect of the time-delay parameter and the strength of the ...
Nonlinear resonance in Duffing oscillator with fixed and integrative ...
Indian Academy of Sciences (India)
2012-03-02
Mar 2, 2012 ... Abstract. We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Duffing oscillator with two types of time-delayed feedbacks, namely, fixed and integrative. Particularly, we analyse the effect of the time-delay parameter α and the ...
Nonlinear dynamics in micromechanical and nanomechanical resonators and oscillators
Dunn, Tyler
In recent years, the study of nonlinear dynamics in microelectromechanical and nanoelectromechanical systems (MEMS and NEMS) has attracted considerable attention, motivated by both fundamental and practical interests. One example is the phenomenon of stochastic resonance. Previous measurements have established the presence of this counterintuitive effect in NEMS, showing that certain amounts of white noise can effectively amplify weak switching signals in nanomechanical memory elements and switches. However, other types of noise, particularly noises with 1/falpha spectra, also bear relevance in these and many other systems. At a more fundamental level, the role which noise color plays in stochastic resonance remains an open question in the field. To these ends, this work presents systematic measurements of stochastic resonance in a nanomechanical resonator using 1/f alpha and Ornstein-Uhlenbeck noise types. All of the studied noise spectra induce stochastic resonance, proving that colored noise can also be beneficial; however, stronger noise correlations suppress the effect, decreasing the maximum signal-to-noise ratio and increasing the optimal noise intensity. Evidence suggests that 1/falpha noise spectra with increasing noise color lead to increasingly asymmetric switching, reducing the achievable amplification. Another manifestly nonlinear effect anticipated in these systems is modal coupling. Measurements presented here demonstrate interactions between various mode types on a wide scale, providing the first reported observations of coupling in bulk longitudinal modes of MEMS. As a result of anharmonic elastic effects, each mode shifts in frequency by an amount proportional to the squared displacement (or energy) of a coupled mode. Since all resonator modes couple in this manner, these effects enable nonlinear measurement of energy and mechanical nonlinear signal processing across a wide range of frequencies. Finally, while these experiments address nonlinear
Nonlinear Oscillations in Biology and Chemistry
1986-01-01
This volume contains the proceedings of a meeting entitled 'Nonlinear Oscillations in Biology and Chemistry', which was held at the University of Utah May 9-11,1985. The papers fall into four major categories: (i) those that deal with biological problems, particularly problems arising in cell biology, (ii) those that deal with chemical systems, (iii) those that treat problems which arise in neurophysiology, and (iv), those whose primary emphasis is on more general models and the mathematical techniques involved in their analysis. Except for the paper by Auchmuty, all are based on talks given at the meeting. The diversity of papers gives some indication of the scope of the meeting, but the printed word conveys neither the degree of interaction between the participants nor the intellectual sparks generated by that interaction. The meeting was made possible by the financial support of the Department of Mathe matics of the University of Utah. I am indebted to Ms. Toni Bunker of the Department of Mathematics for...
Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane
Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.
2018-01-01
We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that
Westra, H.J.R.
2012-01-01
In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like
Experimental analysis of nonlinear oscillations in the undergraduate physics laboratory
International Nuclear Information System (INIS)
Moreno, R; Page, A; Riera, J; Hueso, J L
2014-01-01
In this paper, we present a simple experiment to introduce the nonlinear behaviour of oscillating systems in the undergraduate physics laboratory. The transverse oscillations of a spring allow reproduction of three totally different scenarios: linear oscillations, nonlinear oscillations reducible to linear for small displacements, and intrinsically nonlinear oscillations. The chosen approach consists of measuring the displacements using video photogrammetry and computing the velocities and the accelerations by means of a numerical differentiation algorithm. In this way, one can directly check the differential equation of the motion without having to integrate it, or perform an experimental study of the potential energy in each of the analysed scenarios. This experiment allows first year students to reflect on the consequences and the limits of the linearity assumption for small displacements that is so often made in technical studies. (paper)
Forced oscillation of hyperbolic equations with mixed nonlinearities
Directory of Open Access Journals (Sweden)
Yutaka Shoukaku
2012-04-01
Full Text Available In this paper, we consider the mixed nonlinear hyperbolic equations with forcing term via Riccati inequality. Some sufficient conditions for the oscillation are derived by using Young inequality and integral averaging method.
Oscillation criteria for fourth-order nonlinear delay dynamic equations
Directory of Open Access Journals (Sweden)
Yunsong Qi
2013-03-01
Full Text Available We obtain criteria for the oscillation of all solutions to a fourth-order nonlinear delay dynamic equation on a time scale that is unbounded from above. The results obtained are illustrated with examples
Oscillation criteria for third order delay nonlinear differential equations
Directory of Open Access Journals (Sweden)
E. M. Elabbasy
2012-01-01
via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results.
Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.
Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang
2017-06-12
Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing
2010-12-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits
Ge, Xiaoqing; Arcak, Murat; Salama, Khaled N.
2010-01-01
Hassan Khalil’s research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents su cient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.
Coupled oscillators in identification of nonlinear damping of a real parametric pendulum
Olejnik, Paweł; Awrejcewicz, Jan
2018-01-01
A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.
OSCILLATION OF NONLINEAR DELAY DIFFERENCE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained.
Nonlinear oscillations of inviscid free drops
Patzek, T. W.; Benner, R. E., Jr.; Basaran, O. A.; Scriven, L. E.
1991-01-01
The present analysis of free liquid drops' inviscid oscillations proceeds through solution of Bernoulli's equation to obtain the free surface shape and of Laplace's equation for the velocity potential field. Results thus obtained encompass drop-shape sequences, pressure distributions, particle paths, and the temporal evolution of kinetic and surface energies; accuracy is verified by the near-constant drop volume and total energy, as well as the diminutiveness of mass and momentum fluxes across drop surfaces. Further insight into the nature of oscillations is provided by Fourier power spectrum analyses of mode interactions and frequency shifts.
SIMULATION OF SYNCHRONIZATION OF NONLINEAR OSCILLATORS BY THE EXTERNAL FIELD
Directory of Open Access Journals (Sweden)
V. M. Kuklin
2017-05-01
Full Text Available In this paper, the self-consistent model was considered, consisting of a system of oscillators, the coupling between them was assumed to be integral (due to the fields formed as a result of their co-radiation. With the help of this model, the features of synchronization by waves of finite amplitude of a system of oscillators were refined, the initial phase values of which are random. The effect of nonlinearity, in particular, due to the change in the mass of the oscillator due to relativistic effects, was taken into account. It was shown that the nonlinearity does not violate the nature of the energy exchange between the wave and the oscillator system, leading only to a slight decrease in the efficiency of such an exchange.
Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier
International Nuclear Information System (INIS)
Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.
2008-01-01
By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.
Electronegative nonlinear oscillating modes in plasmas
Panguetna, Chérif Souleman; Tabi, Conrad Bertrand; Kofané, Timoléon Crépin
2018-02-01
The emergence of nonlinear modulated waves is addressed in an unmagnetized electronegative plasma made of Boltzmann electrons, Boltzmann negative ions and cold mobile positive ions. The reductive perturbation method is used to reduce the dynamics of the whole system to a cubic nonlinear Schrödinger equation, whose the nonlinear and dispersion coefficients, P and Q, are function of the negative ion parameters, namely the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). It is observed that these parameters importantly affect the formation of modulated ion-acoustic waves, either as exact solutions or via the activation of modulational instability. Especially, the theory of modulational instability is used to show the correlation between the parametric analysis and the formation of modulated solitons, obtained here as bright envelopes and kink-wave solitons.
Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach
Directory of Open Access Journals (Sweden)
Ricardo Aguilar-López
2014-01-01
Full Text Available The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Multisynchronization of chaotic oscillators via nonlinear observer approach.
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L
2014-01-01
The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Classical Mechanics as Nonlinear Quantum Mechanics
International Nuclear Information System (INIS)
Nikolic, Hrvoje
2007-01-01
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Vibrational mechanics nonlinear dynamic effects, general approach, applications
Blekhman, Iliya I
2000-01-01
This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
Controllability of nonlinear delay oscillating systems
Directory of Open Access Journals (Sweden)
Chengbin Liang
2017-05-01
Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.
Chaotic Motion of Nonlinearly Coupled Quintic Oscillators | Adeloye ...
African Journals Online (AJOL)
With a fixed energy, we investigate the motion of two nonlinearly coupled quintic oscillators for various values of the coupling strength with the aid of the Poincare surface of section. It is observed that chaotic motion sets in for coupling strength as low as 0.001. The degree of chaoticity generally increases as the coupling ...
Oscillation criteria for first-order forced nonlinear difference equations
Grace Said R; Agarwal Ravi P; Smith Tim
2006-01-01
Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)xμ(n+1) = q2(n)xλ(n+1)+e(n), where λ, μ are the ratios of positive odd integers 0 <μ < 1 and λ > 1, are established.
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...
An exactly solvable three-dimensional nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A.; Morris, J. R.
2013-01-01
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states
An exactly solvable three-dimensional nonlinear quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
Nonlinear Dynamic Phenomena in Mechanics
Warminski, Jerzy; Cartmell, Matthew P
2012-01-01
Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear
Suppressing nonlinear resonances in an impact oscillator using SMAs
International Nuclear Information System (INIS)
Sitnikova, Elena; Pavlovskaia, Ekaterina; Ing, James; Wiercigroch, Marian
2012-01-01
In this paper, we study the resonant responses of an impact oscillator with a one sided SMA motion constraint operating in the pseudoelastic regime. The effectiveness of the SMA restraint in suppressing nonlinear resonances of the impact oscillator is assessed by comparing the dynamic responses of the impact oscillator with SMA and elastic restraints. It is shown that the hysteretic behaviour of the SMA restraint provides an overall vibration reduction in the resonant frequency ranges. Due to the softening behaviour of the SMA element, the resonant frequencies for the SMA oscillator were found to be lower than for the oscillator with an elastic restraint. At each resonance, a single periodic response for the oscillator with the elastic restraint corresponds to two co-existing periodic responses of the SMA oscillator. While at the first resonance peak the emergence of one of the co-existing responses is associated with the hardening effect of the SMA restraint when the pseudoelastic force varies over a complete transformation cycle, at higher frequency resonances incomplete phase transformations in the SMA were detected for both responses. The experimental study undertaken verified the response-modification effects predicted by the numerical analysis conducted under the isothermal approximation. The experimental results showed a good quantitative correspondence with the mathematical modelling. (paper)
Discrete oscillator design linear, nonlinear, transient, and noise domains
Rhea, Randall W
2014-01-01
Oscillators are an essential part of all spread spectrum, RF, and wireless systems, and today's engineers in the field need to have a firm grasp on how they are designed. Presenting an easy-to-understand, unified view of the subject, this authoritative resource covers the practical design of high-frequency oscillators with lumped, distributed, dielectric and piezoelectric resonators. Including numerous examples, the book details important linear, nonlinear harmonic balance, transient and noise analysis techniques. Moreover, the book shows you how to apply these techniques to a wide range of os
Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.
Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C
2015-05-21
In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.
Nonlinear dynamics of a nonsmooth shape memory alloy oscillator
International Nuclear Information System (INIS)
Cardozo dos Santos, Bruno; Amorim Savi, Marcelo
2009-01-01
In the last years, there is an increasing interest in nonsmooth system dynamics motivated by different applications including rotor dynamics, oil drilling and machining. Besides, shape memory alloys (SMAs) have been used in various applications exploring their high dissipation capacity related to their hysteretic behavior. This contribution investigates the nonlinear dynamics of shape memory alloy nonsmooth systems considering a linear oscillator with a discontinuous support built with an SMA element. A constitutive model developed by Paiva et al. [Paiva A, Savi MA, Braga AMB, Pacheco PMCL. A constitutive model for shape memory alloys considering tensile-compressive asymmetry and plasticity. Int J Solids Struct 2005;42(11-12):3439-57] is employed to describe the thermomechanical behavior of the SMA element. Numerical investigations show results where the SMA discontinuous support can dramatically change the system dynamics when compared to those associated with a linear elastic support system. A parametric study is of concern showing the system behavior for different system characteristics, forcing excitation and also gaps. These results show that smart materials can be employed in different kinds of mechanical systems exploring some of the remarkable properties of these alloys.
Nonlinear oscillation system of mass with serial linear and nonlinear springs
DEFF Research Database (Denmark)
Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S
2013-01-01
In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...... alternatives to overcome the difficulty of capturing the periodic behavior of the solution, as the most evident characteristic of oscillators. It can be clearly observed that approximate frequencies and periodic solutions are in excellent agreement with the exact ones. First approximation leads to high...
Self-synchronization in an ensemble of nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Ostrovsky, L. A., E-mail: lev.ostrovsky@gmail.com [Physical Science Division, NOAA Earth Science Research Laboratory, and University of Colorado, Boulder, Colorado 80305 (United States); Galperin, Y. V.; Skirta, E. A. [Department of Mathematics, East Stroudsburg University, East Stroudsburg, Pennsylvania 18301 (United States)
2016-06-15
The paper describes the results of study of a system of coupled nonlinear, Duffing-type oscillators, from the viewpoint of their self-synchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (random-phase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system.
Quantum dynamics and breakdown of classical realism in nonlinear oscillators
International Nuclear Information System (INIS)
Gat, Omri
2007-01-01
The leading nonclassical term in the quantum dynamics of nonlinear oscillators is calculated in the Moyal quasi-trajectory representation. The irreducibility of the quantum dynamics to phase-space trajectories is quantified by the discrepancy of the canonical quasi-flow and the quasi-flow of a general observable. This discrepancy is shown to imply the breakdown of classical realism that can give rise to a dynamical violation of Bell's inequalities. (fast track communication)
Closed-loop suppression of chaos in nonlinear driven oscillators
Aguirre, L. A.; Billings, S. A.
1995-05-01
This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.
Experimental demonstration of revival of oscillations from death in coupled nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Senthilkumar, D. V., E-mail: skumarusnld@gmail.com [School of Physics, Indian Institute of Science Education and Research, Thiruvananthapuram 695016 (India); Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Suresh, K. [Department of Physics, Anjalai Ammal-Engineering College, Kovilvenni 614 403, Tamilnadu (India); Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Chandrasekar, V. K. [Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613 401 (India); Zou, Wei [School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 (China); Centre for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074 (China); Dana, Syamal K. [CSIR-Indian Institute of Chemical Biology, Kolkata 700032 (India); Kathamuthu, Thamilmaran [Centre for Nonlinear Dynamics, Bharathidasan University, Trichy 620024, Tamilnadu (India); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, Telegrafenberg, Potsdam D-14415 (Germany); Institute of Physics, Humboldt University Berlin, Berlin D-12489 (Germany); Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3FX (United Kingdom); Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod (Russian Federation)
2016-04-15
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity
Paul Asir, M.; Jeevarekha, A.; Philominathan, P.
This paper deals with the generation of chaotic beats in a system of two forced dissipative LCR oscillators sharing a nonlinear element. The presence of two external periodic excitations and a common nonlinear element in the chosen system enables the facile generation of chaotic beats. Thus rendered chaotic beats were characterized in both time domain and phase space. Lyapunov exponents and envelope of the beats were computed to diagnose the chaotic nature of the signals. The role of common nonlinearity on the complexity of the generated beats is discussed. Real-time experimental hardware implementation has also been done to confirm the subsistence of the phenomenon, for the first time. Extensive Multisim simulations were carried out to understand, a bit more about the shrinkage and revivals of state variables in phase space.
Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity
DEFF Research Database (Denmark)
Sfahania, M. G.; Ganji, S. S.; Barari, Amin
2010-01-01
This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...
Cardiovascular oscillations: in search of a nonlinear parametric model
Bandrivskyy, Andriy; Luchinsky, Dmitry; McClintock, Peter V.; Smelyanskiy, Vadim; Stefanovska, Aneta; Timucin, Dogan
2003-05-01
We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.
Oscillations in the spectrum of nonlinear Thomson-backscattered radiation
Directory of Open Access Journals (Sweden)
C. A. Brau
2004-02-01
Full Text Available When an electron beam collides with a high-intensity laser beam, the spectrum of the nonlinear Thomson scattering in the backward direction shows strong oscillations like those in the spectrum of an optical klystron. Laser gain on the backward Thomson scattering is estimated using the Madey theorem, and the results suggest that Thomson-backscatter free-electron lasers are possible at wavelengths extending to the far uv using a terawatt laser beam from a chirped-pulse amplifier and a high-brightness electron beam from a needle cathode.
Signatures of nonlinearity in single cell noise-induced oscillations.
Thomas, Philipp; Straube, Arthur V; Timmer, Jens; Fleck, Christian; Grima, Ramon
2013-10-21
A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spectrum which measures the dependence of the oscillatory signal's power with frequency. In this paper we derive an approximate closed-form expression for the power spectrum of any monostable biochemical system close to a Hopf bifurcation, where noise-induced oscillations are most pronounced. Unlike the commonly used linear noise approximation which is valid in the macroscopic limit of large volumes, our theory is valid over a wide range of volumes and hence affords a more suitable description of single cell noise-induced oscillations. Our theory predicts that the spectra have three universal features: (i) a dominant peak at some frequency, (ii) a smaller peak at twice the frequency of the dominant peak and (iii) a peak at zero frequency. Of these, the linear noise approximation predicts only the first feature while the remaining two stem from the combination of intrinsic noise and nonlinearity in the law of mass action. The theoretical expressions are shown to accurately match the power spectra determined from stochastic simulations of mitotic and circadian oscillators. Furthermore it is shown how recently acquired single cell rhythmic fibroblast data displays all the features predicted by our theory and that the experimental spectrum is well described by our theory but not by the conventional linear noise approximation. © 2013 Elsevier Ltd. All rights reserved.
Computing With Quantum Mechanical Oscillators
National Research Council Canada - National Science Library
Parks, A
1991-01-01
Despite the obvious practical considerations (e.g., stability, controllability), certain quantum mechanical systems seem to naturally lend themselves in a theoretical sense to the task of performing computations...
DEFF Research Database (Denmark)
Blekhman, I. I.; Sorokin, V. S.
2016-01-01
A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics.......g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics....... equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient...
Chimera states in mechanical oscillator networks
DEFF Research Database (Denmark)
Martens, Erik Andreas; Thutupalli, Shashi; Fourrière, Antoine
2013-01-01
of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of "chimera states," in which the symmetry of the oscillator population is broken into a synchronous part and an asynchronous part. However, a striking lack of empirical evidence raises the question...... of whether chimeras are indeed characteristic of natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled...... in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed...
Parametric excitation of nonlinear longitudinal oscillations in a magnetoactive plasma
International Nuclear Information System (INIS)
Demchenko, V.V.
1977-01-01
Parametric excitation by HF field of nonlinear longitudinal electron oscillations in the region of hybrid resonances of a cold nonrelativistic plasma has been investigated. It is shown that the inhomogeneity of a pumping field and that of the equilibrium plasma density result in the parametric instability. Expressions are derived for the increments of instable oscillations and the widths of the instability regions are determined. The increments of instable oscillations in the order of magnitude due to the inhomogeneities of the pumping field (γsub(E)) or of the plasma density (γsub(N)) are egual to γsub(E) approximately k(zetasub(0)) ωsub(pe), γsub(N) approximately (zetasub(0))/Lωsub(pe), where (zetasub(0))=(e)Esub(0)/msub(e)ωsub(0)sup(2) is the amplitude of displacement of an electron from the equilibrium state, k, ω 0 , E 0 are the wave number, frequency and amplitude of the pumping field, L is the characteristic size of the inhomogeneity of the plasma density, ωsub(pe) is the electron plasma frequency
Chimera states in mechanical oscillator networks.
Martens, Erik Andreas; Thutupalli, Shashi; Fourrière, Antoine; Hallatschek, Oskar
2013-06-25
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature uses to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony and disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of "chimera states," in which the symmetry of the oscillator population is broken into a synchronous part and an asynchronous part. However, a striking lack of empirical evidence raises the question of whether chimeras are indeed characteristic of natural systems. This calls for a palpable realization of chimera states without any fine-tuning, from which physical mechanisms underlying their emergence can be uncovered. Here, we devise a simple experiment with mechanical oscillators coupled in a hierarchical network to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns. We identify a wide spectrum of complex states, encompassing and extending the set of previously described chimeras. Our mathematical model shows that the self-organization observed in our experiments is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems. The symmetry-breaking mechanism revealed by our experiments may thus be prevalent in systems exhibiting collective behavior, such as power grids, optomechanical crystals, or cells communicating via quorum sensing in microbial populations.
Ganji, S. S.; Domairry, G.; Davodi, A. G.; Babazadeh, H.; Seyedalizadeh Ganji, S. H.
The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt-Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the solutions. In particular, APL-PM works well for the whole range of oscillation amplitudes and excellent agreement of the approximate frequency with the exact one has been demonstrated. The approximate period derived here is accurate and close to the exact solution. This method has a distinguished feature which makes it simple to use, and also it agrees with the exact solutions for various parameters.
Nonlinear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
Directory of Open Access Journals (Sweden)
A. Fereidoon
2012-01-01
Full Text Available In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifth-order nonlinearity for two examples using He's Frequency-Amplitude Formulation (HFAF.The effectiveness and convenience of the method is illustrated in these examples. It will be shown that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems.
A nonlinear oscillator with parametric coloured noise: some analytical results
International Nuclear Information System (INIS)
Mallick, Kirone; Marcq, Philippe
2005-01-01
The asymptotic behaviour of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is coloured because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (PDF) of the system and to derive the behaviour of physical observables in the long time limit
History of nonlinear oscillations theory in France (1880-1940)
Ginoux, Jean-Marc
2017-01-01
This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...
Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities
van Rooij, A.C.L.M.
2017-01-01
Aerodynamic non-linearities, such as shock waves, boundary layer separation or boundary layer transition, may cause an amplitude limitation of the oscillations induced by the fluid flow around a structure. These aeroelastic limit-cycle oscillations (LCOs) resulting from aerodynamic non-linearities
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
International Nuclear Information System (INIS)
Schulze-Halberg, Axel; Gordon, Christopher R.
2013-01-01
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators
International Nuclear Information System (INIS)
Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito
2008-01-01
This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions
Granular Segregation by an Oscillating Ratchet Mechanism
International Nuclear Information System (INIS)
Igarashi, A.; Horiuchi, Ch.
2004-01-01
We report on a method to segregate granular mixtures which consist of two kinds of particles by an oscillating ''ratchet'' mechanism. The segregation system has an asymmetrical sawtooth-shaped base which is vertically oscillating. Such a ratchet base produces a directional current of particles owing to its transport property. It is a counterintuitive and interesting phenomenon that a vertically vibrated base transports particles horizontally. This system is studied with numerical simulations, and it is found that we can apply such a system to segregation of mixtures of particles with different properties (radius or mass). Furthermore, we find out that an appropriate inclination of the ratchet-base makes the quality of segregation high. (author)
Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators
Talukdar, Abdul Hafiz
2011-05-01
Exceptional behaviours of Memristor are illustrated in Memristor based second order (Wien oscillator) and third order (phase shift oscillator) oscillator systems in this Thesis. Conventional concepts about sustained oscillation have been argued by demonstrating the possibility of sustained oscillation with oscillating resistance and dynamic poles. Mathematical models are also proposed for analysis and simulations have been presented to support the surprising characteristics of the Memristor based oscillator systems. This thesis also describes a comparative study among the Wien family oscillators with one Memristor. In case of phase shift oscillator, one Memristor and three Memristors systems are illustrated and compared to generalize the nonlinear dynamics observed for both 2nd order and 3rd order system. Detail explanations are provided with analytical models to simplify the unconventional properties of Memristor based oscillatory systems.
Nonlinear oscillation regime of electromagnetic disturbances in the equatorial F region
International Nuclear Information System (INIS)
Sazonov, S.V.
1990-01-01
Nonlinear oscillation regime of electromagnetic dicturbances within equatorial ionosphere F-region resulted from Rayleigh-Taylor instability, gradient-drift instability and recombination processes is investigated on the basis of two-liquid quasihydrodynamics equations. It is shown, that at positive linear increment the oscillations are developing in regime with aggregation and are terminated by increment the effect of threshold destabilization, when under certain initial conditions underlgoes oscillation nonlinear swinging, resulting, as well, in bubble formation in contrast to small damping oscillations, is detected
Noise-induced chaos in a quadratically nonlinear oscillator
International Nuclear Information System (INIS)
Gan Chunbiao
2006-01-01
The present paper focuses on the noise-induced chaos in a quadratically nonlinear oscillator. Simple zero points of the stochastic Melnikov integral theoretically mean the necessary rising of noise-induced chaotic response in the system based on the stochastic Melnikov method. To quantify the noise-induced chaos, the boundary of the system's safe basin is firstly studied and it is shown to be incursively fractal when chaos arises. Three cases are considered in simulating the safe basin of the system, i.e., the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, and only by the Gaussian white noise excitation. Secondly, the leading Lyapunov exponent by Rosenstein's algorithm is shown to quantify the chaotic nature of the sample time series of the system. The results show that the boundary of the safe basin can also be fractal even if the system is excited only by the external Gaussian white noise. Most importantly, the almost-harmonic, the noise-induced chaotic and the thoroughly random responses can be found in the system
On the mechanism of oscillations in neutrophils
DEFF Research Database (Denmark)
Brasen, Jens Christian; Barington, Torben; Olsen, Lars Folke
2010-01-01
We have investigated the regulation of the oscillatory generation of H(2)O(2) and oscillations in shape and size in neutrophils in suspension. The oscillations are independent of cell density and hence do not represent a collective phenomena. Furthermore, the oscillations are independent...... of the external glucose concentration and the oscillations in H(2)O(2) production are 180 degrees out of phase with the oscillations in NAD(P)H. Cytochalasin B blocked the oscillations in shape and size whereas it increased the period of the oscillations in H(2)O(2) production. 1- and 2-butanol also blocked...... the oscillations in shape and size, but only 1-butanol inhibited the oscillations in H(2)O(2) production. We conjecture that the oscillations are likely to be due to feedback regulations in the signal transduction cascade involving phosphoinositide 3-kinases (PI3K). We have tested this using a simple mathematical...
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragó n, J. L.; Barrio, R. A.; Woolley, T. E.; Baker, R. E.; Maini, P. K.
2012-01-01
consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos
Non-linear oscillations of fluid in a container
Verhagen, J.H.G.; van Wijngaarden, L.
1965-01-01
This paper is concerned with forced oscillations of fluid in a rectangular container. From the linearized approximation of the equations governing these oscillations, resonance frequencies are obtained for which the amplitude of the oscillations becomes infinite. Observation shows that under these
Isochronous Liénard-type nonlinear oscillators of arbitrary dimensions
Indian Academy of Sciences (India)
2015-10-13
Oct 13, 2015 ... Isochronous system; Liénard-type system; singular and nonsingular Hamiltonian. ... Liénard-type nonlinear oscillators exhibiting isochronous properties, including linear, quadratic and ... Pramana – Journal of Physics | News.
Oscillating particle-like solutions of nonlinear Klein-Gordon equation
International Nuclear Information System (INIS)
Bogolubsky, I.L.
1976-01-01
A denumerable set of oscillating spherically-symmetric particle-like solutions of the Klein-Gordon equation with cubic nonlinearity is found. Extended particles modelled by them turn out to be slightly radiating and long-lived
Coordination of the Walking Stick Insect Using a System of Nonlinear Coupled Oscillators
National Research Council Canada - National Science Library
Marvin, Daryl J
1992-01-01
The area of walking machines is investigated. A design for a central pattern generator composed of nonlinear coupled oscillators which generates the characteristic gaits of the walking stick insect is presented...
Oscillation of solutions to neutral nonlinear impulsive hyperbolic equations with several delays
Directory of Open Access Journals (Sweden)
Jichen Yang
2013-01-01
Full Text Available In this article, we study oscillatory properties of solutions to neutral nonlinear impulsive hyperbolic partial differential equations with several delays. We establish sufficient conditions for oscillation of all solutions.
Analysis of highly nonlinear oscillation systems using He's max–min ...
Indian Academy of Sciences (India)
Min–max method; nonlinear oscillation; duffing equation; homo- .... where c and ε are the linear and cubic stiffness which do not need to be small in the ..... an easy and direct procedure for determining approximations to the periodic solutions.
International Nuclear Information System (INIS)
Suarez Antola, R.
2008-11-01
The cores of nuclear reactors, including its structural parts and cooling fluids, are complex mechanical systems able to vibrate in a set of normal modes and frequencies, if suitable perturbed. The cyclic variations in the strain state of the core materials may produce changes in density. Changes in density modify the reactivity. Changes in reactivity modify thermal power. Modifications in thermal power produce variations in temperature fields. Variations in temperature produce variations in strain due to thermal-elastic effects. If the variation of the temperature field is fast enough and if the Doppler Effect and other stabilizing prompt effects in the fuel are weak enough, a fast oscillatory instability could be produced, coupled with mechanical vibrations of small amplitude. A recently constructed, simple mathematical model of nuclear reactor kinetics, that improves the one due to A.S. Thompson, is reviewed. It was constructed in order to study, in a first approximation, the stability of the reactor: a nonlinear nuclear-thermal oscillator (that corresponds to reactor point kinetics with thermal-elastic feedback and with frozen delayed neutron effects) is coupled nonlinearly with a linear mechanical-thermal oscillator (that corresponds to the first normal mode of mechanical vibrations excited by thermo-elastic effects). This mathematical model is studied here from the standpoint of mechanical vibrations. It is shown how, under certain conditions, a suitable mechanical perturbation could elicit fast and growing oscillatory instabilities in the reactor power. Applying the asymptotic method due to Krylov, Bogoliubov and Mitropolsky, analytical formulae that may be used in the calculation of the time varying amplitude and phase of the mechanical oscillations are given, as functions of the mechanical, thermal and nuclear parameters of the reactor. The consequences for the mechanical integrity of the reactor are assessed. Some conditions, mainly, but not exclusively
Methods of stability analysis in nonlinear mechanics
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.
1989-01-01
We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs
Flutter and limit cycle oscillation suppression using linear and nonlinear tuned vibration absorbers
Verstraelen, Edouard; Kerschen, Gaëtan; Dimitriadis, Grigorios
2017-01-01
Aircraft are more than ever pushed to their limits for performance reasons. Consequently, they become increasingly nonlinear and they are more prone to undergo aeroelastic limit cycle oscillations. Structural nonlinearities affect aircraft such as the F-16, which can undergo store-induced limit cycle oscillations (LCOs). Furthermore, transonic buzz can lead to LCOs because of moving shock waves in transonic flight conditions on many aircraft. This study presents a numerical investigation o...
Self-oscillations of aircraft landing gear shock-strut at considerable non-linear friction
Directory of Open Access Journals (Sweden)
Б.М. Шифрин
2004-01-01
Full Text Available The report considers self-oscillations at ε >1. The previous works were dedicated to the elastic frictional L.G. shock strut oscillations, the mathematical model of which is a non-linear differential equation with low ε parameter of its right-hand part.
Nonlinear coherent beam-beam oscillations in the rigid bunch model
International Nuclear Information System (INIS)
Dikansky, N.; Pestrikov, D.
1990-01-01
Within the framework of the rigid bunch model coherent oscillations of strong-strong colliding bunches are described by equations which are specific for the weak-strong beam case. In this paper some predictions of the model for properties of nonlinear coherent oscillations as well as for associated limitations of the luminosity are discussed. 14 refs.; 6 figs
Non-linear neutron star oscillations viewed as deviations from an equilibrium state
International Nuclear Information System (INIS)
Sperhake, U
2002-01-01
A numerical technique is presented which facilitates the evolution of non-linear neutron star oscillations with a high accuracy essentially independent of the oscillation amplitude. We apply this technique to radial neutron star oscillations in a Lagrangian formulation and demonstrate the superior performance of the new scheme compared with 'conventional' techniques. The key feature of our approach is to describe the evolution in terms of deviations from an equilibrium configuration. In contrast to standard perturbation analysis we keep all higher order terms in the evolution equations and thus obtain a fully non-linear description. The advantage of our scheme lies in the elimination of background terms from the equations and the associated numerical errors. The improvements thus achieved will be particularly significant in the study of mildly non-linear effects where the amplitude of the dynamic signal is small compared with the equilibrium values but large enough to warrant non-linear effects. We apply the new technique to the study of non-linear coupling of Eigenmodes and non-linear effects in the oscillations of marginally stable neutron stars. We find non-linear effects in low amplitude oscillations to be particularly pronounced in the range of modes with vanishing frequency which typically mark the onset of instability. (author)
Institute of Scientific and Technical Information of China (English)
应阳君; 黄祖洽
2001-01-01
Frequency catastrophe is found in a cell Ca2+ nonlinear oscillation model with time delay. The relation of the frequency transition to the time delay is studied by numerical simulations and theoretical analysis. There is a range of parameters in which two kinds of attractors with great frequency differences co-exist in the system. Along with parameter changes, a critical phenomenon occurs and the oscillation frequency changes greatly. This mechanism helps us to deepen the understanding of the complex dynamics of delay systems, and might be of some meaning in cell signalling.
International Nuclear Information System (INIS)
Donko, Z.; Schulze, J.; Czarnetzki, U.; Luggenhoelscher, D.
2009-01-01
At low pressures, nonlinear self-excited plasma series resonance (PSR) oscillations are known to drastically enhance electron heating in geometrically asymmetric capacitively coupled radio frequency discharges by nonlinear electron resonance heating (NERH). Here we demonstrate via particle-in-cell simulations that high-frequency PSR oscillations can also be excited in geometrically symmetric discharges if the driving voltage waveform makes the discharge electrically asymmetric. This can be achieved by a dual-frequency (f+2f) excitation, when PSR oscillations and NERH are turned on and off depending on the electrical discharge asymmetry, controlled by the phase difference of the driving frequencies
Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei
2016-07-01
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
Signatures of nonlinearity in single cell noise-induced oscillations
Thomas, P.; Straube, A.V.; Timmer, J.; Fleck, C.; Grima, R.
2013-01-01
A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power
Non-linear frequency and amplitude modulation of a nano-contact spin torque oscillator
Muduli, P. K.; Pogoryelov, Ye.; Bonetti, S.; Consolo, G.; Mancoff, Fred; Åkerman, Johan
2009-01-01
We study the current controlled modulation of a nano-contact spin torque oscillator. Three principally different cases of frequency non-linearity ($d^{2}f/dI^{2}_{dc}$ being zero, positive, and negative) are investigated. Standard non-linear frequency modulation theory is able to accurately describe the frequency shifts during modulation. However, the power of the modulated sidebands only agrees with calculations based on a recent theory of combined non-linear frequency and amplitude modulation.
Computational mechanics of nonlinear response of shells
Energy Technology Data Exchange (ETDEWEB)
Kraetzig, W.B. (Bochum Univ. (Germany, F.R.). Inst. fuer Statik und Dynamik); Onate, E. (Universidad Politecnica de Cataluna, Barcelona (Spain). Escuela Tecnica Superior de Ingenieros de Caminos) (eds.)
1990-01-01
Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs.
Computational mechanics of nonlinear response of shells
International Nuclear Information System (INIS)
Kraetzig, W.B.; Onate, E.
1990-01-01
Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs
Equivalent Representation Form of Oscillators with Elastic and Damping Nonlinear Terms
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others.
Chimera States in Mechanical Oscillator Networks
Martens, Erik Andreas; Thutupalli, Shashi; Fourrière, Antoine; Hallatschek, Oskar
2013-01-01
The synchronization of coupled oscillators is a fascinating manifestation of self-organization that nature uses to orchestrate essential processes of life, such as the beating of the heart. Although it was long thought that synchrony and disorder were mutually exclusive steady states for a network of identical oscillators, numerous theoretical studies in recent years have revealed the intriguing possibility of “chimera states,” in which the symmetry of the oscillator population is broken into...
Quantum-mechanical Green's functions and nonlinear superposition law
International Nuclear Information System (INIS)
Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P. de T.S.
1986-01-01
The quantum-mechanical Green's function is derived for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field. (Author) [pt
Quantum-mechanical Green's function and nonlinear superposition law
International Nuclear Information System (INIS)
Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P.T.S.
1986-01-01
It is derived the quantum-mechanical Green's function for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic-oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field
Building better oscillators using nonlinear dynamics and pattern ...
Indian Academy of Sciences (India)
Frequency and time references play an essential role in modern technology and in liv- ... of noise and improve the frequency precision of oscillators, with particular ..... signal is cyclostationary (the statistics is periodic rather than stationary) the ...
Dynamics of nonlinear oscillators with time-varying conjugate coupling
Indian Academy of Sciences (India)
oscillators. We analyze the behavior of coupled systems with respect to the coupling switching frequency using ..... are of potential utility in appropriate design strategies and/or understanding of complex systems with dynamic interaction ...
Validity of the cumulant method for a pulse nonlinear Kerr oscillator
International Nuclear Information System (INIS)
Grygiel, K.; Leonski, W.; Szlachetka, P.
1998-01-01
We study the dynamics of an anharmonic oscillator driven by a train of pulses. The cumulant expansion and quantum evolution operator approaches are presented and compared. The modifications introduced by quantum mechanics into the dynamics of classical systems which manifest chaos are a problem of great importance. It is known that quantization modifies the dynamics of classical system is usually studied by means of the equation for the Wigner function derived from the quantum Liouville equation. In Wigner's formulation of quantum mechanics we treat a quantum system in a 'classical way' including all their quantum features. And what is more, we can contrast the quantum and classical dynamics within the framework of one formalism. The problem is, that the equations for the Wigner functions are mathematically cumbersome and their analytic solutions for most nonlinear systems are unknown. However, instead of the equation for the Wigner function we can use the set of equations for statistical moments generated by our equation for the Wigner function. It is obvious that in this approach a quantum system is governed by an infinite set of equations. Therefore, for numerical reasons the set of equations for statistical moments has to be truncated at a finite number, which means approximating it. It is known that first cumulant approximation represents the classical dynamics. The second cumulant approximation adds the first quantum corrections to the classical dynamics. In this paper we compare some aspects of the cumulant method and the method used by Leonski and Tanas to study an anharmonic oscillator driven by a train of pulses. The Kerr oscillator model is the same ad that is discussed in an earlier paper albeit without the damping mechanism
Elwakil, Ahmed S.
2009-04-28
Two novel sinusoidal oscillator structures with an explicit tanh(x) nonlinearity are proposed. The oscillators have the attractive feature: the higher the operating frequency, the lower the necessary gain required to start oscillations. A nonlinear model for the two oscillators is derived and verified numerically. Spice simulations using AMS BiCMOS 0.35 μ model parameters and experimental results are shown. Copyright © 2009 John Wiley & Sons, Ltd.
Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.
2018-01-01
In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.
From kaons to neutrinos: quantum mechanics of particle oscillations
International Nuclear Information System (INIS)
Zralek, M.
1998-01-01
The problem of particle oscillation is considered in a pedagogical and comprehensive way. Examples from K, B and neutrino physics are given. Conceptual difficulties of the traditional approach to particle oscillation are discussed. It is shown how the probability current density and the wave packet treatments of particle oscillations resolve some problems. It is also shown that only full field theoretical approach is free from conceptual difficulties. The possibility of oscillation of particles produced together with kaons or neutrinos is considered in full wave packet quantum mechanics language. Precise definition of the oscillation of particles which recoil against mixed states is given. The general amplitude which describes the oscillation of two particles in the final states is found. Using this EPR-type amplitude the problem of oscillation of particles recoiling against kaons or neutrinos is resolved. The relativistic EPR correlations on distances of the order of coherence lengths are considered. (author)
International Nuclear Information System (INIS)
Belendez, A.; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A.
2008-01-01
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities
Spontaneous blood pressure oscillations in mechanically ventilated patients with sepsis
DEFF Research Database (Denmark)
Berg, Ronan M G; Plovsing, Ronni R; Greve, Anders M
2016-01-01
OBJECTIVE: In the present hypothesis-generating study, we investigated whether spontaneous blood pressure oscillations are suppressed to lower frequencies, and whether abolished oscillations are associated with an adverse outcome in mechanically ventilated patients with sepsis. METHODS: We...... retrospectively subjected invasive steady-state blood pressure recordings from 65 mechanically ventilated patients with sepsis to spectral analysis. Modified spectral bands were visually identified by plotting spectral power against frequency. RESULTS: Modified middle-frequency and low-frequency (MF' and LF......') oscillations were absent in 9% and 22% of the patients, respectively. In patients in whom spontaneous blood pressure oscillations were preserved, the MF' oscillations occurred at 0.021 Hz (median, interquartile range 0.013-0.030), whereas the LF' oscillations occurred at 0.009 Hz (median, interquartile range 0...
International Nuclear Information System (INIS)
Pradeep, R. Gladwin; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2009-01-01
In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden-type nonlinear oscillator equation with linear forcing, xe+αxx+βx 3 +γx=0, which preserves the form of the time independent integral, conservative Hamiltonian, and the equation of motion. Generalizing this transformation we prove the existence of nonstandard conservative Hamiltonian structure for a general class of damped nonlinear oscillators including Lienard-type systems. Further, using the above Hamiltonian structure for a specific example, namely, the generalized modified Emden equation xe+αx q x+βx 2q+1 =0, where α, β, and q are arbitrary parameters, the general solution is obtained through appropriate canonical transformations. We also present the conservative Hamiltonian structure of the damped Mathews-Lakshmanan oscillator equation. The associated Lagrangian description for all the above systems is also briefly discussed.
PERFORMANCE IMPROVEMENT OF A CHEMICAL REACTOR BY NONLINEAR NATURAL OSCILLATIONS
RAY, AK
1995-01-01
The dynamic behaviour of two coupled continuous stirred tank reactors in sequence is studied when the first reactor is being operated under limit cycle regimes producing self-sustained natural oscillations. The periodic output from the first reactor is then used as a forced input into the second
SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÃ–DINGER
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T B Prayitno
2012-02-01
Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master SchrÃ¶dinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution canâ€™t be normalized. Â Keywords : harmonic oscillator, nonlinear SchrÃ¶dinger.
Oscillation criteria for third order nonlinear delay differential equations with damping
Directory of Open Access Journals (Sweden)
Said R. Grace
2015-01-01
Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.
Yang, Tao; Cao, Qingjie
2018-03-01
This work presents analytical studies of the stiffness nonlinearities SD (smooth and discontinuous) oscillator under displacement and velocity feedback control with a time delay. The SD oscillator can capture the qualitative characteristics of quasi-zero-stiffness and negative-stiffness. We focus mainly on the primary resonance of the quasi-zero-stiffness SD oscillator and the stochastic resonance (SR) of the negative-stiffness SD oscillator. Using the averaging method, we have been analyzed the amplitude response of the quasi-zero-stiffness SD oscillator. In this regard, the optimum time delay for changing the control intensity according to the optimization standard proposed can be obtained. For the optimum time delay, increasing the displacement feedback intensity is advantageous to suppress the vibrations in resonant regime where vibration isolation is needed, however, increasing the velocity feedback intensity is advantageous to strengthen the vibrations. Moreover, the effects of time-delayed feedback on the SR of the negative-stiffness SD oscillator are investigated under harmonic forcing and Gaussian white noise, based on the Langevin and Fokker-Planck approaches. The time-delayed feedback can enhance the SR phenomenon where vibrational energy harvesting is needed. This paper established the relationship between the parameters and vibration properties of a stiffness nonlinearities SD which provides the guidance for optimizing time-delayed control for vibration isolation and vibrational energy harvesting of the nonlinear systems.
Remote synchronization of amplitudes across an experimental ring of non-linear oscillators
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Center for Mind/Brain Science, University of Trento, 38123 Mattarello TN, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2015-12-15
In this paper, the emergence of remote synchronization in a ring of 32 unidirectionally coupled non-linear oscillators is reported. Each oscillator consists of 3 negative voltage gain stages connected in a loop to which two integrators are superimposed and receives input from its preceding neighbour via a “mixing” stage whose gains form the main system control parameters. Collective behaviour of the network is investigated numerically and experimentally, based on a custom-designed circuit board featuring 32 field-programmable analog arrays. A diverse set of synchronization patterns is observed depending on the control parameters. While phase synchronization ensues globally, albeit imperfectly, for certain control parameter values, amplitudes delineate subsets of non-adjacent but preferentially synchronized nodes; this cannot be trivially explained by synchronization paths along sequences of structurally connected nodes and is therefore interpreted as representing a form of remote synchronization. Complex topology of functional synchronization thus emerges from underlying elementary structural connectivity. In addition to the Kuramoto order parameter and cross-correlation coefficient, other synchronization measures are considered, and preliminary findings suggest that generalized synchronization may identify functional relationships across nodes otherwise not visible. Further work elucidating the mechanism underlying this observation of remote synchronization is necessary, to support which experimental data and board design materials have been made freely downloadable.
SPECIALTY OF ROTOR’S DRIVE MECHANISM OSCILLATIONS
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V. S. Loveikin
2016-02-01
Full Text Available Purpose. Scientific work is devoted to study the influence of dynamic coefficients of bearings segment (coefficients of resistance and recirculating power on stability and subharmonics self-oscillating components of the rotor vibration in unstable region of rotational speeds. Methodology. The study is based on the methods: the theory of vibrations of mechanical systems with lumped parameters; Lagrange functions; linear algebra. Findings. The researchers made: a justification of the discrete two-mass model of an unbalanced rotor, which takes into account the influence of rotation on dynamic coefficients; b analysis and improvement of methods for engineering analysis of stability and parameter subharmonic self-oscillations in the unstable range of frequencies of rotation of the rotor; c installation and classification of the main rotor causes of vibrations constructive or those arising in the manufacture, assembly and operation of the machine, and on the other hand, rotary systems specific for non-conservative forces, that lead under certain conditions to the self-oscillation; d determination (identification the characteristics/differences of rotor vibration, which lies in the fact that in most cases they are associated with the transverse vibrations of the rotors, while torsional or longitudinal oscillations play the incomparably smaller role, and therefore the last in this study were rejected; eit is shown that the characteristic feature of the functioning of rotor systems of modern machines and units have no direct relationship with the level of vibration with amount of power that is transmitted through them or produced engine. Originality. In this paper the authors first considered the nonlinear response bearing lubrication layer, namely the coefficients of resistance and circulating forces that determine the dynamic coefficient of segment bearings. Practical value. The engineering calculations subharmonic stability and self-oscillations of
Transfer of non-Gaussian quantum states of mechanical oscillator to light
Filip, Radim; Rakhubovsky, Andrey A.
2015-11-01
Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.
Reactor noise analysis based on nonlinear dynamic theory - application to power oscillation
International Nuclear Information System (INIS)
Suzudo, Tomoaki
1993-01-01
The information dimension is one of the simplest quantities that can be used to determine the asymptotic motion of the time evolution of a nonlinear system. The application of this quantity to reactor noise analysis is proposed, and the possibility of its application to power oscillation analysis is examined. The information dimension of this regime is equal to the number of independent oscillating modes, which is an intuitive physical variable. Time series data from computer experiments and experiments with an actual physical system are used for the analysis. The results indicate that the method is useful for a detailed analysis of reactor power oscillation
Large time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics
Jochmann, Frank
2005-01-01
The anharmonic oscillator model describing the propagation of electromagnetic waves in an exterior domain containing a nonlinear dielectric medium is investigated. The system under consideration consists of a generally nonlinear second order differential equation for the dielectrical polarization coupled with Maxwell's equations for the electromagnetic field. Local decay of the electromagnetic field for t to infinity in the charge free case is shown for a large class of potentials. (This pape...
Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.
2018-01-01
The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.
Nonlinear behavior of nonradial oscillations in ε Per
International Nuclear Information System (INIS)
Smith, M.A.
1987-01-01
The authors conducted a simultaneous spectroscopic/photometric campaign of ε Per (BO.7 III) during five nights in November, 1984. The spectroscopic data consist of 300 observations of the Si III λλ4552-74 triplet, while the photometric data were obtained at two different observatories. In both sets of data they find a dominant 3.85+-.02 hr. period. The analysis of line profiles in the context of nonradial pulsation (NRP) indicates this oscillation is caused by a -m=iota =4 mode. In this context the line profiles also indicate the presence of a secondary -m=iota =6 mode with a period of 2.25+-.03 hr, an oscillation below the detection threshold in the photometric data. These periodicities and mode identifications have been reported by Penrod on other occasions. They may be considered to be stable except that their amplitudes vary from epoch to epoch
Nonlinear effects on Turing patterns: Time oscillations and chaos
Aragón, J. L.
2012-08-08
We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic oscillations without modifying the underlying Turing pattern. A Ruelle-Takens-Newhouse route to chaos is identified. We also examine the Turing conditions for obtaining a diffusion-driven instability and show that the patterns obtained are not necessarily stationary for certain values of the diffusion coefficients. These results demonstrate the limitations of the linear analysis for reaction-diffusion systems. © 2012 American Physical Society.
International Nuclear Information System (INIS)
Crebbin, K.C.
1985-05-01
Uniform magnetic field perturbations cause a closed orbit distortion in a circular accelerator. If the magnetic guide field is non-linear these perturbations can also cause a Nu shift in the betatron oscillations. Such a shift in radial Nu values has been observed in the Bevalac while studying the low energy resonant extraction system. In the Bevalac, the radial perturbation comes from the quadrants being magnetically about 0.8% longer than 90 0 . The normal effect of this type of perturbation is a radial closed orbit shift and orbit distortion. The Nu shift, associated with this type of perturbation in the presence of a non-linear guide field, is discussed in this paper. A method of handling the non-linear n values is discussed as well as the mechanism for the associated Nu shift. Computer calculations are compared to measurements. 2 refs., 4 figs
Nonlinear optomechanical measurement of mechanical motion
DEFF Research Database (Denmark)
Brawley, G.A.; Vanner, M R; Larsen, Peter Emil
2016-01-01
Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with oth......Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing...... with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator...... by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can...
Rational extension and Jacobi-type Xm solutions of a quantum nonlinear oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, Axel; Roy, Barnana
2013-01-01
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X m exceptional orthogonal polynomials
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator
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Alex Elías-Zúñiga
2013-01-01
oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.
Rational extension and Jacobi-type X{sub m} solutions of a quantum nonlinear oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Roy, Barnana [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2013-12-15
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X{sub m} exceptional orthogonal polynomials.
An Apparatus to Demonstrate Linear and Nonlinear Oscillations of a Pendulum
Mayer, V. V.; Varaksina, E. I.
2016-01-01
A physical pendulum with a magnetic load is proposed for comparison of linear and nonlinear oscillations. The magnetic load is repelled by permanent magnets which are disposed symmetrically relative to the load. It is established that positions of the pendulum and the magnets determine the dependence of restoring force on displacement of the load.…
RF Spectrum Sensing Based on an Overdamped Nonlinear Oscillator Ring for Cognitive Radios
Directory of Open Access Journals (Sweden)
Zhi-Ling Tang
2016-06-01
Full Text Available Existing spectrum-sensing techniques for cognitive radios require an analog-to-digital converter (ADC to work at high dynamic range and a high sampling rate, resulting in high cost. Therefore, in this paper, a spectrum-sensing method based on a unidirectionally coupled, overdamped nonlinear oscillator ring is proposed. First, the numerical model of such a system is established based on the circuit of the nonlinear oscillator. Through numerical analysis of the model, the critical condition of the system’s starting oscillation is determined, and the simulation results of the system’s response to Gaussian white noise and periodic signal are presented. The results show that once the radio signal is input into the system, it starts oscillating when in the critical region, and the oscillating frequency of each element is fo/N, where fo is the frequency of the radio signal and N is the number of elements in the ring. The oscillation indicates that the spectrum resources at fo are occupied. At the same time, the sampling rate required for an ADC is reduced to the original value, 1/N. A prototypical circuit to verify the functionality of the system is designed, and the sensing bandwidth of the system is measured.
Nonlinear continuum mechanics and large inelastic deformations
Dimitrienko, Yuriy I
2010-01-01
This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...
Seismic metamaterials based on isochronous mechanical oscillators
Energy Technology Data Exchange (ETDEWEB)
Finocchio, G., E-mail: gfinocchio@unime.it; Garescì, F.; Azzerboni, B. [Department of Electronic Engineering, Industrial Chemistry and Engineering, University of Messina, C.da di Dio, I-98166 Messina (Italy); Casablanca, O.; Chiappini, M. [Istituto Nazionale di Geofisica e Vulcanologia (INGV), Via Vigna Murata 605, 00143 Roma (Italy); Ricciardi, G. [Department of Civil, Informatic, Architectural, and Environmental Engineering and Applied Mathematics, C.da di Dio, I-98166 Messina (Italy); Alibrandi, U. [Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576 (Singapore)
2014-05-12
This Letter introduces a seismic metamaterial (SM) composed by a chain of mass-in-mass system able to filter the S-waves of an earthquake. We included the effect of the SM into the mono dimensional model for the soil response analysis. The SM modifies the soil behavior and in presence of an internal damping the amplitude of the soil amplification function is reduced also in a region near the resonance frequency. This SM can be realized by a continuous structure with inside a 3d-matrix of isochronous oscillators based on a sphere rolling over a cycloidal trajectory.
Nonlinear Klein-Gordon soliton mechanics
International Nuclear Information System (INIS)
Reinisch, G.
1992-01-01
Nonlinear Klein-Gordon solitary waves - or solitons in a loose sense - in n+1 dimensions, driven by very general external fields which must only satisfy continuity - together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom - which may be conservative or not - of the second Newton's law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics. This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems
4th International Conference on Nonlinear Mechanics
Maugin, G
2003-01-01
The mechanics of electromagnetic materials and structures has been developing rapidly with extensive applications in, e. g. , electronics industry, nuclear engineering, and smart materials and structures. Researchers in this interdisciplinary field are with diverse background and motivation. The Symposium on the Mechanics of Electromagnetic Materials and Structures of the Fourth International Conference on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 provided an opportunity for an intimate gathering of researchers and exchange of ideas. This volume contains papers based on most of the presentations at the symposium, and articles from a few invited contributors. These papers reflect some of the recent activities in the mechanics of electromagnetic materials and structures. The first twelve papers are in the order in which they were listed in the program of the conference. These are followed by six invited papers in alphabetical order of the last names of the first authors. We would like to exte...
Two Kinds of Self-Oscillating Circuits Mechanically Demonstrated
Shiang-Hwua Yu; Po-Hsun Wu
2015-01-01
This study introduces two types of self-oscillating circuits that are frequently found in power electronics applications. Special effort is made to relate the circuits to the analogous mechanical systems of some important scientific inventions: Galileo’s pendulum clock and Coulomb’s friction model. A little touch of related history and philosophy of science will hopefully encourage curiosity, advance the understanding of self-oscillating systems and satisfy the aspiration ...
Special function solutions of a spectral problem for a nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A; Morris, J R
2012-01-01
We construct exact solutions of a spectral problem involving the Schrödinger equation for a nonlinear, one-parameter oscillator potential. In contrast to a previous analysis of the problem (Carinena et al 2007 Ann. Phys. 322 434–59), where solutions were given through a Rodrigues-type formula, our approach leads to closed-form representations of the solutions in terms of special functions, not containing any derivative operators. We show normalizability and orthogonality of our solutions, as well as correct reduction of the problem to the harmonic oscillator model, if the parameter in the potential gets close to zero. (paper)
Directory of Open Access Journals (Sweden)
Qi Wang
2012-01-01
Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.
Flavor Oscillations in the Supernova Hot Bubble Region: Nonlinear Effects of Neutrino Background
Pastor, Sergio; Raffelt, Georg
2002-10-01
The neutrino flux close to a supernova core contributes substantially to neutrino refraction so that flavor oscillations become a nonlinear phenomenon. One unexpected consequence is efficient flavor transformation for antineutrinos in a region where only neutrinos encounter a Mikheyev-Smirnov-Wolfenstein resonance or vice versa. Contrary to previous studies we find that in the neutrino-driven wind the electron fraction Ye always stays below 0.5, corresponding to a neutron-rich environment as required by r-process nucleosynthesis. The relevant range of masses and mixing angles includes the region indicated by LSND, but not the atmospheric or solar oscillation parameters.
Dynamics of a nonlinear oscillator and a low-amplitude frequency-modulated wave
International Nuclear Information System (INIS)
White, R.C.; McNamara, B.
1987-01-01
When the frequency of a small amplitude plane wave is varied slowly over a large enough bandwidth and this wave is incident upon a nonlinear oscillator, the resulting perturbed motion can exhibit stochastic behavior. Applications for the study of this system are wide and varied. We apply Lie-transform perturbation theory and mapping techniques in the analysis of the stochastic transition and the consequent induced diffusion in the oscillator phase space. A constant of the motion to the first order in a peturbation parameter is calculated, a mapping approximation is derived, and diffusion calculations from the mapping are given. Copyright 1987 Academic Press, Inc
Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio
2015-12-01
An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.
Comparative performance analysis of a dual-solenoid mechanical oscillator
International Nuclear Information System (INIS)
Lee, V C C; Lee, H V; Harno, H G; Woo, K C
2015-01-01
An innovative dual-solenoid electro-mechanical-vibro-impact system has been constructed and experimentally studied. Comparative studies against a mechanical spring system and a permanent magnet system have been performed, where it is shown that the dual-solenoid system is able to produce oscillations better than the permanent magnet system and more energy efficiently. Comparison with a higher-powered dual solenoid system has also been conducted where a stationary solenoid has shown to be a more dominant parameter. In addition, it is also discovered that a mechanical oscillator in the dual-solenoid system is independent of the angular frequency. (paper)
Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity
International Nuclear Information System (INIS)
Lai, S K; Chow, K W
2012-01-01
Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)
Energy Technology Data Exchange (ETDEWEB)
Emenheiser, Jeffrey [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Chapman, Airlie; Mesbahi, Mehran [William E. Boeing Department of Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195 (United States); Pósfai, Márton [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Crutchfield, James P. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Physics, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); D' Souza, Raissa M. [Complexity Sciences Center, University of California, Davis, California 95616 (United States); Department of Computer Science, University of California, Davis, California 95616 (United States); Santa Fe Institute, Santa Fe, New Mexico 87501 (United States); Department of Mechanical and Aerospace Engineering, University of California, Davis, California 95616 (United States)
2016-09-15
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between distinct trajectories in a network of synchronized oscillators. Our system, consisting of nonlinear amplitude-phase oscillators arranged in a ring topology with reactive nearest-neighbor coupling, is simple and connects directly to experimental realizations. We seek to understand how the multiple stable synchronized states connect to each other in state space by applying Gaussian white noise to each of the oscillators' phases. To do this, we first analytically identify a set of locally stable limit cycles at any given coupling strength. For each of these attracting states, we analyze the effect of weak noise via the covariance matrix of deviations around those attractors. We then explore the noise-induced attractor switching behavior via numerical investigations. For a ring of three oscillators, we find that an attractor-switching event is always accompanied by the crossing of two adjacent oscillators' phases. For larger numbers of oscillators, we find that the distribution of times required to stochastically leave a given state falls off exponentially, and we build an attractor switching network out of the destination states as a coarse-grained description of the high-dimensional attractor-basin architecture.
A Possible Mechanism for Driving Oscillations in Hot Giant Planets
International Nuclear Information System (INIS)
Dederick, Ethan; Jackiewicz, Jason
2017-01-01
The κ -mechanism has been successful in explaining the origin of observed oscillations of many types of “classical” pulsating variable stars. Here we examine quantitatively if that same process is prominent enough to excite the potential global oscillations within Jupiter, whose energy flux is powered by gravitational collapse rather than nuclear fusion. Additionally, we examine whether external radiative forcing, i.e., starlight, could be a driver for global oscillations in hot Jupiters orbiting various main-sequence stars at defined orbital semimajor axes. Using planetary models generated by the Modules for Experiments in Stellar Astrophysics and nonadiabatic oscillation calculations, we confirm that Jovian oscillations cannot be driven via the κ -mechanism. However, we do show that, in hot Jupiters, oscillations can likely be excited via the suppression of radiative cooling due to external radiation given a large enough stellar flux and the absence of a significant oscillatory damping zone within the planet. This trend does not seem to be dependent on the planetary mass. In future observations, we can thus expect that such planets may be pulsating, thereby giving greater insight into the internal structure of these bodies.
A Possible Mechanism for Driving Oscillations in Hot Giant Planets
Energy Technology Data Exchange (ETDEWEB)
Dederick, Ethan; Jackiewicz, Jason, E-mail: dederiej@nmsu.edu, E-mail: jasonj@nmsu.edu [New Mexico State University, Las Cruces, NM (United States)
2017-03-10
The κ -mechanism has been successful in explaining the origin of observed oscillations of many types of “classical” pulsating variable stars. Here we examine quantitatively if that same process is prominent enough to excite the potential global oscillations within Jupiter, whose energy flux is powered by gravitational collapse rather than nuclear fusion. Additionally, we examine whether external radiative forcing, i.e., starlight, could be a driver for global oscillations in hot Jupiters orbiting various main-sequence stars at defined orbital semimajor axes. Using planetary models generated by the Modules for Experiments in Stellar Astrophysics and nonadiabatic oscillation calculations, we confirm that Jovian oscillations cannot be driven via the κ -mechanism. However, we do show that, in hot Jupiters, oscillations can likely be excited via the suppression of radiative cooling due to external radiation given a large enough stellar flux and the absence of a significant oscillatory damping zone within the planet. This trend does not seem to be dependent on the planetary mass. In future observations, we can thus expect that such planets may be pulsating, thereby giving greater insight into the internal structure of these bodies.
Quantifying non-linear dynamics of mass-springs in series oscillators via asymptotic approach
Starosta, Roman; Sypniewska-Kamińska, Grażyna; Awrejcewicz, Jan
2017-05-01
Dynamical regular response of an oscillator with two serially connected springs with nonlinear characteristics of cubic type and governed by a set of differential-algebraic equations (DAEs) is studied. The classical approach of the multiple scales method (MSM) in time domain has been employed and appropriately modified to solve the governing DAEs of two systems, i.e. with one- and two degrees-of-freedom. The approximate analytical solutions have been verified by numerical simulations.
Hamiltonian formulation and statistics of an attracting system of nonlinear oscillators
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Tasso, H.
1987-10-01
An attracting system of r nonlinear oscillators of an extended van der Pol type was investigated with respect to Hamiltonian formulation. The case of r=2 is rather simple, though nontrivial. For r>2 the tests with Jacobi's identity and Frechet derivatives are negative if Hamiltonians in the natural variables are looked for. Independently, a Liouville theorem is proved and equilibrium statistics is made possible, which leads to a Gaussian distribution in the natural variables. (orig.)
International Nuclear Information System (INIS)
El Kinani, A.H; Daoud, M.
2001-10-01
This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states a la Gazeau-Klauder and those a la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways. (author)
On the non-linear dynamics of potential relaxation oscillations in bounded plasmas
International Nuclear Information System (INIS)
Krssak, M.; Skalny, J.D.; Gyergyek, T.; Cercek, M.
2007-01-01
Plasma in a 1-dimensional diode is studied theoretically and the computer simulations are used for verification of the theoretical model. When collector in the diode is biased positively, a double-layer is created in the system and consequently, we are able to observe oscillations of the potential, density and other plasma parameters. When external periodic forcing is applied, spectra of these oscillations are changed and effects of synchronisation and periodic pulling can be observed. Both of these effects are of non-linear nature and a good explanation is found using the analogy with Van der Pol oscillators. Following [1] and [2] approximate analytical solutions are found and then compared with computer simulations obtained using a 1-dimensional particle-in-cell code XPDP1. (author)
On the quantization of a nonlinear oscillator with quasi-harmonic behaviour
International Nuclear Information System (INIS)
Ranada, M.F.; Carinena, J.F.; Satander, M.
2006-01-01
Full text: (author)The quantum version of a non-linear oscillator, depending of a parameter λ, is studied. This λ-dependent system can be considered deformation of the harmonic oscillator in the sense that for λ→0 all the characteristics of the linear oscillator are recovered. This is a problem of quantization of a system with position-dependent mass and with a λ-dependent nonpolynominal rational potential. The quantization problem is solved using existence of a Killing vector, the λ-dependent Schroedinger equation is exactly solved and λ-dependent eigenenergies and eigenfunctions are obtained. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as deformations of the standard Hermite polynomials. In the second part, it is proved the superintegrability of the two-dimensional system
International Nuclear Information System (INIS)
Javanainen, Juha
2010-01-01
We study theoretically an atomic Bose-Einstein condensate in a double-well trap, both quantum-mechanically and classically, under conditions such that in the classical model an unstable equilibrium dissolves into large-scale oscillations of the atoms between the potential wells. Quantum mechanics alone does not exhibit such nonlinear dynamics, but measurements of the atom numbers in the potential wells may nevertheless cause the condensate to behave essentially classically.
Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity
Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.
2018-04-01
Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.
Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Marquez, A.; Neipp, C.
2008-01-01
We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems
International Nuclear Information System (INIS)
Kurkin, S. A.; Koronovski, A. A.; Hramov, A. E.
2009-01-01
Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.
Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation
Saghir, Shahid
2016-01-01
The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear
The Human Cochlear Mechanical Nonlinearity Inferred via Psychometric Functions
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Nizami Lance
2013-12-01
Extension of the model of Schairer and colleagues results in credible cochlear nonlinearities in man, suggesting that forward-masking provides a non-invasive way to infer the human mechanical cochlear nonlinearity.
Directory of Open Access Journals (Sweden)
Zong Weikai
2017-01-01
Full Text Available Nonlinear mode interactions are difficult to observe from ground-based telescopes as the typical periods of the modulations induced by those nonlinear phenomena are on timescales of weeks, months, even years. The launch of space telescopes, e.g., Kepler, has tremendously changed the situation and shredded new light on this research field. We present results from Kepler photometry showing evidence that nonlinear interactions between modes occur in the two compact pulsators KIC 8626021, a DB white dwarf, and KIC 10139564, a short period hot B subdwarf. KIC 8626021 and KIC 10139564 had been monitored by Kepler in short-cadence for nearly two years and more than three years without interruption, respectively. By analyzing these high-quality photometric data, we found that the modes within the triplets induced by rotation clearly reveal different behaviors: their frequencies and amplitudes may exhibit either periodic or irregular modulations, or remain constant. These various behaviors of the amplitude and of the frequency modulations of the oscillation modes observed in these two stars are in good agreement with those predicted within the amplitude equation formalism in the case of the nonlinear resonant mode coupling mechanism.
Zhang, Zhen; Koroleva, I; Manevitch, L I; Bergman, L A; Vakakis, A F
2016-09-01
We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "NL pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the
Two-oscillator model of trapped-modes interaction in a nonlinear bilayer fish-scale metamaterial
Tuz, Vladimir R.; Kochetov, Bogdan A.; Kochetova, Lyudmila A.; Mladyonov, Pavel L.; Prosvirnin, Sergey L.
2014-01-01
We discuss the similarity between the nature of resonant oscillations in two nonlinear systems, namely, a chain of coupled Duffing oscillators and a bilayer fish-scale metamaterial. In such systems two different resonant states arise which differ in their spectral lines. The spectral line of the first resonant state has a Lorentzian form, while the second one has a Fano form. This difference leads to a specific nonlinear response of the systems which manifests itself in appearance of closed l...
Comparison among nonlinear excitation control strategies used for damping power system oscillations
International Nuclear Information System (INIS)
Leon, A.E.; Solsona, J.A.; Valla, M.I.
2012-01-01
Highlights: ► A description and comparison of nonlinear control strategies for synchronous generators are presented. ► Advantages of using nonlinear controllers are emphasized against the use of classical PSSs. ► We find that a particular selection of IDA gains achieve the same performance that FL controllers. - Abstract: This work is focused on the problem of power system stability. A thorough description of nonlinear control strategies for synchronous generator excitation, which are designed for damping oscillations and improving transient stability on power systems, is presented along with a detailed comparison among these modern strategies and current solutions based on power system stabilizers. The performance related to damping injection in each controller, critical time enhancement, robustness against parametric uncertainties, and control signal energy consumption is analyzed. Several tests are presented to validate discussions on various advantages and disadvantages of each control strategy.
Nonlinear structural mechanics theory, dynamical phenomena and modeling
Lacarbonara, Walter
2013-01-01
Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...
Lectures in nonlinear mechanics and chaos theory
Stetz, Albert W
2016-01-01
This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...
Comments on microscopic mechanics, generalizations of classical mechanics and Planck's oscillators
International Nuclear Information System (INIS)
Yussouff, M.
1983-05-01
The new microscopic mechanics removes the dichotomy of physics into classical and quantum phenomena. Its physical picture and connections with generalizations of classical mechanics are discussed. It gives a new meaning to Bohr's frequency relation and Planck's oscillators. (author)
A simple mechanical model for the isotropic harmonic oscillator
International Nuclear Information System (INIS)
Nita, Gelu M
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels.
The Mechanical Transient Process at Asynchronous Motor Oscillating Mode
Antonovičs, Uldis; Bražis, Viesturs; Greivulis, Jānis
2009-01-01
The research object is squirrel-cage asynchronous motor connected to single-phase sinusoidal. There are shown, that by connecting to the stator windings a certain sequence of half-period positive and negative voltage, a motor rotor is rotated, but three times slower than in the three-phase mode. Changing the connecting sequence of positive and negative half-period voltage to stator windings, motor can work in various oscillating modes. It is tested experimentally. The mechanical transient processes had been researched in rotation and oscillating modes.
Directory of Open Access Journals (Sweden)
Jian Dang
2016-01-01
Full Text Available Due to the fact that the slight fault signals in early failure of mechanical system are usually submerged in heavy background noise, it is unfeasible to extract the weak fault feature via the traditional vibration analysis. Stochastic resonance (SR, as a method of utilizing noise to amplify weak signals in nonlinear dynamical systems, can detect weak signals overwhelmed in the noise. However, based on the analysis of the impact of noise intensity on SR effect, it is concluded that the detection results are dramatically limited by the noise intensity of measured signals, especially for incipient fault feature of mechanical system with poor working environment. Therefore, this paper proposes a partly Duffing oscillator SR method to extract the fault feature of mechanical system. In this method, to locate the appearance of weak fault feature and decrease noise intensity, the permutation entropy index is constructed to select the measured signals for the input of Duffing oscillator system. Then, according to the regulation of system parameters, a reasonable match between the selected signals and Duffing oscillator model is achieved to produce a SR phenomenon and realize the fault diagnosis of mechanical system. Experiment results demonstrate that the proposed method achieves a better effect on the fault diagnosis of mechanical system.
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations
Energy Technology Data Exchange (ETDEWEB)
Sandhu, Rimple [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Poirel, Dominique [Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, Ontario (Canada); Pettit, Chris [Department of Aerospace Engineering, United States Naval Academy, Annapolis, MD (United States); Khalil, Mohammad [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada); Sarkar, Abhijit, E-mail: abhijit.sarkar@carleton.ca [Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario (Canada)
2016-07-01
A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.
Directory of Open Access Journals (Sweden)
M. Ordu
2017-09-01
Full Text Available Germanium optical fibers hold great promise in extending semiconductor photonics into the fundamentally important mid-infrared region of the electromagnetic spectrum. The demonstration of nonlinear response in fabricated Ge fiber samples is a key step in the development of mid-infrared fiber materials. Here we report the observation of detuning oscillations in a germanium fiber in the mid-infrared region using femtosecond dispersed pump-probe spectroscopy. Detuning oscillations are observed in the frequency-resolved response when mid-infrared pump and probe pulses are overlapped in a fiber segment. The oscillations arise from the nonlinear frequency resolved nonlinear (χ(3 response in the germanium semiconductor. Our work represents the first observation of coherent oscillations in the emerging field of germanium mid-infrared fiber optics.
Han, Qun; Xu, Wei; Sun, Jian-Qiao
2016-09-01
The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.
International Nuclear Information System (INIS)
Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.
2008-01-01
He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient
Effect of state-dependent delay on a weakly damped nonlinear oscillator.
Mitchell, Jonathan L; Carr, Thomas W
2011-04-01
We consider a weakly damped nonlinear oscillator with state-dependent delay, which has applications in models for lasers, epidemics, and microparasites. More generally, the delay-differential equations considered are a predator-prey system where the delayed term is linear and represents the proliferation of the predator. We determine the critical value of the delay that causes the steady state to become unstable to periodic oscillations via a Hopf bifurcation. Using asymptotic averaging, we determine how the system's behavior is influenced by the functional form of the state-dependent delay. Specifically, we determine whether the branch of periodic solutions will be either sub- or supercritical as well as an accurate estimation of the amplitude. Finally, we choose a few examples of state-dependent delay to test our analytical results by comparing them to numerical continuation.
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.
Ryu, Jung-Wan; Kim, Jong-Ho; Son, Woo-Sik; Hwang, Dong-Uk
2017-08-01
We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.
Self-synchronization of populations of nonlinear oscillators in the thermodynamic limit
International Nuclear Information System (INIS)
Bonilla, L.L.; Casado, J.M.; Morillo, M.
1987-01-01
A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase transition from a stationary to a time-periodic probability density. Below the transition line, the population of oscillators is in a quiescent state with order parameter equal to zero. Above the transition line, there is a state of collective rhythmicity characterized by a time-periodic behavior of the order parameter and all moments of the probability distribution. The information entropy of the ensemble is a constant both below and above the critical line. Analytical and numerical analyses of the model are provided
Botari, Tiago; Leonel, Edson D
2013-01-01
A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.
Quantum perturbation solution of sextic nonlinear oscillator and its classical limit
International Nuclear Information System (INIS)
Jafarpour, M.; Ashrafpour, M.
2000-01-01
We consider the time evolution of the perturbed coherent states to solve the quantum sex tic nonlinear oscillator, in the framework of time dependent perturbation theory. An appropriate limit, h-bar → 0, (absolute value of α)→ ∞,(absolute value of α )√h-bar fixed, is then taken and the classical Poincare'-Landsat series is retrieved. We observe that a proper renormalization of the amplitude and the frequency is needed, if a meaningful comparison between the quantum and the classical results are to be made
The Study of a Nonlinear Duffing – Type Oscillator Driven by Two Voltage Sources
Directory of Open Access Journals (Sweden)
J. O. Maaita
2013-10-01
Full Text Available In the present work, a detailed study of a nonlinear electrical oscillator with damping and external excitation is presented. The system under study consists of a Duffing-type circuit driven by two sinusoidal voltage sources having different frequencies. The dynamical behavior of the proposed system is investigated numerically, by solving the system of state equations and simulating its behavior as a circuit using MultiSim. The tools of the theoretical approach are the bifurcation diagrams, the Poincaré sections, the phase portraits, and the maximum Lyapunov exponent. The numerical investigation showed that the system has rich complex dynamics including phenomena such as quasiperiodicity, 3-tori, and chaos.
Jahanbakhsh, F.; Honarasa, G.
2018-04-01
The potential of nonharmonic systems has several applications in the field of quantum physics. The photon-added coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function, Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.
Oscillation of Nonlinear Delay Differential Equation with Non-Monotone Arguments
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Özkan Öcalan
2017-07-01
Full Text Available Consider the first-order nonlinear retarded differential equation $$ x^{\\prime }(t+p(tf\\left( x\\left( \\tau (t\\right \\right =0, t\\geq t_{0} $$ where $p(t$ and $\\tau (t$ are function of positive real numbers such that $%\\tau (t\\leq t$ for$\\ t\\geq t_{0},\\ $and$\\ \\lim_{t\\rightarrow \\infty }\\tau(t=\\infty $. Under the assumption that the retarded argument is non-monotone, new oscillation results are given. An example illustrating the result is also given.
Observation of a Pomeau-Manneville intermittent route to chaos in a nonlinear oscillator
International Nuclear Information System (INIS)
Jeffries, C.; Perez, J.
1982-01-01
For a driven nonlinear semiconductor oscillator which shows a period-doubling pitchfork bifurcation route to chaos, we report an additional route to chaos: the Pomeau-Manneville intermittency route, characterized by a periodic (laminar) phase interrupted by bursts of aperiodic behavior. This occurs near a tangent bifurcation as the system driving parameter is reduced by epsilon from the threshold value for a periodic window. Data are presented for the dependence of the average laminar length on epsilon, and also on additive random noise voltage. The results are in reasonable agreement with the intermittency theory of Hirsch, Huberman, and Scalapino. The distribution P(l) is also reported
Hawes, D. H.; Langley, R. S.
2018-01-01
Random excitation of mechanical systems occurs in a wide variety of structures and, in some applications, calculation of the power dissipated by such a system will be of interest. In this paper, using the Wiener series, a general methodology is developed for calculating the power dissipated by a general nonlinear multi-degree-of freedom oscillatory system excited by random Gaussian base motion of any spectrum. The Wiener series method is most commonly applied to systems with white noise inputs, but can be extended to encompass a general non-white input. From the extended series a simple expression for the power dissipated can be derived in terms of the first term, or kernel, of the series and the spectrum of the input. Calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived. The resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration. The results are validated both numerically and experimentally using a base-excited cantilever beam with a nonlinear restoring force produced by magnets.
The mechanical environment modulates intracellular calcium oscillation activities of myofibroblasts.
Directory of Open Access Journals (Sweden)
Charles Godbout
Full Text Available Myofibroblast contraction is fundamental in the excessive tissue remodeling that is characteristic of fibrotic tissue contractures. Tissue remodeling during development of fibrosis leads to gradually increasing stiffness of the extracellular matrix. We propose that this increased stiffness positively feeds back on the contractile activities of myofibroblasts. We have previously shown that cycles of contraction directly correlate with periodic intracellular calcium oscillations in cultured myofibroblasts. We analyze cytosolic calcium dynamics using fluorescent calcium indicators to evaluate the possible impact of mechanical stress on myofibroblast contractile activity. To modulate extracellular mechanics, we seeded primary rat subcutaneous myofibroblasts on silicone substrates and into collagen gels of different elastic modulus. We modulated cell stress by cell growth on differently adhesive culture substrates, by restricting cell spreading area on micro-printed adhesive islands, and depolymerizing actin with Cytochalasin D. In general, calcium oscillation frequencies in myofibroblasts increased with increasing mechanical challenge. These results provide new insight on how changing mechanical conditions for myofibroblasts are encoded in calcium oscillations and possibly explain how reparative cells adapt their contractile behavior to the stresses occurring in normal and pathological tissue repair.
Energy Technology Data Exchange (ETDEWEB)
Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)
2014-11-03
We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.
Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao
2014-10-06
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.
Energy Technology Data Exchange (ETDEWEB)
Robinson, Brandon [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Rocha da Costa, Leandro Jose [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering; Poirel, Dominique [Royal Military College of Canada, Kingston (Canada). Dept. of Mechanical and Aerospace Engineering; Pettit, Chris [US Naval Academy, Annapolis, MD (United States). Dept. of Mechanical and Aerospace Engineering; Khalil, Mohammad [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sarkar, Abhijit [Carleton Univ., Ottawa, ON (Canada). Dept. of Civil and Environmental Engineering
2017-09-01
Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from the fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.
Dynamic mechanical oscillations during metamorphosis of the monarch butterfly
Pelling, Andrew E; Wilkinson, Paul R; Stringer, Richard; Gimzewski, James K
2008-01-01
The mechanical oscillation of the heart is fundamental during insect metamorphosis, but it is unclear how morphological changes affect its mechanical dynamics. Here, the micromechanical heartbeat with the monarch chrysalis (Danaus plexippus) during metamorphosis is compared with the structural changes observed through in vivo magnetic resonance imaging (MRI). We employ a novel ultra-sensitive detection approach, optical beam deflection, in order to measure the microscale motions of the pupae during the course of metamorphosis. We observed very distinct mechanical contractions occurring at regular intervals, which we ascribe to the mechanical function of the heart organ. Motion was observed to occur in approximately 15 min bursts of activity with frequencies in the 0.4–1.0 Hz range separated by periods of quiescence during the first 83 per cent of development. In the final stages, the beating was found to be uninterrupted until the adult monarch butterfly emerged. Distinct stages of development were characterized by changes in frequency, amplitude, mechanical quality factor and de/repolarization times of the mechanical pulsing. The MRI revealed that the heart organ remains functionally intact throughout metamorphosis but undergoes morphological changes that are reflected in the mechanical oscillation. PMID:18682363
International Conference on Differential Equations and Nonlinear Mechanics
2001-01-01
The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Ae...
Periodic oscillations in linear continuous media coupled with nonlinear discrete systems
International Nuclear Information System (INIS)
Lupini, R.
1998-01-01
A general derivation of partial differential equations with boundary conditions in the form of ordinary differential equations is obtained using the principle of stationary action for a Lagrangian function composed of continuous plus discrete parts in interaction across the boundaries of a 1-dimensional medium. This approach leads directly to the theorem of energy conservation. For linear continuous medium, homogeneous Dirichlet condition at one boundary, and nonlinear oscillator at the other boundary, the entire differential problem reduces to a nonlinear differential-difference equation of neutral type and of the second order. The lag parameter is τ = l/c, where c is the phase speed, l the length of the continuum. The Author investigate the problem of the occurrence of periodic solutions of period integer multiple of the lag (super harmonic solutions) in the case of zero inertia of the boundary system. The problem for such oscillations is shown to reduce to systems of ordinary differential equations with matching conditions in a phase space of lower dimensionality: Phase-plane techniques are used to determine solutions of period 4τ, 8τ and 6τ
Nature's Autonomous Oscillators
Mayr, H. G.; Yee, J.-H.; Mayr, M.; Schnetzler, R.
2012-01-01
Nonlinearity is required to produce autonomous oscillations without external time dependent source, and an example is the pendulum clock. The escapement mechanism of the clock imparts an impulse for each swing direction, which keeps the pendulum oscillating at the resonance frequency. Among nature's observed autonomous oscillators, examples are the quasi-biennial oscillation and bimonthly oscillation of the Earth atmosphere, and the 22-year solar oscillation. The oscillations have been simulated in numerical models without external time dependent source, and in Section 2 we summarize the results. Specifically, we shall discuss the nonlinearities that are involved in generating the oscillations, and the processes that produce the periodicities. In biology, insects have flight muscles, which function autonomously with wing frequencies that far exceed the animals' neural capacity; Stretch-activation of muscle contraction is the mechanism that produces the high frequency oscillation of insect flight, discussed in Section 3. The same mechanism is also invoked to explain the functioning of the cardiac muscle. In Section 4, we present a tutorial review of the cardio-vascular system, heart anatomy, and muscle cell physiology, leading up to Starling's Law of the Heart, which supports our notion that the human heart is also a nonlinear oscillator. In Section 5, we offer a broad perspective of the tenuous links between the fluid dynamical oscillators and the human heart physiology.
Non-linear finite element analysis in structural mechanics
Rust, Wilhelm
2015-01-01
This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.
Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model
Energy Technology Data Exchange (ETDEWEB)
Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br [Associate Laboratory for Computing and Applied Mathematics - LAC, Brazilian National Institute for Space Research - INPE (Brazil); Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de [Department of Physics and Astronomy, University of Potsdam, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Av. 23, 606950, Nizhni Novgorod (Russian Federation)
2015-04-15
We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.
Balaji, Nidish Narayanaa; Krishna, I. R. Praveen; Padmanabhan, C.
2018-05-01
The Harmonic Balance Method (HBM) is a frequency-domain based approximation approach used for obtaining the steady state periodic behavior of forced dynamical systems. Intrinsically these systems are non-autonomous and the method offers many computational advantages over time-domain methods when the fundamental period of oscillation is known (generally fixed as the forcing period itself or a corresponding sub-harmonic if such behavior is expected). In the current study, a modified approach, based on He's Energy Balance Method (EBM), is applied to obtain the periodic solutions of conservative systems. It is shown that by this approach, periodic solutions of conservative systems on iso-energy manifolds in the phase space can be obtained very efficiently. The energy level provides the additional constraint on the HBM formulation, which enables the determination of the period of the solutions. The method is applied to the linear harmonic oscillator, a couple of nonlinear oscillators, the elastic pendulum and the Henon-Heiles system. The approach is used to trace the bifurcations of the periodic solutions of the last two, being 2 degree-of-freedom systems demonstrating very rich dynamical behavior. In the process, the advantages offered by the current formulation of the energy balance is brought out. A harmonic perturbation approach is used to evaluate the stability of the solutions for the bifurcation diagram.
International Nuclear Information System (INIS)
Fujimoto, Kazuya; Tsubota, Makoto
2011-01-01
We consider a trapped atomic Bose-Einstein condensate penetrated by a repulsive Gaussian potential and theoretically investigate the dynamics induced by oscillating the Gaussian potential. Our study is based on the numerical calculation of the two-dimensional Gross-Pitaevskii equation. Our calculation reveals the dependence of the characteristic behavior of the condensate on the amplitude and frequency of the oscillating potential. These dynamics are deeply related to the nucleation and dynamics of quantized vortices and solitons. When the potential oscillates with a large amplitude, it nucleates many vortex pairs that move away from the potential. When the amplitude of the oscillation is small, it nucleates solitons through an annihilation of vortex pairs. We discuss three issues concerning the nucleation of vortices. The first is the phase diagram for the nucleation of vortices and solitons near the oscillating potential. The second is the mechanism and critical velocity of the nucleation. The critical velocity of the nucleation is an important issue in quantum fluids, and we propose an expression for the velocity containing both the coherence length and the size of the potential. The third is the divergence of the nucleation time, which is the time it takes for the potential to nucleate vortices, near the critical parameters for vortex nucleation.
International Nuclear Information System (INIS)
Eliasi, H.; Menhaj, M.B.; Davilu, H.
2011-01-01
Research highlights: → In this work, a robust nonlinear model predictive control algorithm is developed. → This algorithm is applied to control the power level for load following. → The state constraints are imposed on the predicted trajectory during optimization. → The xenon oscillations are the main constraint for the load following problem. → In this algorithm, xenon oscillations are bounded within acceptable limits. - Abstract: One of the important operations in nuclear power plants is load-following in which imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation considered to be a constraint for the load-following operation. In this paper, a robust nonlinear model predictive control for the load-following operation problem is proposed that ensures xenon oscillations are kept bounded within acceptable limits. The proposed controller uses constant axial offset (AO) strategy to maintain xenon oscillations to be bounded. The constant AO is a robust state constraint for load-following problem. The controller imposes restricted state constraints on the predicted trajectory during optimization which guarantees robust satisfaction of state constraints without restoring to a min-max optimization problem. Simulation results show that the proposed controller for the load-following operation is so effective so that the xenon oscillations kept bounded in the given region.
Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators
Talukdar, Abdul Hafiz
2011-01-01
Exceptional behaviours of Memristor are illustrated in Memristor based second order (Wien oscillator) and third order (phase shift oscillator) oscillator systems in this Thesis. Conventional concepts about sustained oscillation have been argued
Michiels, Wim; Nijmeijer, Henk
2009-09-01
We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties
Sage, Cindy
2015-01-01
The 'informational content' of Earth's electromagnetic signaling is like a set of operating instructions for human life. These environmental cues are dynamic and involve exquisitely low inputs (intensities) of critical frequencies with which all life on Earth evolved. Circadian and other temporal biological rhythms depend on these fluctuating electromagnetic inputs to direct gene expression, cell communication and metabolism, neural development, brainwave activity, neural synchrony, a diversity of immune functions, sleep and wake cycles, behavior and cognition. Oscillation is also a universal phenomenon, and biological systems of the heart, brain and gut are dependent on the cooperative actions of cells that function according to principles of non-linear, coupled biological oscillations for their synchrony. They are dependent on exquisitely timed cues from the environment at vanishingly small levels. Altered 'informational content' of environmental cues can swamp natural electromagnetic cues and result in dysregulation of normal biological rhythms that direct growth, development, metabolism and repair mechanisms. Pulsed electromagnetic fields (PEMF) and radiofrequency radiation (RFR) can have the devastating biological effects of disrupting homeostasis and desynchronizing normal biological rhythms that maintain health. Non-linear, weak field biological oscillations govern body electrophysiology, organize cell and tissue functions and maintain organ systems. Artificial bioelectrical interference can give false information (disruptive signaling) sufficient to affect critical pacemaker cells (of the heart, gut and brain) and desynchronize functions of these important cells that orchestrate function and maintain health. Chronic physiological stress undermines homeostasis whether it is chemically induced or electromagnetically induced (or both exposures are simultaneous contributors). This can eventually break down adaptive biological responses critical to health
DEFF Research Database (Denmark)
Hjorth, Poul G.
2008-01-01
We discuss nonlinear mechanical systems containing several oscillators whose frequecies are all much higher than frequencies associated with the remaining degrees of freedom. In this situation a near constant of the motion, an adiabatic invariant, exists which is the sum of all the oscillator...... actions. The phenomenon is illustrated, and calculations of the small change of the adiabatic invariant is outlined....
Oscillation matrices and kernels and small vibrations of mechanical systems
Gantmacher, F R
2002-01-01
Fifty years after the original Russian Edition, this classic work is finally available in English for the general mathematical audience. This book lays the foundation of what later became "Krein's Theory of String". The original ideas stemming from mechanical considerations are developed with exceptional clarity. A unique feature is that it can be read profitably by both research mathematicians and engineers. The authors study in depth small oscillations of one-dimensional continua with a finite or infinite number of degrees of freedom. They single out an algebraic property responsible for the
Non-linear Vibration of Oscillation Systems using Frequency-Amplitude Formulation
DEFF Research Database (Denmark)
Fereidoon, A.; Ghadimi, M.; Barari, Amin
2012-01-01
In this paper we study the periodic solutions of free vibration of mechanical systems with third and fifthorder nonlinearity for two examples using He’s Frequency Amplitude Formulation (HFAF).The effectiveness and convenience of the method is illustrated in these examples. It will be shown that t...... that the solutions obtained with current method have a fabulous conformity with those achieved from time marching solution. HFAF is easy with powerful concepts and the high accuracy, so it can be found widely applicable in vibrations, especially strong nonlinearity oscillatory problems....
The effect of nonlinear forces on coherently oscillating space-charge-dominated beams
International Nuclear Information System (INIS)
Celata, C.M.
1987-03-01
A particle-in-cell computer simulation code has been used to study the transverse dynamics of nonrelativistic misaligned space-charge-dominated coasting beams in an alternating gradient focusing channel. In the presence of nonlinear forces due to dodecapole or octupole imperfections of the focusing fields or to image forces, the transverse rms emittance grows in a beat pattern. Analysis indicates that this emittance dilution is due to the driving of coherent modes of the beam near their resonant frequencies by the nonlinear force. The effects of the dodecapole and images forces can be made to effectively cancel for some boundary conditions, but the mechanism is not understood at this time
Directory of Open Access Journals (Sweden)
P. Musumeci
2013-10-01
Full Text Available The evolution of picosecond modulations of the longitudinal profile of an electron beam generated in an rf photoinjector is analyzed and optimized with the goal of obtaining high peak current electron bunch trains at very high frequencies (≥THz. Taking advantage of nonlinear longitudinal space charge forces, it is found that more than 500 A peak current 1 THz bunch trains can be generated using a standard 1.6 cell SLAC/UCLA/BNL rf gun. Postacceleration is used to freeze the longitudinal phase space dynamics after one half plasma oscillation. Applications range from tunable narrow bandwidth THz radiation generation to drivers for high frequency high gradient accelerators.
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.
Chimera regimes in a ring of oscillators with local nonlinear interaction
Shepelev, Igor A.; Zakharova, Anna; Vadivasova, Tatiana E.
2017-03-01
One of important problems concerning chimera states is the conditions of their existence and stability. Until now, it was assumed that chimeras could arise only in ensembles with nonlocal character of interactions. However, this assumption is not exactly right. In some special cases chimeras can be realized for local type of coupling [1-3]. We propose a simple model of ensemble with local coupling when chimeras are realized. This model is a ring of linear oscillators with the local nonlinear unidirectional interaction. Chimera structures in the ring are found using computer simulations for wide area of values of parameters. Diagram of the regimes on plane of control parameters is plotted and scenario of chimera destruction are studied when the parameters are changed.
Rotation and oscillation of nonlinear dipole vortex in the drift-unstable plasma
International Nuclear Information System (INIS)
Orito, Kohtaro; Hatori, Tadatsugu.
1997-10-01
The behaviors of the nonlinear dipole vortex in the drift unstable plasma are studied by numerical approaches. Model equations used in numerical simulation are derived from two-fluid model and are composed of two equations with respect to the electrostatic potential and the density perturbation. When the initial dipole vortex is inclined at some angle with respect to the direction of the drift velocity, the dipole vortex oscillates or rotates in the first stage. These phenomenon also happen in the stable system. In the second stage, one part of the dipole vortex grows and another decays because of the destabilization. The shrunk vortex rotates around the enlarged vortex. Consequently, a monopole vortex appears out of the dipole vortex. (author)
Directory of Open Access Journals (Sweden)
Zhonghai Guo
2012-01-01
Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
Mansingka, Abhinav S.
2012-07-29
This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.
Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator
Mansingka, Abhinav S.; Radwan, Ahmed G.; Salama, Khaled N.; Zidan, Mohammed A.
2012-01-01
This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation.
Robust Nonlinear Regulation of Limit Cycle Oscillations in UAVs Using Synthetic Jet Actuators
Directory of Open Access Journals (Sweden)
Natalie Ramos Pedroza
2014-09-01
Full Text Available In this paper, a synthetic jet actuators (SJA-based nonlinear robust controller is developed, which is capable of completely suppressing limit cycle oscillations (LCO in UAV systems with parametric uncertainty in the SJA dynamics and unmodeled external disturbances. Specifically, the control law compensates for uncertainty in an input gain matrix, which results from the unknown airflow dynamics generated by the SJA. Challenges in the control design include compensation for input-multiplicative parametric uncertainty in the actuator dynamic model. The result was achieved via innovative algebraic manipulation in the error system development, along with a Lyapunov-based robust control law. A rigorous Lyapunov-based stability analysis is utilized to prove asymptotic LCO suppression, considering a detailed dynamic model of the pitching and plunging dynamics. Numerical simulation results are provided to demonstrate the robustness and practical performance of the proposed control law.
Hoefer, Mark A.
This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued
Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics
Yavari, Arash; Goriely, Alain
2012-01-01
but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed
Hybrid Systems: Cold Atoms Coupled to Micro Mechanical Oscillators =
Montoya Monge, Cris A.
Micro mechanical oscillators can serve as probes in precision measurements, as transducers to mediate photon-phonon interactions, and when functionalized with magnetic material, as tools to manipulate spins in quantum systems. This dissertation includes two projects where the interactions between cold atoms and mechanical oscillators are studied. In one of the experiments, we have manipulated the Zeeman state of magnetically trapped Rubidium atoms with a magnetic micro cantilever. The results show a spatially localized effect produced by the cantilever that agrees with Landau-Zener theory. In the future, such a scalable system with highly localized interactions and the potential for single-spin sensitivity could be useful for applications in quantum information science or quantum simulation. In a second experiment, work is in progress to couple a sample of optically trapped Rubidium atoms to a levitated nanosphere via an optical lattice. This coupling enables the cooling of the center-of-mass motion of the nanosphere by laser cooling the atoms. In this system, the atoms are trapped in the optical lattice while the sphere is levitated in a separate vacuum chamber by a single-beam optical tweezer. Theoretical analysis of such a system has determined that cooling the center-of-mass motion of the sphere to its quantum ground state is possible, even when starting at room temperature, due to the excellent environmental decoupling achievable in this setup. Nanospheres cooled to the quantum regime can provide new tests of quantum behavior at mesoscopic scales and have novel applications in precision sensing.
Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.
2018-07-01
The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.
International Nuclear Information System (INIS)
Shukla, Anant Kant; Ramamohan, T R; Srinivas, S
2014-01-01
In this paper we propose a technique to obtain limit cycles and quasi-periodic solutions of forced nonlinear oscillators. We apply this technique to the forced Van der Pol oscillator and the forced Van der Pol Duffing oscillator and obtain for the first time their limit cycles (periodic) and quasi-periodic solutions analytically. We introduce a modification of the homotopy analysis method to obtain these solutions. We minimize the square residual error to obtain accurate approximations to these solutions. The obtained analytical solutions are convergent and agree well with numerical solutions even at large times. Time trajectories of the solution, its first derivative and phase plots are presented to confirm the validity of the proposed approach. We also provide rough criteria for the determination of parameter regimes which lead to limit cycle or quasi-periodic behaviour. (papers)
Michiels, W.; Nijmeijer, H.
2009-01-01
We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the
International Nuclear Information System (INIS)
Akopyan, A A; Oganesyan, D L
1998-01-01
It is shown that the wave equation can be solved by the method of unidirectional waves for a pulse with a duration of several oscillation periods in a medium with a quadratic nonlinearity, such as a group-3m crystal. The wave equation reduces to a system of two equations for waves with different polarisations. (laser applications and other topics in quantum electronics)
Existence of periodic orbits in nonlinear oscillators of Emden–Fowler form
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Mancas, Stefan C., E-mail: mancass@erau.edu [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Camino a la presa San José 2055, Col. Lomas 4a Sección, 78216 San Luis Potosí, SLP (Mexico)
2016-01-28
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden–Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric solution. Through an invariant transformation we find periodic solutions to a certain class of EF equations that pass an integrability condition. We show that this condition is necessary to have periodic solutions and via the ODE analysis we also find the sufficient condition for periodic orbits. EF equations that do not pass integrability conditions can be made integrable via an invariant transformation which also allows us to construct periodic solutions to them. Two other nonlinear equations, a zero-frequency Ermakov equation and a positive power Emden–Fowler equation, are discussed in the same context. - Highlights: • An invariant transformation is used to find periodic solution of EF equations. • Phase plane study of the EF autonomous two-dimensional ODE system is performed. • Three examples are presented from the standpoint of the phase plane analysis.
SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics
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Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-09-01
This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed
BOERTJENS, G. J.; VAN HORSSEN, W. T.
2000-08-01
In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.
Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads
Directory of Open Access Journals (Sweden)
Donald Mark Santee
2006-01-01
Full Text Available The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.
Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics
Yavari, Arash
2012-03-09
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.
Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death.
Gorban, Alexander N; Tyukina, Tatiana A; Smirnova, Elena V; Pokidysheva, Lyudmila I
2016-09-21
In 1938, Selye proposed the notion of adaptation energy and published 'Experimental evidence supporting the conception of adaptation energy.' Adaptation of an animal to different factors appears as the spending of one resource. Adaptation energy is a hypothetical extensive quantity spent for adaptation. This term causes much debate when one takes it literally, as a physical quantity, i.e. a sort of energy. The controversial points of view impede the systematic use of the notion of adaptation energy despite experimental evidence. Nevertheless, the response to many harmful factors often has general non-specific form and we suggest that the mechanisms of physiological adaptation admit a very general and nonspecific description. We aim to demonstrate that Selye׳s adaptation energy is the cornerstone of the top-down approach to modelling of non-specific adaptation processes. We analyze Selye׳s axioms of adaptation energy together with Goldstone׳s modifications and propose a series of models for interpretation of these axioms. Adaptation energy is considered as an internal coordinate on the 'dominant path' in the model of adaptation. The phenomena of 'oscillating death' and 'oscillating remission' are predicted on the base of the dynamical models of adaptation. Natural selection plays a key role in the evolution of mechanisms of physiological adaptation. We use the fitness optimization approach to study of the distribution of resources for neutralization of harmful factors, during adaptation to a multifactor environment, and analyze the optimal strategies for different systems of factors. Copyright © 2016 Elsevier Ltd. All rights reserved.
Osherovich, V. A.; Fainberg, J.
2018-01-01
We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.
International Nuclear Information System (INIS)
Shokair, I.R.
1991-01-01
Phase mixing of transverse oscillations changes the nature of the ion hose instability from an absolute to a convective instability. The stronger the phase mixing, the faster an electron beam reaches equilibrium with the guiding ion channel. This is important for long distance propagation of relativistic electron beams where it is desired that transverse oscillations phase mix within a few betatron wavelengths of injection and subsequently an equilibrium is reached with no further beam emittance growth. In the linear regime phase mixing is well understood and results in asymptotic decay of transverse oscillations as 1/Z 2 for a Gaussian beam and channel system, Z being the axial distance measured in betatron wavelengths. In the nonlinear regime (which is likely mode of propagation for long pulse beams) results of the spread mass model indicate that phase mixing is considerably weaker than in the regime. In this paper we consider this problem of phase mixing in the nonlinear regime. Results of the spread mass model will be shown along with a simple analysis of phase mixing for multiple oscillator models. Particle simulations also indicate that phase mixing is weaker in nonlinear regime than in the linear regime. These results will also be shown. 3 refs., 4 figs
Tracking Control of Nonlinear Mechanical Systems
Lefeber, A.A.J.
2000-01-01
The subject of this thesis is the design of tracking controllers for certain classes of mechanical systems. The thesis consists of two parts. In the first part an accurate mathematical model of the mechanical system under consideration is assumed to be given. The goal is to follow a certain
Nonlinear wave mechanics from classical dynamics and scale covariance
International Nuclear Information System (INIS)
Hammad, F.
2007-01-01
Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed
International Nuclear Information System (INIS)
Tatchim Bemmo, D.; Siewe Siewe, M.; Tchawoua, C.
2011-01-01
The continuous FitzHugh-Nagumo (FHN for short) model is transformed into modified van der Pol oscillator with asymmetry under external and two-frequency parametric excitations. At the first, the dependence of the solutions on a combined external and two-frequency parametric stimulus forcing is investigated. By using the multiple scale method, ranges of applied current and/or parametric forcing in which nonlinear oscillations are observed are described. Second, when the multiple scale method cannot be used, we numerically prove that in the modified van der Pol oscillator with asymmetry under external and two-frequency parametric excitations, chaos and periodic solution depending on the combination between different frequencies of the model should appear. We also show that the amplitude of the oscillations can be reduced or increased. To do this, we perform the study of the FHN model by choosing a range of parameters exhibiting Hopf bifurcation and two qualitative different regimes in phase portrait. - Highlights: → We model both external and two-frequency parametric excitations in FHN equations. → We examine effects of harmonic forcing on coupled nonlinear oscillator. → Jump and hysteresis phenomena are observed in the dynamical response. → By increasing the constant stimulus we obtain limit cycle. → Some combinations of frequencies produce limit cycle and chaos for other.
A Mechanism Denial Study on the Madden-Julian Oscillation
Directory of Open Access Journals (Sweden)
In-Sik Kang
2011-12-01
Full Text Available A series of Madden-Julian oscillation (MJO mechanism-denial experiments is performed using an atmospheric general circulation model (AGCM. Daily climatological seasonal cycles of i surface latent heat flux, ii net radiative heating rate, and iii surface wind stress are obtained from a control simulation and prescribed in place of the normal interactive computations of these fields in order to turn off the i wind-induced surface heat exchange (WISHE, ii cloud-radiation interaction (CRI, and iii frictional wave-CISK (FWC mechanisms, respectively. Dual and triple mechanism denial experiments are also conducted by switching off multiple mechanisms together. The influence of each mechanism is assessed by comparing experiments with that mechanism turned off to those in which it is not. CRI and WISHE are both found to be important to the simulated MJO amplitude and propagation speed, while FWC has weaker and less systematic effects. The MJO is weakened when CRI is turned off, but strengthened when WISHE is turned off, indicating that CRI amplifies the MJO in the control simulation while WISHE weakens it. The negative influence of WISHE is shown to result from simulated phase relationships between surface winds, surface fluxes and convection which differ significantly from those found in observations, and thus is not interpreted as evidence against a positive role for WISHE in the development and maintenance of the observed MJO. The positive influence of CRI in the model is consistent with a strong simulated relationship between daily grid-point column-integrated radiative and convective heating; the mean ratio of the latter to the former exceeds 0.2 for rain rates less than 14 mm d-1. CRI is also shown to suppress an excessive excitation of the convectively coupled Kelvin wave so that the amplitude and frequency of the MJO is maintained.
International Nuclear Information System (INIS)
Chae, Jongchul; Litvinenko, Yuri E.
2017-01-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D 2 and H α lines.
Energy Technology Data Exchange (ETDEWEB)
Chae, Jongchul [Astronomy Program, Department of Physics and Astronomy, Seoul National University, Seoul 08826 (Korea, Republic of); Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand)
2017-08-01
The vertical propagation of nonlinear acoustic waves in an isothermal atmosphere is considered. A new analytical solution that describes a finite-amplitude wave of an arbitrary wavelength is obtained. Although the short- and long-wavelength limits were previously considered separately, the new solution describes both limiting cases within a common framework and provides a straightforward way of interpolating between the two limits. Physical features of the nonlinear waves in the chromosphere are described, including the dispersive nature of low-frequency waves, the steepening of the wave profile, and the influence of the gravitational field on wavefront breaking and shock formation. The analytical results suggest that observations of three-minute oscillations in the solar chromosphere may reveal the basic nonlinear effect of oscillations with combination frequencies, superposed on the normal oscillations of the system. Explicit expressions for a second-harmonic signal and the ratio of its amplitude to the fundamental harmonic amplitude are derived. Observational evidence of the second harmonic, obtained with the Fast Imaging Solar Spectrograph, installed at the 1.6 m New Solar Telescope of the Big Bear Observatory, is presented. The presented data are based on the time variations of velocity determined from the Na i D{sub 2} and H α lines.
Effect of Magnetic Twist on Nonlinear Transverse Kink Oscillations of Line-tied Magnetic Flux Tubes
Terradas, J.; Magyar, N.; Van Doorsselaere, T.
2018-01-01
Magnetic twist is thought to play an important role in many structures of the solar atmosphere. One of the effects of twist is to modify the properties of the eigenmodes of magnetic tubes. In the linear regime standing kink solutions are characterized by a change in polarization of the transverse displacement along the twisted tube. In the nonlinear regime, magnetic twist affects the development of shear instabilities that appear at the tube boundary when it is oscillating laterally. These Kelvin–Helmholtz instabilities (KHI) are produced either by the jump in the azimuthal component of the velocity at the edge of the sharp boundary between the internal and external part of the tube or by the continuous small length scales produced by phase mixing when there is a smooth inhomogeneous layer. In this work the effect of twist is consistently investigated by solving the time-dependent problem including the process of energy transfer to the inhomogeneous layer. It is found that twist always delays the appearance of the shear instability, but for tubes with thin inhomogeneous layers the effect is relatively small for moderate values of twist. On the contrary, for tubes with thick layers, the effect of twist is much stronger. This can have some important implications regarding observations of transverse kink modes and the KHI itself.
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
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Liu, Yunqiao [MOE Key Laboratory of Hydrodynamics, Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240 (China); Calvisi, Michael L [Department of Mechanical and Aerospace Engineering, University of Colorado, Colorado Springs, CO 80918, United States of America (United States); Wang, Qianxi, E-mail: yunqiaoliu@sjtu.edu.cn [School of Mathematics, University of Birmingham, Birmingham B15 2TT (United Kingdom)
2017-04-15
Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent collapsing EMBs to cells and tissues in clinical settings have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The system modeled consists of the external liquid, membrane and internal gases of an EMB. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow and viscoelasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single- and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency—this enriched acoustic spectrum can enhance blood-tissue contrast and improve the quality of sonographic images. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the encapsulated bubble, thereby improving the efficacy and safety of contrast-enhanced agents. (paper)
Classical and quantum mechanics of the damped harmonic oscillator
International Nuclear Information System (INIS)
Dekker, H.
1981-01-01
The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a historical survey typical features of the problem are discussed on the basis of Havas' classical Hamiltonian and the quantum mechanical Suessmann-Hasse-Albrecht models as coined by the Muenchen/Garching nuclear physics group. It is then shown how by imposing a restriction on the classical trajectories in order to connect the Hamiltonian with the energy, the time-independent Bateman-Morse-Feshbach-Bopp Hamiltonian leads to the time-dependent Caldirola-Kanai Hamiltonian. Canonical quantization of either formulation entails a violation of Heisenberg's principle. By means of a unified treatment of both the electrical and mechanical semi-infinite transmission line, this defect is related to the disregard of additional quantum fluctuations that are intrinsically connected with the dissipation. The difficulties of these models are discussed. Then it is proved that the Bateman dual Hamiltonian is connected to a recently developed complex symplectic formulation by a simple canonical transformation. (orig.)
Directory of Open Access Journals (Sweden)
seyd ghasem enayati
2017-01-01
Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.
Meyer, Yves
2001-01-01
Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals. The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics invo...
International Nuclear Information System (INIS)
Litak, Grzegorz; Syta, Arkadiusz; Borowiec, Marek
2007-01-01
We examine the Melnikov criterion for transition to chaos in case of one degree of freedom non-linear oscillator with non-symmetric potential. This system, when subjected to an external periodic force, shows homoclinic transition from regular vibrations to chaos just before escape from a potential well. We focus especially on the effect of a second resonant excitation with a different phase on the system transition to chaos. We propose a way of its control
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy); Center for Mind/Brain Sciences, University of Trento, Trento (Italy); Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge [Center for Mind/Brain Sciences, University of Trento, Trento (Italy); D' Incerti, Ludovico [Neuroradiology Unit, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2015-03-15
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.
International Nuclear Information System (INIS)
Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge; D'Incerti, Ludovico
2015-01-01
In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D 2 ), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
Control mechanisms for a nonlinear model of international relations
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Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
Experimental analysis of nonlinear problems in solid mechanics
International Nuclear Information System (INIS)
1982-01-01
The booklet presents abstracts of papers from the Euromech Colloqium No. 152 held from Sept. 20th to 24th, 1982 in Wuppertal, Federal Republic of Germany. All the papers are dealing with Experimental Analysis of Nonlinear Problems in Solid Mechanics. (RW)
Casciaro, Sergio; Palmizio Errico, Rosa; Errico, Rosa Palmizio; Conversano, Francesco; Demitri, Christian; Distante, Alessandro
2007-02-01
We sought to characterize the acoustical behavior of the experimental ultrasound contrast agent BR14 by determining the acoustic pressure threshold above which nonlinear oscillation becomes significant and investigating microbubble destruction mechanisms. We used a custom-designed in vitro setup to conduct broadband attenuation measurements at 3.5 MHz varying acoustic pressure (range, 50-190 kPa). We also performed granulometric analyses on contrast agent solutions to accurately measure microbubble size distribution and to evaluate insonification effects. Attenuation did not depend on acoustic pressure less than 100 kPa, indicating this pressure as the threshold for the appearance of microbubble nonlinear behavior. At the lowest excitation amplitude, attenuation increased during insonification, while, at higher excitation levels, the attenuation decreased over time, indicating microbubble destruction. The destruction rate changed with pressure amplitude suggesting different destruction mechanisms, as it was confirmed by granulometric analysis. Microbubbles showed a linear behavior until 100 kPa, whereas beyond this value significant nonlinearities occurred. Observed destruction phenomena seem to be mainly due to gas diffusion and bubble fragmentation mechanisms.
Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics
Baumann, Gerd
2005-01-01
Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A...
Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics
Beretta, Gian Paolo
2006-01-01
We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy stat...
Directory of Open Access Journals (Sweden)
Gang Chen
2012-01-01
Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.
Ulvila, Ville; Phillips, C R; Halonen, Lauri; Vainio, Markku
2013-11-01
We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ(2) nonlinearities, which can substantially increase the effective χ(3) nonlinearity in MgO:LiNbO3, leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (-30 dB) frequency comb centered at 1.56 μm.
Foundations of the non-linear mechanics of continua
Sedov, L I
1966-01-01
International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable
N=4 supersymmetric mechanics with nonlinear chiral supermultiplet
International Nuclear Information System (INIS)
Bellucci, S.; Beylin, A.; Krivonos, S.; Nersessian, A.; Orazi, E.
2005-01-01
We construct N=4 supersymmetric mechanics using the N=4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S 2 and go into the bosonic components of the standard chiral multiplet when the radius of the sphere goes to infinity. We construct the most general action and demonstrate that the nonlinearity of the supermultiplet results in the deformation of the connection, which couples the fermionic degrees of freedom with the background, and of the bosonic potential. Also a non-zero magnetic field could appear in the system
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.; Scacchi, S.; Zampini, Stefano
2015-01-01
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.
2015-07-18
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
The electronic system for mechanical oscillation parameters registration
Directory of Open Access Journals (Sweden)
Bulavin L. A.
2008-08-01
Full Text Available On the basis of the 8-bit microcontroller Microchip PIC16F630 the digital electronic device for harmonic oscillation parameters registration was developed. The device features are simple electric circuit and high operating speed (response time is less than 10 microseconds. The relevant software for the computer-controlled recording of harmonic oscillation parameters was designed. The device can be used as a part of the experimental setup for consistent fluids rheological parameters measurements.
International Nuclear Information System (INIS)
Aya, Izuo; Nariai, Hideki.
1988-01-01
Pressure and fluid oscillations with steam injection into pool water were discussed from the view point of the conversion of thermal energy into mechanical work. When the change of fluid state moves clockwise in the p-V diagram, the oscillation sustains since the thermal energy changes into positive work. The equations difining the mechanical work at the condensation oscillations were presented. The oscillation threshold determined by the condition that mechanical work became zero, coincided with the values derived by the linear oscillation theory. The changes of pressure and specific volume during chugging were also shown with one dimensional simulation analysis. The p-V diagrams at various chugging modes were presented with the movement of steam water interface, and the conversion efficiency of thermal energy to mechanical work was also discussed. (author)
Hybrid spin-nanomechanics with single spins in diamond mechanical oscillators
Barfuss, Arne
2017-01-01
Hybrid spin-oscillator systems, formed by single spins coupled to mechanical oscillators, have attracted ever-increasing attention over the past few years, triggered largely by the prospect of employing such devices as high-performance nanoscale sensors or transducers in multi-qubit networks. Provided the spin-oscillator coupling is strong and robust, such systems can even serve as test-beds for studying macroscopic objects in the quantum regime. In this thesis we present a novel hybrid sp...
Mechanics of inter-modal tunneling in nonlinear waveguides
Jiao, Weijian; Gonella, Stefano
2018-02-01
In this article, we investigate the mechanics of nonlinearly induced inter-modal energy tunneling between flexurally-dominated and axially-dominated modes in phononic waveguides. Special attention is devoted to elucidating the role played by the coupling between axial and flexural degrees of freedom in the determination of the available mode hopping conditions and the associated mechanisms of deformation. Waveguides offer an ideal test bed to investigate the mechanics of nonlinear energy tunneling, due to the fact that they naturally feature, even at low frequencies, families of modes (flexural and axial) that are intrinsically characterized by extreme complementarity. Moreover, thanks to their geometric simplicity, their behavior can be explained by resorting to intuitive structural mechanics models that effectively capture the dichotomy and interplay between flexural and axial mechanisms. After having delineated the fundamental mechanics of flexural-to-axial hopping using the benchmark example of a homogeneous structure, we adapt the analysis to the case of periodic waveguides, in which the complex dispersive behavior due to periodicity results in additional richness of mode hopping mechanisms. We finally extend the analysis to periodic waveguides with internal resonators, in which the availability of locally-resonant bandgaps implies the possibility to activate the resonators even at relatively low frequencies, thus increasing the degree of modal complementarity that is available in the acoustic range. In this context, inter-modal tunneling provides an unprecedented mechanism to transfer conspicuous packets of energy to the resonating microstructure.
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.
Verhagen, E; Deléglise, S; Weis, S; Schliesser, A; Kippenberg, T J
2012-02-01
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P.; van Dijk, Pim
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of
Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?
Wit, Hero P; van Dijk, Pim
2012-08-01
Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of SOAEs.
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...
International Nuclear Information System (INIS)
Donoso, Guillermo; Ladera, Celso L
2012-01-01
We study the nonlinear oscillations of a forced and weakly dissipative spring–magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the oscillating magnetic driving force on the system. From the magnet–coil interactions, we obtain, analytically, the nonlinear motion equation of the system, found to be a forced and damped cubic Duffing oscillator moving in a quartic potential. The relative strengths of the coefficients of the motion equation can be easily set by varying the coils’ dc and ac currents. We demonstrate, theoretically and experimentally, the nonlinear behaviour of this oscillator, including its oscillation modes and nonlinear resonances, the fold-over effect, the hysteresis and amplitude jumps, and its chaotic behaviour. It is an oscillating system suitable for teaching an advanced experiment in nonlinear dynamics both at senior undergraduate and graduate levels. (paper)
Wang, Chenggen; Zhou, Qian; Gao, Shuning; Luo, Jia; Diao, Junchao; Zhao, Haoran; Bu, Jing
2018-04-01
This paper reviews the recent studies of Sub-Synchronous Oscillation(SSO) in wind farms. Mechanisms and analysis methods are the main concerns of this article. A classification method including new types of oscillation occurred between wind farms and HVDC systems and oscillation caused by Permanent Magnet Synchronous Generators(PMSG) is proposed. Characteristics of oscillation analysis techniques are summarized.
International Nuclear Information System (INIS)
Belendez, A.; Fernandez, E.; Rodes, J.J.; Fuentes, R.; Pascual, I.
2009-01-01
In a previous short communication [A. Belendez, E. Fernandez, J.J. Rodes, R. Fuentes, I. Pascual, Phys. Lett. A 373 (2009) 735] the nonlinear oscillations of a punctual charge in the electric field of a charged ring were analyzed. Approximate frequency-amplitude relations and periodic solutions were obtained using the harmonic balance method. Now we clarify an important aspect about of this oscillation charge. Taking into account Earnshaw's theorem, this punctual charge cannot be a free charge and so it must be confined, for example, on a finite conducting wire placed along the axis of the ring. Then, the oscillatory system may consist of a punctual charge on a conducting wire placed along the axis of the uniformly charged ring.
Flexible mechanism of magnetic microbeads chains in an oscillating field
Li, Yan-Hom; Yen, Chia-Yen
2018-05-01
To investigate the use of magnetic microbeads for swimming at low Reynolds number, the flexible structure of microchains comprising superparamagnetic microbeads under the influence of oscillating magnetic fields is examined experimentally and theoretically. For a ductile chain, each particle has its own phase angle trajectory and phase-lag angle to the overall field. This present study thoroughly discusses the synchronicity of the local phase angle trajectory between each dyad of beads and the external field. The prominently asynchronous trajectories between the central and outer beads significantly dominate the flexible structure of the oscillating chain. In addition, the dimensionless local Mason number (Mnl) is derived as the solo controlling parameter to evaluate the structure of each dyad of beads in a flexible chain. The evolution of the local Mason number within an oscillating period implies the most unstable position locates near the center of the chain around 0.6P
Statistical mechanics of quantum one-dimensional damped harmonic oscillator
International Nuclear Information System (INIS)
Borges, E.N.M.; Borges, O.N.; Ribeiro, L.A.A.
1985-01-01
We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola-Kanai Hamiltonian
Fluid mechanics and heat transfer advances in nonlinear dynamics modeling
Asli, Kaveh Hariri
2015-01-01
This valuable new book focuses on new methods and techniques in fluid mechanics and heat transfer in mechanical engineering. The book includes the research of the authors on the development of optimal mathematical models and also uses modern computer technology and mathematical methods for the analysis of nonlinear dynamic processes. It covers technologies applicable to both fluid mechanics and heat transfer problems, which include a combination of physical, mechanical, and thermal techniques. The authors develop a new method for the calculation of mathematical models by computer technology, using parametric modeling techniques and multiple analyses for mechanical system. The information in this book is intended to help reduce the risk of system damage or failure. Included are sidebar discussions, which contain information and facts about each subject area that help to emphasize important points to remember.
He, Yong
2017-06-23
We utilize the surface plasmon field of a metal nanoparticle (MNP) to show strain-mediated coupling in a quantum dot-mechanical resonator hybrid system including a quantum dot (QD) embedded within a conical nanowire (NW) and a MNP in the presence of an external field. Based on the numerical solutions of the master equation, we find that a slow oscillation, originating from the strain-mediated coupling between the QD and the NW, appears in the time evolution of the plasmon field enhancement. The results show that the period (about [Formula: see text]) of the slow oscillation is equal to that of the mechanical resonator of NW, which suggests that the time-resolved measurement of the plasmon field enhancement can be easily achieved based on the current experimental conditions. Its amplitude increases with the increasing strain-mediated coupling strength, and under certain conditions there is a linear relationship between them. The slow oscillation of the plasmon field enhancement provides valuable tools for measurements of the mechanical frequency and the strain-mediated coupling strength.
Hidden Area and Mechanical Nonlinearities in Freestanding Graphene
Nicholl, Ryan J. T.; Lavrik, Nickolay V.; Vlassiouk, Ivan; Srijanto, Bernadeta R.; Bolotin, Kirill I.
2017-06-01
We investigated the effect of out-of-plane crumpling on the mechanical response of graphene membranes. In our experiments, stress was applied to graphene membranes using pressurized gas while the strain state was monitored through two complementary techniques: interferometric profilometry and Raman spectroscopy. By comparing the data obtained through these two techniques, we determined the geometric hidden area which quantifies the crumpling strength. While the devices with hidden area ˜0 % obeyed linear mechanics with biaxial stiffness 428 ±10 N /m , specimens with hidden area in the range 0.5%-1.0% were found to obey an anomalous nonlinear Hooke's law with an exponent ˜0.1 .
Reconstructing a nonlinear dynamical framework for testing quantum mechanics
International Nuclear Information System (INIS)
Jordan, T.F.
1993-01-01
The nonlinear generalization of quantum dynamics constructed by Weinberg as a basis for experimental tests is reconstructed in terms of density-matrix elements to allow independent dynamics for subsystems. Dynamics is generated with a Lie bracket and a nonlinear Hamiltonian function. It takes density matrices to density matrices and pure states to pure states. Each density matrix has a Hamiltonian operator that makes its evolution for an infinitesimal time, but the Hamiltonian operator may be different for different density matrices and may change in time as the density matrix changes. A Hamiltonian function for a subsystem serves also for the entire system. Independence of separate subsystems is confirmed by seeing that brackets are zero for functions from different subsystems and by looking at the Hamiltonian operator for each density matrix. Scaling properties of Hamiltonian functions are found to be important in connection with locality. An example of all this is obtained from every one of the local nonlinear Schroedinger equations described by Bialynicki-Birula and Mycielski. Examples are worked out for spins coupled together or to fields, demonstrating Hamiltonian functions and equations of motion written directly in terms of physical mean values. Observables and states are taken to be the same as in ordinary quantum mechanics. An attempt to find nonlinear representations of observables by characterizing propositions as functions equal to their squares yields a negative result. Sharper interpretation of mixed states is proposed. In a mixture of parts that are prepared separately, time dependence must be calculated separately for each part so different mixtures that yield the same density matrix can be distinguished. No criticism has shown that a consistent interpretation cannot be made this way. Thus, nonlinearity remains a viable hypothesis for experimental tests. 16 refs
Is there a relativistic nonlinear generalization of quantum mechanics?
Energy Technology Data Exchange (ETDEWEB)
Elze, Hans-Thomas [Dipartimento di Fisica ' Enrico Fermi' , Largo Pontecorvo 3, I-56127 Pisa (Italy)
2007-05-15
Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.
On the asymptotic stability of nonlinear mechanical switched systems
Platonov, A. V.
2018-05-01
Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.
Quantum mechanical analysis of nonlinear optical response of interacting graphene nanoflakes
Directory of Open Access Journals (Sweden)
Hanying Deng
2018-01-01
Full Text Available We propose a distant-neighbor quantum-mechanical (DNQM approach to study the linear and nonlinear optical properties of graphene nanoflakes (GNFs. In contrast to the widely used tight-binding description of the electronic states that considers only the nearest-neighbor coupling between the atoms, our approach is more accurate and general, as it captures the electron-core interactions between all atoms in the structure. Therefore, as we demonstrate, the DNQM approach enables the investigation of the optical coupling between two closely separated but chemically unbound GNFs. We also find that the optical response of GNFs depends crucially on their shape, size, and symmetry properties. Specifically, increasing the size of nanoflakes is found to shift their accommodated quantum plasmon oscillations to lower frequency. Importantly, we show that by embedding a cavity into GNFs, one can change their symmetry properties, tune their optical properties, or enable otherwise forbidden second-harmonic generation processes.
Directory of Open Access Journals (Sweden)
Li Gang
2016-01-01
Full Text Available This investigation is to solve the power-level control issue of a nonlinear pressurized water reactor core with xenon oscillations. A nonlinear pressurized water reactor core is modeled using the lumped parameter method, and a linear model of the core is then obtained through the small perturbation linearization way. The H∞loop shapingcontrolis utilized to design a robust controller of the linearized core model.The calculated H∞loop shaping controller is applied to the nonlinear core model. The nonlinear core model and the H∞ loop shaping controller build the nonlinear core power-level H∞loop shaping control system.Finally, the nonlinear core power-level H∞loop shaping control system is simulatedconsidering two typical load processes that are a step load maneuver and a ramp load maneuver, and simulation results show that the nonlinear control system is effective.
Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators
Gopal, R.; Chandrasekar, V. K.; Senthilkumar, D. V.; Venkatesan, A.; Lakshmanan, M.
2018-06-01
A complex collective emerging behavior characterized by coexisting coherent and incoherent domains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and complete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely Rössler oscillators and Stuart-Landau oscillators.
Outline of a nonlinear, relativistic quantum mechanics of extended particles
International Nuclear Information System (INIS)
Mielke, E.W.
1981-01-01
A quantum theory of intrinsically extended particles similar to de Broglie's theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)
Outline of a nonlinear, relativistic quantum mechanics of extended particles
International Nuclear Information System (INIS)
Mielke, E.W.
1981-01-01
A quantum theory of intrinsically extended particles similar to de Broglie's Theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)
Supersymmetric quantum mechanics approach to a nonlinear lattice
International Nuclear Information System (INIS)
Ricotta, Regina Maria; Drigo Filho, Elso
2011-01-01
Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)
Nonlinear Viscoelastic Mechanism for Aftershock Triggering and Decay
Shcherbakov, R.; Zhang, X.
2016-12-01
Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In one prominent example, they typically occur after large earthquakes. They also occur in other natural or experimental systems, for example, in solar flares, in fracture experiments on porous materials and acoustic emissions, after stock market crashes, in the volatility of stock prices returns, in internet traffic variability and e-mail spamming, to mention a few. The observed aftershock sequences usually obey several well defined non-trivial empirical laws in magnitude, temporal, and spatial domains. In many cases their characteristics follow scale-invariant distributions. The occurrence of aftershocks displays a prominent temporal behavior due to time-dependent mechanisms of stress and/or energy transfer. In this work, we consider a slider-block model to mimic the behavior of a seismogenic fault. In the model, we introduce a nonlinear viscoelastic coupling mechanism to capture the essential characteristics of crustal rheology and stress interaction between the blocks and the medium. For this purpose we employ nonlinear Kelvin-Voigt elements consisting of an elastic spring and a dashpot assembled in parallel to introduce viscoelastic coupling between the blocks and the driving plate. By mapping the model into a cellular automaton we derive the functional form of the stress transfer mechanism in the model. We show that the nonlinear viscoelasticity plays a critical role in triggering of aftershocks. It explains the functional form of the Omori-Utsu law and gives physical interpretation of its parameters. The proposed model also suggests that the power-law rheology of the fault gauge and underlying lower crust and upper mantle control the decay rate of aftershocks. To verify this, we analyze several prominent aftershock sequences to estimate their decay rates and correlate with the rheological properties of the underlying lower crust and
International Nuclear Information System (INIS)
Fan Hongyi; Yu Shenxi
1994-01-01
We show that the differential form of the fundamental completeness relation in quantum mechanics and the technique of differentiation within an ordered product (DWOP) of operators provide a new approach for calculating normal product expansions of some nonlinear operators and study some nonlinear transformations. Their usefulness in perturbative calculations is pointed out. (orig.)
On One Means of Hard Excitation of Oscillations in Nonlinear Flutter Systems
Directory of Open Access Journals (Sweden)
S. D. Glyzin
2014-01-01
Full Text Available Considered are so-called finite-dimensional flutter systems, i.e. systems of ordinary differential equations, arising from Galerkin approximations of certain boundary value problems of aeroelasticity theory as well as from a number of radiophysics applications. We study small oscillations of these equations in case of 1 : 3 resonance. By combining analytical and numerical methods, it is concluded that the mentioned resonance can cause a hard excitation of oscillations. Namely, for flutter systems shown is the possibility of coexistence, along with the stable zero state, of stable invariant tori of arbitrary finite dimension as well as chaotic attractors.
Linear differential equations to solve nonlinear mechanical problems: A novel approach
Nair, C. Radhakrishnan
2004-01-01
Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...
Linear and nonlinear piezoelectric shunting strategies for vibration mitigation
Directory of Open Access Journals (Sweden)
Soltani P.
2014-01-01
Full Text Available This paper studies linear and nonlinear piezoelectric vibration absorbers that are designed based on the equal-peak method. A comparison between the performance of linear mechanical and electrical tuned vibration absorbers coupled to a linear oscillator is first performed. Nonlinearity is then introduced in the primary oscillator to which a new nonlinear electrical tuned vibration absorber is attached. Despite the frequency-energy dependence of nonlinear oscillations, we show that the nonlinear absorber is capable of effectively mitigating the vibrations of the nonlinear primary system in a large range of forcing amplitudes.
Gao, Peng
2018-04-01
This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.
Gao, Peng
2018-06-01
This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.
Non-linear Shape Oscillations of Rising Drops and Bubbles: Experiments and Simulations.
Czech Academy of Sciences Publication Activity Database
Lalanne, B.; Abi Chebel, N.; Vejražka, Jiří; Tanguy, S.; Masbernat, O.; Risso, F.
2015-01-01
Roč. 27, č. 12 (2015), s. 123305 ISSN 1070-6631. [Conference of European Colloid and Interface Society /27./. Sofia, 01.09.2013-06.09.2013] R&D Projects: GA MŠk(CZ) LD13018 Institutional support: RVO:67985858 Keywords : shape oscillations * nonlinearitites * interface dynamics Subject RIV: CI - Industrial Chemistry, Chemical Engineering Impact factor: 2.017, year: 2015
An exactly solvable model of an oscillator with nonlinear coupling and zeros of Bessel functions
Dodonov, V. V.; Klimov, A. B.
1993-01-01
We consider an oscillator model with nonpolynomial interaction. The model admits exact solutions for two situations: for energy eigenvalues in terms of zeros of Bessel functions, that were considered as functions of the continuous index; and for the corresponding eigenstates in terms of Lommel polynomials.
Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts
DEFF Research Database (Denmark)
Schilder, Frank; Rübel, Jan; Starke, Jens
2008-01-01
We present a numerical method for the investigation of quasiperiodic oscillations in applications modeled by systems of ordinary differential equations. We focus on systems with parts that have a significant rotational speed. An important element of our approach is that it allows us to verify whe...
Nonlinear Aeroelastic Study of Stall Induced Oscillation in a Symmetric Airfoil
Sarkar, S.; Bijl, H.
2006-01-01
In this paper the aeroelastic stability of a wind turbine rotor in the dynamic stall regime is investigated. Increased flexibility of modern turbine blades makes them more susceptible to aeroelastic instabilities. Complex oscillation modes like flap/lead-lag are of particular concern, which give way
Explodator: A new skeleton mechanism for the halate driven chemical oscillators
Noszticzius, Z.; Farkas, H.; Schelly, Z. A.
1984-06-01
In the first part of this work, some shortcomings in the present theories of the Belousov-Zhabotinskii oscillating reaction are discussed. In the second part, a new oscillatory scheme, the limited Explodator, is proposed as an alternative skeleton mechanism. This model contains an always unstable three-variable Lotka-Volterra core (the ``Explodator'') and a stabilizing limiting reaction. The new scheme exhibits Hopf bifurcation and limit cycle oscillations. Finally, some possibilities and problems of a generalization are mentioned.
Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation
Saghir, Shahid
2016-12-01
The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear static and dynamic behavior of rectangular microplates under small and large actuating forces. In the first part, we present and compare various approaches to develop reduced order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. In the second part, we present an investigation of the static and dynamic behavior of a fully clamped microplate. We investigate the effect of different non-dimensional design parameters on the static response. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of midplane stretching. However, the behavior switches to softening as the DC load is increased. Next, near-square plates are studied to understand the effect of geometric imperfections of microplates. In the final part of the dissertation, we investigate the mechanical behavior of
Methodic of practical study teaching on subject 'Characteristic mechanical oscillations'
International Nuclear Information System (INIS)
Tenchurina, A.R.
2006-01-01
In this article the methodic of the undertaking the practical lesson for subject 'the own mechanical vibrations' is considered and offered the algorithm of the problem decision the finding of the vibration period for the different mechanical systems. (author)
DEFF Research Database (Denmark)
Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi
In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations...
Spatiotemporal Oscillations in Tokamak Edge Layer and their Generation by Various Mechanisms
Energy Technology Data Exchange (ETDEWEB)
Daybelge, U.; Yarim, C., E-mail: daybelge@itu.edu.tr [Istanbul Technical University, Istanbul (Turkey); Nicolai, A. [Forschungszentrum Juelich, Juelich (Germany)
2012-09-15
Full text: Toroidal and poloidal rotations of plasma at the edge region of tokamak devices have long been known to play an important role, such as enhancing the confinement properties by suppressing turbulent behaviour, improving tolerance to error fields and increasing stability to neoclassical tearing modes. Hence, understanding of creation and evolution of rotation is important, since external momentum would not be enough or could not even be realized especially for future large fusion devices. In addition to the externally applied momentum, several mechanisms have been suggested to explain the reasons for spontaneous toroidal rotation of plasmas. For a tokamak edge region as found, for example, within the operational boundaries of the ASDEX upgrade, relevance of the collisional neoclassical theory was recently emphasized. In this regime gyrostresses play a considerable role in modifying the coupled flux surface averaged continuity, energy and momentum equations. Examination of the terms in these equations that are responsible for diffusion or reaction and acting as sources, can show the share of the neoclassical mechanisms to terms like intrinsic rotation, etc. Using similarities of our equations to the nonlinear reaction-diffusion equations with a susceptibility to the Turing instability and applying some robust numerical methods, we present here an approach based on the spatiotemporal simulation of the oscillations in plasma temperature, density, toroidal and poloidal rotation velocities under various perturbative effects. Present study considers a subsonic, collisional plasma in front of the magnetic separatrix. Study indicates a nonlinear, three-time-scales-coupling between the evolutions of the density, temperature and poloidal and toroidal rotation velocities. Numerical solutions of the coupled system for the vector W = [T,N,U{sub {phi}}, U{sub {theta}}] were studied under various given sources such as a periodic pellet injection or loop voltage variation
Nonlinear oscillations of a coupled autoparametrical system with ideal and nonideal sources of power
Directory of Open Access Journals (Sweden)
Sado Danuta
2006-01-01
Full Text Available An ideal and nonideal autoparametrical system excited by DC motor with unbalanced mass is presented in this work. The system consists of the body of mass M which is hung on a nonlinear spring with a nonlinear damper, and a pendulum of the length l and mass m mounted to the body of mass M. It is assumed that the motion of the pendulum is damped by nonlinear resistive forces. Vibrations of both models (ideal and nonideal are researched. Solutions for the system response are presented for specific values of the parameters of system and the energy transfer between modes of vibrations is studied. Next excited vibrations for both models have been examined analytically and numerically. Except different kinds of periodic vibrations, there may also appear chaotic vibrations.
Energy Technology Data Exchange (ETDEWEB)
Rahmani, S.; Hassanabadi, H. [Shahrood University of Technology, Physics Department, Shahrood (Iran, Islamic Republic of)
2017-09-15
Employing generalized quantum isotonic oscillator potential we determine wave function for mesonic system in nonrelativistic formalism. Then we investigate branching ratios of leptonic decays for heavy-light mesons including a charm quark. Next, by applying the Isgur-Wise function we obtain branching ratios of semileptonic decays for mesons including a bottom quark. The weak decay of the B{sub c} meson is also analyzed to study the life time. Comparison with other available theoretical approaches is presented. (orig.)
Nonlinear dynamics in a laser field: spontaneous oscillation of mesoscopic soft matter
Nomura, S; Yoshikawa, K
2003-01-01
Experimental studies on the utilization of a laser to create a thermodynamically open system in a mesoscopic scale have been performed, where the laser has the roles to generate attractive and scattering forces on an optically trapped object. We have succeeded in the observation of various novel oscillatory phenomena under laser illumination. In this paper, we present the results of new experiments on the cyclic oscillation of a single giant molecule and periodic bursting in a cluster of micrometer sized beads.
Numerical Analysis of Strongly Nonlinear Oscillation Systems using He's Max-Min Method
DEFF Research Database (Denmark)
Babazadeh, H; Domairry, G; Barari, Amin
2011-01-01
Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method...
The negative-differential-resistance (NDR) mechanism of a hydroelastic microfluidic oscillator
International Nuclear Information System (INIS)
Xia, H M; Wu, J W; Wang, Z P
2017-01-01
A microfluidic oscillator is of interest because it converts a stable laminar flow to oscillatory flow, especially in view of the fact that turbulence is typically absent in miniaturized fluidic devices. One important design approach is to utilize hydroelastic effect-induced autonomous oscillations to modify the flow, so to reduce the reliance on external controllers. However, as complex fluid-structure interactions are involved, the prediction of its mechanism is rather challenging. Here, we present a simple equivalent circuit model and investigate the negative-differential-resistance (NDR) mechanism of a hydroelastic microfluidic oscillator. We show that a variety of complex flow behaviors including the onset of oscillation, formation of different oscillation patterns, collapse of the channel, etc can be well explained by this model. It provides a generic approach for construction of microfluidic NDR oscillators, following which a new design is also proposed. Relevant findings give more insights into the hydroelastic instability problems in microfluidics, and enrich the study of microfluidic flow control devices based on the electric circuit theory. (paper)
International Nuclear Information System (INIS)
Bliokh, Yu.P.
2001-01-01
During more than 50 years of Plasma Electronics development a great number of experimental and theoretical results have been achieved. These results allow understanding of physical processes which originate under charged particles beams interaction with a plasma. However, one essential aspect of such interaction remains insufficiently studied. The question is about a correlation between conditions of microwave excitation by a beam in plasma and plasma parameters. Each of these effects, namely the influence of plasma parameters on conditions of microwave excitation by a beam and plasma parameters variations under the influence of propagating microwave radiation are well known and investigated enough. However their common action under beam-plasma instability (BPI) development were not studied systematically, although the role of such reciprocal influence on character of these processes may be very large. The aim of this report is a review of recent theoretical and experimental investigations of such plasma nonlinearity in plasma-filled trawling-wave tubes. N.M.Zemlyansky and E.A.Kornilov have done experiments in Kharkov Institute of Physics and Technology (KhPhTI). Development of the theoretical model was started in KhPhTI (Yu.P.Bliokh, Ya.B.Fainberg, M.G.Lyubarsky, and V.O.Podobinsky) and continues by author in Technion. The developed theory takes into account two main reasons of the plasma density redistribution: high frequency pressure (HFP) force which ''push out'' plasma from the regions with increased microwave amplitude, or microwave discharge, which appears in the region where amplitude is large enough. Displaced (under HFP action) or additionally originating (under (BPD) development) plasma propagates from the disturbance source in the form of slow plasma waves (for example, ion-sound or magneto-sound waves), and the BPI develops in the nonhomogeneous plasma. It changes both magnitude and longitudinal distribution of excited microwave amplitude. As a result
International Nuclear Information System (INIS)
Song Yongli; Tadé, Moses O; Zhang Tonghua
2009-01-01
In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained
The slow oscillation in cortical and thalamic networks: mechanisms and functions
Directory of Open Access Journals (Sweden)
Garrett T. Neske
2016-01-01
Full Text Available During even the most quiescent behavioral periods, the cortex and thalamus express rich spontaneous activity in the form of slow (<1 Hz, synchronous network state transitions. Throughout this so-called slow oscillation, cortical and thalamic neurons fluctuate between periods of intense synaptic activity (Up states and almost complete silence (Down states. The two decades since the original characterization of the slow oscillation in the cortex and thalamus have seen considerable advances in deciphering the cellular and network mechanisms associated with this pervasive phenomenon. There are, nevertheless, many questions regarding the slow oscillation that await more thorough illumination, particularly the mechanisms by which Up states initiate and terminate, the functional role of the rhythmic activity cycles in unconscious or minimally conscious states, and the precise relation between Up states and the activated states associated with waking behavior. Given the substantial advances in multineuronal recording and imaging methods in both in vivo and in vitro preparations, the time is ripe to take stock of our current understanding of the slow oscillation and pave the way for future investigations of its mechanisms and functions. My aim in this Review is to provide a comprehensive account of the mechanisms and functions of the slow oscillation, and to suggest avenues for further exploration.
Mechanical Properties of Laminate Materials: From Surface Waves to Bloch Oscillations
DEFF Research Database (Denmark)
Liang, Z.; Willatzen, Morten; Christensen, Johan
2015-01-01
for designing Bloch oscillations in classical plate structures and show how mechanical Bloch oscillations can be generated in arrays of solid plates when the modal wavelength is gradually reduced. The design recipe describes how Bloch oscillations in classical structures of arbitrary dimensions can be generated......We propose hitherto unexplored and fully analytical insights into laminate elastic materials in a true condensed-matter-physics spirit. Pure mechanical surface waves that decay as evanescent waves from the interface are discussed, and we demonstrate how these designer Scholte waves are controlled......, and we demonstrate this numerically for structures with millimeter and centimeter dimensions in the kilohertz to megahertz range. Analytical predictions agree entirely with full wave simulations showing how elastodynamics can mimic quantum-mechanical condensed-matter phenomena....
Lembong, Josephine; Sabass, Benedikt; Stone, Howard A.
2017-08-01
The maintenance of tissue integrity is essential for the life of multicellular organisms. Healing of a skin wound is a paradigm for how various cell types localize and repair tissue perturbations in an orchestrated fashion. To investigate biophysical mechanisms associated with wound localization, we focus on a model system consisting of a fibroblast monolayer on an elastic substrate. We find that the creation of an edge in the monolayer causes cytosolic calcium oscillations throughout the monolayer. The oscillation frequency increases with cell density, which shows that wound-induced calcium oscillations occur collectively. Inhibition of myosin II reduces the number of oscillating cells, demonstrating a coupling between actomyosin activity and calcium response. The spatial distribution of oscillating cells depends on the stiffness of the substrate. For soft substrates with a Young’s modulus E ~ 360 Pa, oscillations occur on average within 0.2 mm distance from the wound edge. Increasing substrate stiffness leads to an average localization of oscillations away from the edge (up to ~0.6 mm). In addition, we use traction force microscopy to determine stresses between cells and substrate. We find that an increase of substrate rigidity leads to a higher traction magnitude. For E ~8 kPa, traction magnitude is on average almost uniform beneath the monolayer. Thus, the spatial occurrence of calcium oscillations correlates with the cell-substrate traction. Overall, the experiments with fibroblasts demonstrate a collective, chemomechanical localization mechanism at the edge of a wound with a potential physiological role.
Nonlinear mechanics a supplement to theoretical mechanics of particles and continua
Fetter, Alexander L
2006-01-01
In their prior Dover book, Theoretical Mechanics of Particles and Continua, Alexander L. Fetter and John Dirk Walecka provided a lucid and self-contained account of classical mechanics, together with appropriate mathematical methods. This supplement-an update of that volume-offers a bridge to contemporary mechanics.The original book's focus on continuum mechanics-with chapters on sound waves in fluids, surface waves on fluids, heat conduction, and viscous fluids-forms the basis for this supplement's discussion of nonlinear continuous systems. Topics include linearized stability analysis; a det
Ultrahigh-Q mechanical oscillators through optical trapping
International Nuclear Information System (INIS)
Chang, D E; Ni, K-K; Painter, O; Kimble, H J
2012-01-01
Rapid advances are being made toward optically cooling a single mode of a micro-mechanical system to its quantum ground state and observing the quantum behavior at macroscopic scales. Reaching this regime in room-temperature environments requires a stringent condition on the mechanical quality factor Q m and frequency f m , Q m f m ≳ k B T bath /h, which so far has been marginally satisfied only in a small number of systems. Here we propose and analyze a new class of systems that should enable one to obtain unprecedented Q-frequency products. The technique is based on the use of optical forces to ‘trap’ and stiffen the motion of a tethered mechanical structure, thereby freeing the resulting mechanical frequencies and decoherence rates from the underlying material properties. (paper)
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.
Directory of Open Access Journals (Sweden)
Olga Kononova
2016-01-01
Full Text Available The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F-deformation (X spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.
Donoso, Guillermo; Ladera, Celso L.
2012-01-01
We study the nonlinear oscillations of a forced and weakly dissipative spring-magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet-spring system. The second coil, located below the…
Vapor plume oscillation mechanisms in transient keyhole during tandem dual beam fiber laser welding
Chen, Xin; Zhang, Xiaosi; Pang, Shengyong; Hu, Renzhi; Xiao, Jianzhong
2018-01-01
Vapor plume oscillations are common physical phenomena that have an important influence on the welding process in dual beam laser welding. However, until now, the oscillation mechanisms of vapor plumes remain unclear. This is primarily because mesoscale vapor plume dynamics inside a millimeter-scale, invisible, and time-dependent keyhole are difficult to quantitatively observe. In this paper, based on a developed three-dimensional (3D) comprehensive model, the vapor plume evolutions in a dynamical keyhole are directly simulated in tandem dual beam, short-wavelength laser welding. Combined with the vapor plume behaviors outside the keyhole observed by high-speed imaging, the vapor plume oscillations in dynamical keyholes at different inter-beam distances are the first, to our knowledge, to be quantitatively analyzed. It is found that vapor plume oscillations outside the keyhole mainly result from vapor plume instabilities inside the keyhole. The ejection velocity at the keyhole opening and dynamical behaviors outside the keyhole of a vapor plume both violently oscillate with the same order of magnitude of high frequency (several kHz). Furthermore, the ejection speed at the keyhole opening and ejection area outside the keyhole both decrease as the beam distance increases, while the degree of vapor plume instability first decreases and then increases with increasing beam distance from 0.6 to 1.0 mm. Moreover, the oscillation mechanisms of a vapor plume inside the dynamical keyhole irradiated by dual laser beams are investigated by thoroughly analyzing the vapor plume occurrence and flow process. The vapor plume oscillations in the dynamical keyhole are found to mainly result from violent local evaporations and severe keyhole geometry variations. In short, the quantitative method and these findings can serve as a reference for further understanding of the physical mechanisms in dual beam laser welding and of processing optimizations in industrial applications.
Conservative Chaos Generators with CCII+ Based on Mathematical Model of Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
J. Slezak
2008-09-01
Full Text Available In this detailed paper, several novel oscillator's configurations which consist only of five positive second generation current conveyors (CCII+ are presented and experimentally verified. Each network is able to generate the conservative chaotic attractors with the certain degree of the structural stability. It represents a class of the autonomous deterministic dynamical systems with two-segment piecewise linear (PWL vector fields suitable also for the theoretical analysis. Route to chaos can be traced and observed by a simple change of the external dc voltage. Advantages and other possible improvements are briefly discussed in the text.
Optimum Design of a Nonlinear Vibration Absorber Coupled to a Resonant Oscillator: A Case Study
Directory of Open Access Journals (Sweden)
H. F. Abundis-Fong
2018-01-01
Full Text Available This paper presents the optimal design of a passive autoparametric cantilever beam vibration absorber for a linear mass-spring-damper system subject to harmonic external force. The design of the autoparametric vibration absorber is obtained by using an approximation of the nonlinear frequency response function, computed via the multiple scales method. Based on the solution given by the perturbation method mentioned above, a static optimization problem is formulated in order to determine the optimum parameters (mass and length of the nonlinear absorber which minimizes the steady state amplitude of the primary mass under resonant conditions; then, a PZT actuator is cemented to the base of the beam, so the nonlinear absorber is made active, thus enabling the possibility of controlling the effective stiffness associated with the passive absorber and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty. Finally, some simulations and experimental results are included to validate and illustrate the dynamic performance of the overall system.
International Nuclear Information System (INIS)
Ünal, Hakkı Ulaş; Michiels, Wim
2013-01-01
The full synchronization of coupled nonlinear oscillators has been widely studied. In this paper we investigate conditions for which partial synchronization of time-delayed diffusively coupled systems arises. The coupling configuration of the systems is described by a directed graph. As a novel quantitative result we first give necessary and sufficient conditions for the presence of forward invariant sets characterized by partially synchronous motion. These conditions can easily be checked from the eigenvalues and eigenvectors of the graph Laplacian. Second, we perform stability analysis of the synchronized equilibria in a (gain,delay) parameter space. For this analysis the coupled nonlinear systems are linearized around the synchronized equilibria and then the resulting characteristic function is factorized. By such a factorization, it is shown that the relation between the behaviour of different agents at the zero of the characteristic function depends on the structure of the eigenvectors of the weighted Laplacian matrix. By determining the structure of the solutions in the unstable manifold, combined with the characterization of invariant sets, we predict which partially synchronous regimes occur and estimate the corresponding coupling gain and delay values. We apply the obtained results to networks of coupled Hindmarsh–Rose neurons and verify the occurrence of the expected partially synchronous regimes by using a numerical simulation. We also make a comparison with an existing approach based on Lyapunov functionals. (paper)
Rigatos, Gerasimos
2014-12-01
A synchronizing control scheme for coupled neural oscillators of the FitzHugh-Nagumo type is proposed. Using differential flatness theory the dynamical model of two coupled neural oscillators is transformed into an equivalent model in the linear canonical (Brunovsky) form. A similar linearized description is succeeded using differential geometry methods and the computation of Lie derivatives. For such a model it becomes possible to design a state feedback controller that assures the synchronization of the membrane's voltage variations for the two neurons. To compensate for disturbances that affect the neurons' model as well as for parametric uncertainties and variations a disturbance observer is designed based on Kalman Filtering. This consists of implementation of the standard Kalman Filter recursion on the linearized equivalent model of the coupled neurons and computation of state and disturbance estimates using the diffeomorphism (relations about state variables transformation) provided by differential flatness theory. After estimating the disturbance terms in the neurons' model their compensation becomes possible. The performance of the synchronization control loop is tested through simulation experiments.
Effect of mechanical vibration generated in oscillating/vibratory ...
African Journals Online (AJOL)
Background: Whole body vibration (WBV) exercise has been used in health sciences. Authors have reported that changes on the concentration of plasma biomarkers could be associated with the WBV effects. The aim of this investigation is to assess the consequences of exposition of 25 Hz mechanical vibration generated ...
Directory of Open Access Journals (Sweden)
Alex Pavlides
2015-12-01
Full Text Available In Parkinson's disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN and the external segment of globus pallidus (GPe. Several alternative models have been proposed to describe the mechanisms for generation of the Parkinsonian beta oscillations. However, a recent experimental study of Tachibana and colleagues yielded results which are challenging for all published computational models of beta generation. That study investigated how the presence of beta oscillations in a primate model of Parkinson's disease is affected by blocking different connections of the STN-GPe circuit. Due to a large number of experimental conditions, the study provides strong constraints that any mechanistic model of beta generation should satisfy. In this paper we present two models consistent with the data of Tachibana et al. The first model assumes that Parkinsonian beta oscillation are generated in the cortex and the STN-GPe circuits resonates at this frequency. The second model additionally assumes that the feedback from STN-GPe circuit to cortex is important for maintaining the oscillations in the network. Predictions are made about experimental evidence that is required to differentiate between the two models, both of which are able to reproduce firing rates, oscillation frequency and effects of lesions carried out by Tachibana and colleagues. Furthermore, an analysis of the models reveals how the amplitude and frequency of the generated oscillations depend on parameters.
Grey-box state-space identification of nonlinear mechanical vibrations
Noël, J. P.; Schoukens, J.
2018-05-01
The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.
Dynamical Chaos Rise in the System of Large Number of Nonlinear Coupled Oscillators
International Nuclear Information System (INIS)
Buts, V.A.; Koval'chuk, I.K.; Tarasov, D.V.
2007-01-01
The problem of dynamical chaos arising in distributed systems is considered. It was shown that in many cases it is possible to allocate relatively isolated subsystem which may be simpler for investigation. We suppose that chaos in this subsystem leads to chaotic behaviour of all system. Besides, the allocated subsystem may be used for describing complex dynamics of nonlinear three-wave interaction, in particular, in plasma systems. The analytical criterion of arising dynamics chaos in distributed system was obtained. This criterion was confirmed by numerical simulation
Intermittently chaotic oscillations for a differential-delay equation with Gaussian nonlinearity
Hamilton, Ian
1992-01-01
For a differential-delay equation the time dependence of the variable is a function of the variable at a previous time. We consider a differential-delay equation with Gaussian nonlinearity that displays intermittent chaos. Although not the first example of a differential-delay equation that displays such behavior, for this example the intermittency is classified as type III, and the origin of the intermittent chaos may be qualitatively understood from the limiting forms of the equation for large and small variable magnitudes.
Internal crisis in a second-order non-linear non-autonomous electronic oscillator
International Nuclear Information System (INIS)
Stavrinides, S.G.; Deliolanis, N.C.; Miliou, A.N.; Laopoulos, Th.; Anagnostopoulos, A.N.
2008-01-01
The internal crisis of a second-order non-linear non-autonomous chaotic electronic circuit is studied. The phase portraits consist of two interacting sub-attractors, a chaotic and a periodic one. Maximal Lyapunov exponents were calculated, for both the periodic and the chaotic waveforms, in order to confirm their nature. Transitions between the chaotic and the periodic sub-attractors become more frequent by increasing the circuit driving frequency. The frequency distribution of the corresponding laminar lengths and their average values indicate that an internal crisis takes place in this circuit, manifested in the intermittent behaviour of the corresponding orbits
From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry
Energy Technology Data Exchange (ETDEWEB)
Latini, D., E-mail: latini@fis.uniroma3.it [Department of Mathematics and Physics and INFN, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy); Riglioni, D. [Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy)
2016-10-14
The coalgebraic structure of the harmonic oscillator is used to underline possible connections between continuous and discrete superintegrable models which can be described in terms of SUSY discrete quantum mechanics. A set of 1-parameter algebraic transformations is introduced in order to generate a discrete representation for the coalgebraic harmonic oscillator. This set of transformations is shown to play a role in the generalization of classical orthogonal polynomials to the realm of discrete orthogonal polynomials in the Askey scheme. As an explicit example the connection between Hermite and Charlier oscillators, that share the same coalgebraic structure, is presented and a two-dimensional maximally superintegrable version of the Charlier oscillator is constructed. - Highlights: • We construct a discrete quantum version of the harmonic oscillator. • We solve the spectral problem on the lattice. • We introduce the coalgebra symmetry in real discrete Quantum Mechanics (rdQM). • The coalgebra is used to extend the system to higher dimensions preserving its superintegrability. • We explicitly write down a discrete version of both the angular momentum and the Demkov–Fradkin Tensor.
Nonlinear analysis of collapse mechanism in superstructure vehicle
Nor, M. K. Mohd; Ho, C. S.; Ma'at, N.
2017-04-01
The EU directive 2001/85/EC is an official European text which describes the specifications for "single deck class II and III vehicles" required to be approved by the regulation UN/ECE no.66 (R66). To prevent the catastrophic consequences by occupant during an accident, the Malaysian government has reinforced the same regulation upon superstructure construction. This paper discusses collapse mechanism analysis of a superstructure vehicle using a Crash D nonlinear analysis computer program based on this regulation. The analysis starts by hand calculation to define the required energy absorption by the chosen structure. Simple calculations were then performed to define the weakest collapse mechanism after undesirable collapse modes are eliminated. There are few factors highlighted in this work to pass the regulation. Using the selected cross section, Crash D simulation showed a good result. Generally, the deformation is linearly correlates to the energy absorption for the structure with low stiffness. Failure of critical members such as vertical lower side wall must be avoided to sustain safety of the passenger compartment and prevent from severe and fatal injuries to the trapped occupant.
Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall
Garashchuk, Ivan R.; Sinelshchikov, Dmitry I.; Kudryashov, Nikolay A.
2018-05-01
Contrast agent microbubbles, which are encapsulated gas bubbles, are widely used to enhance ultrasound imaging. There are also several new promising applications of the contrast agents such as targeted drug delivery and noninvasive therapy. Here we study three models of the microbubble dynamics: a nonencapsulated bubble oscillating close to an elastic wall, a simple coated bubble and a coated bubble near an elastic wall.We demonstrate that complex dynamics can occur in these models. We are particularly interested in the multistability phenomenon of bubble dynamics. We show that coexisting attractors appear in all of these models, but for higher acoustic pressures for the models of an encapsulated bubble.We demonstrate how several tools can be used to localize the coexisting attractors. We provide some considerations why the multistability can be undesirable for applications.
Direct Visualization of Mechanical Beats by Means of an Oscillating Smartphone
Giménez, Marcos H.; Salinas, Isabel; Monsoriu, Juan A.; Castro-Palacio, Juan C.
2017-01-01
The resonance phenomenon is widely known in physics courses. Qualitatively speaking, resonance takes place in a driven oscillating system whenever the frequency approaches the natural frequency, resulting in maximal oscillatory amplitude. Very closely related to resonance is the phenomenon of mechanical beating, which occurs when the driving and…
Marshall, T.R.; Boer, Sebastiaan den; Cools, R.; Jensen, O.; Fallon, S.J.; Zumer, J.
2018-01-01
Selective attention is reflected neurally in changes in the power of posterior neural oscillations in the alpha (8–12 Hz) and gamma (40–100 Hz) bands. Although a neural mechanism that allows relevant information to be selectively processed has its advantages, it may lead to lucrative or dangerous
Technical report on micro-mechanical versus conventional modelling in non-linear fracture mechanics
International Nuclear Information System (INIS)
2001-07-01
While conventional fracture mechanics is capable of predicting crack growth behaviour if sufficient experimental observations are available, micro-mechanical modelling can both increase the accuracy of these predictions and model phenomena that are inaccessible by the conventional theory such as the ductile-cleavage temperature transition. A common argument against micro-mechanical modelling is that it is too complicated for use in routine engineering applications. This is both a computational and an educational problem. That micro-mechanical modelling is unnecessarily complicated is certainly true in many situations. The on-going development of micro-mechanical models, computational algorithms and computer speed will however most probably diminish the computational problem rather rapidly. Compare for instance the rate of development of computational methods for structural analysis. Meanwhile micro-mechanical modelling may serve as a tool by which more simplified engineering methods can be validated. The process of receiving a wide acceptance of the new methods is probably much slower. This involves many steps. First the research community must be in reasonable agreement on the methods and their use. Then the methods have to be implemented into computer software and into code procedures. The development and acceptance of conventional fracture mechanics may serve as an historical example of the time required before a new methodology has received a wide usage. The CSNI Working Group on Integrity and Ageing (IAGE) decided to carry out a report on micro-mechanical modeling to promote this promising and valuable technique. The report presents a comparison with non-linear fracture mechanics and highlights key aspects that could lead to a better knowledge and accurate predictions. Content: - 1. Introduction; - 2. Concepts of non-linear fracture mechanics with point crack tip modelling; - 3. Micro-mechanical models for cleavage fracture; - 4, Micro-mechanical modelling of
Investigation of power oscillation mechanisms based on noise analysis at Forsmark-1 BWR
International Nuclear Information System (INIS)
Oguma, Ritsuo
1996-01-01
Noise analysis has been performed for stability test data collected during reactor start-up in January 1989 at the boiling water reactor (BWR) Forsmark unit 1. A unique instrumentation to measure local coolant flow in this reactor allowed investigation of dynamic interactions between neutron flux and coolant flow noise signals at different radial positions in the core. The causal relationship for these signals was evaluated based on a method called signal transmission path (STP) analysis with the aim of identifying the principal mechanism of power oscillations in this reactor. The results of the present study indicated that large amplitude power oscillations were induced by two instability mechanisms concurrent in the core. The first is the global void reactivity feedback effect which played the most significant role to power oscillations at a resonant frequency of about 0.53 Hz. The second is the thermal-hydraulics coupling with neutron kinetics, inducing resonant oscillations at about 0.45 Hz. The latter was found to be active only in a certain core region. A peculiar phenomenon of amplitude modulations observed in some local power range monitor (LPRM) signals was also examined. It was interpreted to occur as the consequence of these two resonant power oscillations, the frequencies of which lie close to each other. The noise analysis technique applied in the present study is expected to be useful to get a deeper understanding of the power oscillation mechanism which is active in the reactor under evaluation. The technique may be applicable to BWRs with instruments to measure local channel flow together with in-core neutron detectors. (Author)
Contributions of non-intrusive coupling in nonlinear structural mechanics
International Nuclear Information System (INIS)
Duval, Mickael
2016-01-01
This PhD thesis, part of the ANR ICARE project, aims at developing methods for complex analysis of large scale structures. The scientific challenge is to investigate very localised areas, but potentially critical as of mechanical systems resilience. Classically, representation models, discretizations, mechanical behaviour models and numerical tools are used at both global and local scales for simulation needs of graduated complexity. Global problem is handled by a generic code with topology (plate formulation, geometric approximation...) and behaviour (homogenization) simplifications while local analysis needs implementation of specialized tools (routines, dedicated codes) for an accurate representation of the geometry and behaviour. The main goal of this thesis is to develop an efficient non-intrusive coupling tool for multi-scale and multi-model structural analysis. Constraints of non-intrusiveness result in the non-modification of the stiffness operator, connectivity and the global model solver, allowing to work in a closed source software environment. First, we provide a detailed study of global/local non-intrusive coupling algorithm. Making use of several relevant examples (cracking, elastic-plastic behaviour, contact...), we show the efficiency and the flexibility of such coupling method. A comparative analysis of several optimisation tools is also carried on, and the interacting multiple patches situation is handled. Then, non-intrusive coupling is extended to globally non-linear cases, and a domain decomposition method with non-linear re-localization is proposed. Such methods allowed us to run a parallel computation using only sequential software, on a high performance computing cluster. Finally, we apply the coupling algorithm to mesh refinement with patches of finite elements. We develop an explicit residual based error estimator suitable for multi-scale solutions arising from the non-intrusive coupling, and apply it inside an error driven local mesh
Generic mechanisms of decoherence of quantum oscillations in magnetic double-well systems
International Nuclear Information System (INIS)
Chudnovsky, Eugene M.
2004-01-01
Fundamental conservation laws mandate parameter-free generic mechanisms of decoherence of quantum oscillations in double-well systems. We consider two examples: tunneling of the magnetic moment in nanomagnets and tunneling between macroscopic current states in SQUIDs. In both cases the decoherence occurs via emission of phonons and photons at the oscillation frequency. We also show that in a system of identical qubits the decoherence greatly increases due to the superradiance of electromagnetic and sound waves. Our findings have important implications for building elements of quantum computers based upon nanomagnets and SQUIDs
Generic mechanisms of decoherence of quantum oscillations in magnetic double-well systems
Energy Technology Data Exchange (ETDEWEB)
Chudnovsky, Eugene M. E-mail: chudnov@lehman.cuny.edu
2004-05-01
Fundamental conservation laws mandate parameter-free generic mechanisms of decoherence of quantum oscillations in double-well systems. We consider two examples: tunneling of the magnetic moment in nanomagnets and tunneling between macroscopic current states in SQUIDs. In both cases the decoherence occurs via emission of phonons and photons at the oscillation frequency. We also show that in a system of identical qubits the decoherence greatly increases due to the superradiance of electromagnetic and sound waves. Our findings have important implications for building elements of quantum computers based upon nanomagnets and SQUIDs.
Non-perturbative solution of a quantum mechanical oscillator interacting with a specific environment
International Nuclear Information System (INIS)
Badralexe, E.; Gupta, R.K.; Scheid, W.
1984-01-01
A quantum mechanical model of an oscillator interacting linearly with an environment is treated by the method of perturbation series expansion. For a special class of environments and interactions, the series is summed up to all orders. An integral equation for the time dependence of the coordinate operator of the oscillator is obtained, which is solved analytically by the method of Laplace transformations. General conditions are stated for a dissipative behaviour of the special class of environments considered. An example, which is widely applicable, is discussed. (author)
Method for determining damping properties of materials using a suspended mechanical oscillator
Biscans, S.; Gras, S.; Evans, M.; Fritschel, P.; Pezerat, C.; Picart, P.
2018-06-01
We present a new approach for characterizing the loss factor of materials, using a suspended mechanical oscillator. Compared to more standard techniques, this method offers freedom in terms of the size and shape of the tested samples. Using a finite element model and the vibration measurements, the loss factor is deduced from the oscillator's ring-down. In this way the loss factor can be estimated independently for shear and compression deformation of the sample over a range of frequencies. As a proof of concept, we present measurements for EPO-TEK 353ND epoxy samples.
International Nuclear Information System (INIS)
Langacker, P.; Petcov, S.T.; Steigman, G.; Toshev, S.
1987-01-01
Mikheyev and Smirnov have recently proposed a novel and plausible solution of the solar neutrino problem, based on the resonant amplification of the neutrino oscillations in matter. We comment on several aspects of this mechanism. (i) For the values of neutrino masses and mixing angles predicted by the seesaw model of grand unified theories, the MSW effect may take place naturally in the Sun, leading to a considerable reduction of the flux of solar electron neutrinos, with the dominant transition being ν e →ν τ (rather than ν e →ν μ ). (ii) Oscillations between the ordinary neutrinos (ν e ,ν μ ,ν τ ) can affect primordial nucleosynthesis, but the effect is small (i.e., the abundance of 4 He is predicted to change by less than 1.3x10 -3 ). (iii) A comparison of some of the general properties of neutrino oscillations in matter and in vacuum is given. (orig.)
Neural mechanisms of mental schema: a triplet of delta, low beta/spindle and ripple oscillations.
Ohki, Takefumi; Takei, Yuichi
2018-02-06
Schemas are higher-level knowledge structures that integrate and organise lower-level representations. As internal templates, schemas are formed according to how events are perceived, interpreted and remembered. Although these higher-level units are assumed to play a fundamental role in our daily life from an early age, the neuronal basis and mechanisms of schema formation and use remain largely unknown. It is important to elucidate how the brain constructs and maintains these higher-level units. In order to examine the possible neural underpinnings of schema, we recapitulate previous work and discuss their findings related to schemas as the brain template. We specifically focused on low beta/spindle oscillations, which are assumed to be the key components of schemas, and propose that the brain template is implemented with a triplet of neural oscillations, that is delta, low beta/spindle and ripple oscillations. © 2018 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.
Yoshimura, K.
2000-11-01
We study analytically the induction phenomenon in the Fermi-Pasta-Ulam β oscillator chain under initial conditions consisting of single mode excitation. Our study is based on the analytical computation of the largest characteristic exponent of an approximate version of the variational equation. The main results can be summarized as follows: (1) the energy density ɛ scaling of the induction time T is given by T~ɛ-1, and T becomes smaller for higher-frequency mode excitation; (2) there is a threshold energy density ɛc such that the induction time diverges when ɛ∞ (3) the threshold ɛc vanishes as ɛc~N-2 in the limit N-->∞ (4) the threshold ɛc does not depend on the mode number k that is excited in the initial condition; (5) the two modes k+/-m have the largest exponential growth rate, and m increases with increasing ɛ as m/N=3βɛ/π. The above analytical results are thoroughly verified in numerical experiments. Moreover, we discuss the energy exchange process after the induction period in some energy density regimes, based on the numerical results.
Marshall, Tom R; den Boer, Sebastiaan; Cools, Roshan; Jensen, Ole; Fallon, Sean James; Zumer, Johanna M
2018-01-01
Selective attention is reflected neurally in changes in the power of posterior neural oscillations in the alpha (8-12 Hz) and gamma (40-100 Hz) bands. Although a neural mechanism that allows relevant information to be selectively processed has its advantages, it may lead to lucrative or dangerous information going unnoticed. Neural systems are also in place for processing rewarding and punishing information. Here, we examine the interaction between selective attention (left vs. right) and stimulus's learned value associations (neutral, punished, or rewarded) and how they compete for control of posterior neural oscillations. We found that both attention and stimulus-value associations influenced neural oscillations. Whereas selective attention had comparable effects on alpha and gamma oscillations, value associations had dissociable effects on these neural markers of attention. Salient targets (associated with positive and negative outcomes) hijacked changes in alpha power-increasing hemispheric alpha lateralization when salient targets were attended, decreasing it when they were being ignored. In contrast, hemispheric gamma-band lateralization was specifically abolished by negative distractors. Source analysis indicated occipital generators of both attentional and value effects. Thus, posterior cortical oscillations support both the ability to selectively attend while at the same time retaining the ability to remain sensitive to valuable features in the environment. Moreover, the versatility of our attentional system to respond separately to salient from merely positively valued stimuli appears to be carried out by separate neural processes reflected in different frequency bands.
Hybrid plasmonic nanodevices: Switching mechanism for the nonlinear emission
Energy Technology Data Exchange (ETDEWEB)
Bragas, Andrea V. [Departamento de Física, FCEyN, Universidad de Buenos Aires, IFIBA CONICET, 1428 Buenos Aires (Argentina); Singh, Mahi R. [Department of Physics and Astronomy, Western University, London (Canada)
2014-03-31
Control of the light emission at the nanoscale is of central interest in nanophotonics due to the many applications in very different fields, ranging from quantum information to biophysics. Resonant excitation of surface plasmon polaritons in metal nanoparticles create nanostructured and enhanced light fields around those structures, which produce their strong interaction in a hybrid nanodevice with other plasmonic or non-plasmonic objects. This interaction may in turn also modulate the far field with important consequences in the applications. We show in this paper that the nonlinear emission from semiconductor quantum dots is strongly affected by the close presence of metal nanoparticles, which are resonantly excited. Using a pulsed laser, optical second harmonic is generated in the quantum dot, and it is highly enhanced when the laser is tuned around the nanoparticle plasmon resonance. Even more interesting is the demonstration of a switching mechanism, controlled by an external continuous-wave field, which can enhance or extinguish the SH signal, even when the pulsed laser is always on. Experimental observations are in excellent agreement with the theoretical calculations, based on the dipole-dipole near-field coupling of the objects forming the hybrid system.
The 2017 Nonlinear Mechanics and Dynamics Research Institute.
Energy Technology Data Exchange (ETDEWEB)
Kuether, Robert J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Allensworth, Brooke Marie [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Peebles, Diane E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2018-02-01
The 2017 Nonlinear Mechanics and Dynamics (NOMAD) Research Institute was successfully held from June 19 to July 28, 2017. NOMAD seeks to bring together participants with diverse tec hnical backgrounds to work in small teams to utilize an interactive approach to cultivate new ideas and approaches in engineering . NOMAD provides an opportunity for researchers - especially early career researchers - to develop lasting collaborations that go beyond what can be established from the limited interactions at their institutions or at annual conferences. A total of 17 students from around the world came to Albuquerque, New Mexico to participate in the six - week long program held at the University of New Mexico campus. The students collaborated on one of six research projects that were developed by various mentors from Sandia National Laboratories, academia, and other government laboratories. In addition to the research activities, the students atte nded weekly technical seminars, toured the National Museum of Nuclear Science & History, and socialized at various off - hour events including an Albuquerque Isotopes baseball game. At the end of the summer, the students gave a final technical presentation o n their research findings that was broadcast via Skype. Many of the research discoveries made at NOMAD are published as proceedings at t echnical conference s and have direct alignment with the critical mission work performed at Sandia.
Quantum noise of a Michelson-Sagnac interferometer with a translucent mechanical oscillator
International Nuclear Information System (INIS)
Yamamoto, Kazuhiro; Friedrich, Daniel; Westphal, Tobias; Gossler, Stefan; Danzmann, Karsten; Schnabel, Roman; Somiya, Kentaro; Danilishin, Stefan L.
2010-01-01
Quantum fluctuations in the radiation pressure of light can excite stochastic motions of mechanical oscillators thereby realizing a linear quantum opto-mechanical coupling. When performing a precise measurement of the position of an oscillator, this coupling results in quantum radiation pressure noise. Up to now this effect has not been observed yet. Generally speaking, the strength of radiation pressure noise increases when the effective mass of the oscillator is decreased or when the power of the reflected light is increased. Recently, extremely light SiN membranes (≅100 ng) with high mechanical Q values at room temperature (≥10 6 ) have attracted attention as low thermal noise mechanical oscillators. However, the power reflectance of these membranes is much lower than unity (<0.4 at a wavelength of 1064 nm) which makes the use of advanced interferometer recycling techniques to amplify the radiation pressure noise in a standard Michelson interferometer inefficient. Here, we propose and theoretically analyze a Michelson-Sagnac interferometer that includes the membrane as a common end mirror for the Michelson interferometer part. In this topology, both power and signal recycling can be used even if the reflectance of the membrane is much lower than unity. In particular, signal recycling is a useful tool because it does not involve a power increase at the membrane. We derive the formulas for the quantum radiation pressure noise and the shot noise of an oscillator position measurement and compare them with theoretical models of the thermal noise of a SiN membrane with a fundamental resonant frequency of 75 kHz and an effective mass of125 ng. We find that quantum radiation pressure noise should be observable with a power of 1 W at the central beam splitter of the interferometer and a membrane temperature of 1 K.
Chen, Bor-Sen; Hsu, Chih-Yuan
2012-10-26
Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI
Effect of the imposition of low-frequency mechanical oscillations on the extraction efficiency
Directory of Open Access Journals (Sweden)
Ju. I. Shitshatskij
2018-01-01
Full Text Available It was shown that the effective transfer of the target component from the raw material occurs under a turbulent regime conditions provided by applying mechanical oscillations to a two-phase system: solid-liquid. Due to this hydrodynamic situation, not only external but also internal diffusion is intensified in the extractor. The method for intensifying the extraction process using low-frequency mechanical oscillations in the case when the vibrational motion is performed by a device with a cheese whey containing suspended porous particles was studied in the work. The experiments were carried out on the laboratory equipment with a supply to a two-phase energy system from the outside, the source of which in the first case was an electromagnet, in the second - a mechanical drive with an eccentric device. Schemes of equipment were also presented in the work. The regime parameters varied in the following ranges: temperature - 40-60 оС, oscillation frequency - 30 - 40 osc / s, amplitude - 1 - 6.5 mm. In the extraction process, the current concentration of extractive substances was obtained from the material balance equation. Extraction curves obtained from experimental data were presented. Increasing extraction of extractive substances in time was observed, it being more intense with the increasing frequency of oscillations. It was found that the growth of the amplitude does not have a significant influence on the change of these indices. The intensity of oscillations was up to 260 mm / s. At the same time, the yield of extractive substances in particular from lupine in the form of grits was 25%, and the duration of the process was 18 min. The experiments showed that the application of the chosen extraction method results into a significant acceleration of the process (up to 2.5 times as compared to extraction in a dense layer. It is concluded that due to the imposition of mechanical oscillations on the surface and in the pores of the solid phase
Nonlinearity and nonclassicality in a nanomechanical resonator
Energy Technology Data Exchange (ETDEWEB)
Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)
2015-12-15
We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)
Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.
2017-11-01
An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.
International Nuclear Information System (INIS)
Yoshimura, H.
1979-01-01
A new dynamical model of the solar cycle has predicted that the cycle should have a hysteretic nature: the behavior of each 11 year cycle should depend on previous cycles. In the light of this new understanding of the dynamical mechanism of the solar cycle, Waldmeier's (hypothetical) law was examined as a yet unexplained characteristic of the cycle by studying the observed sunspot frequency curve. Contrary to this hypothetical law, however, it was found that sunspot cycle curves did not form a single-parameter family characterized by the maximum amplitude of the cycle. The evolutionary trajectories in period-amplitude phase space verified the hysteretic nature of the observed cycle and revealed long-term (55 year instead of the previously claimed 80 year) periodic modulations, called here 55 year grand cycles. Each 55 year grand cycle forms a loop in the phase space, and the characteristics of each 11 year cycle depend on its position in the ascending or descending phase of the grand cycle. This new law was analyzed by the nonlinear multiple-period dynamo oscillation model which has predicted the hysteretic nature. The era from cycle 11 to cycle 15 turned out to be an anomalous one characterized by alternating amplitudes for odd and even cycles. Cycles 16--20 seem to constitute one grand cycle. If this is true, cycle 21 would be the beginning of another grand maximum and the model predicts that its duration would be short
Weyl geometry and the nonlinear mechanics of distributed point defects
Yavari, A.; Goriely, A.
2012-01-01
The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects
Riemann-Cartan geometry of nonlinear disclination mechanics
Yavari, A.; Goriely, A.
2012-01-01
In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining
Oscillators - an approach for a better understanding
DEFF Research Database (Denmark)
Lindberg, Erik
2003-01-01
The aim of this tutorial is to provide an electronic engineer knowledge and insight for a better understanding of the mechanisms behind the behaviour of electronic oscillators. A linear oscillator is a mathematical fiction which can only be used as a starting point for the design of a real...... oscillator based on the Barkhausen criteria. Statements in textbooks and papers saying that the nonlinearities are bringing back the poles to the imaginary axis are wrong. The concept of "frozen eigenvalues" is introduced by means of piece-wise-linear modelling of the nonlinear components which are necessary...
Shakurov, R. F.; Sitnikov, O. R.; Galimova, A. I.; Sabitova, A. F.
2018-03-01
The article presents an analysis of the used methods of recycling of waste rubber products. The worn out tires are exposed to natural decomposition only after 50 - 100 years, and toxic organic compounds used in the manufacture constitute a danger to the environment. It contemplates a method of recycling waste rubber products in devices where pulsating combustion is realized. The dependence of the influence of acoustic pulsation parameters on the combustion mechanism of waste rubber products and on the composition of combustion products was experimentally investigated and established. For this purpose, the setup scheme based on the Rijke effect is optimized. The resonance pipe is coaxially embedded in the shaft. The known mathematical model of finding the combustion zones in the Rijke pipe, corresponding to the gas flow oscillations with the maximum amplitude, is applied to the chosen scheme. Investigations were carried out for three positions of the grate relative to the lower section of the experimental pipe, in which 1st, 2nd, 3rd modes of oscillation are formed. There are favorable conditions arise for the secondary combustion of mechanical particles entrained in the gas flow in the tube. The favorable conditions for afterburning also include the fact that through the upper section of the resonant pipe, the ambient air, caused by the features of the standing wave, is mixed into the gas stream. A comparative analysis of the change of gas concentration composition along the length of the resonance tube is carried out. It is established that the basic mode of oscillations contributes to the reduction of nitrogen oxides, in comparison with the oscillations occurring simultaneously at several harmonics, considering the main one. The results of research for the three positions of the grate in relation to the lower section of the installation are presented in tabular form, in which 1, 2, 3 modes of oscillation are formed. The analysis of experimental results confirms
DEFF Research Database (Denmark)
Lindberg, Erik
1997-01-01
In order to obtain insight in the nature of nonlinear oscillators the eigenvalues of the linearized Jacobian of the differential equations describing the oscillator are found and displayed as functions of time. A number of oscillators are studied including Dewey's oscillator (piecewise linear wit...... with negative resistance), Kennedy's Colpitts-oscillator (with and without chaos) and a new 4'th order oscillator with hyper-chaos....
Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light.
Schäfermeier, Clemens; Kerdoncuff, Hugo; Hoff, Ulrich B; Fu, Hao; Huck, Alexander; Bilek, Jan; Harris, Glen I; Bowen, Warwick P; Gehring, Tobias; Andersen, Ulrik L
2016-11-29
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics.
Nonlinear Distortion Mechanisms and Efficiency of Balanced-Armature Loudspeakers
DEFF Research Database (Denmark)
Jensen, Joe
are inherently nonlinear devices, since any displacement of the loudspeaker diaphragm in- evitably changes the magnetic and electrical characteristics of the loudspeaker. Additionally, for the balanced-armature loudspeaker the signal has to be transmitted through the magnetic domain (as a magnetic B -field...... and to validate simpler equivalent circuit models. A large scale model of a balanced-armature loudspeaker has been developed and its inherent nonlinear parameters have been measured and compared to the theoretically predicted values. A measurement setup for determining the magnetic properties of soft magnetic...... materials has also been developed, since it is of great importance to understand what kind of linear and nonlinear transformations the magnetic materials impose on the signal. In hearing aid applications the power efficiency of the loudspeaker is important because every reduction in power consumption...
Directory of Open Access Journals (Sweden)
D. A. Goncharov
2015-01-01
Full Text Available In this paper we investigate small axisymmetric oscillations of a liquid in an elastic tank. We also take into account the influence of surface tension forces. For this, we turn to the mechanical analogue of the considered mechanical system. To realize the transition to mechanical analogue we use the energy method: postulating the equality of kinetic and potential energy for the investigated mechanical system and the mechanical system analog. Due to this transition we can further investigate the oscillations of a mechanical analogue. As a mechanical analogue, we consider the oscillator in the spring. The mass of the oscillator is calculated as the weight of the fluid to make oscillations. The oscillator spring constant is calculated using the identity of equations, namely, equation of free small oscillations of the oscillator and equation of free small oscillations of the system under investigation: the fluid in the elastic tank. The identity of equations allows us to draw conclusion about the identity of the natural frequencies for the source mechanical system and the system of a mechanical analogue. Next, we take into consideration the action of the surface tension. We record the Laplace condition for excess pressure because of the forces of surface tension. Then we compile the expression for the generalized force, taking into account the phenomenon of the surface tension. Next, we write the equation of oscillations of a mechanical analogue. The surface tension, due to the introduction of the generalized force in the equation for small oscillations of the mechanical analogue will change the natural frequency of the mechanical analogue. The paper presents the appropriate dependencies. The abovementioned allows us to investigate the stability of small motions of fluid in microgravity or low gravity by studying the stability of small motions of mechanical analogue. The latter is especially important due to the design and development of advanced
Identification of stochastic interactions in nonlinear models of structural mechanics
Kala, Zdeněk
2017-07-01
In the paper, the polynomial approximation is presented by which the Sobol sensitivity analysis can be evaluated with all sensitivity indices. The nonlinear FEM model is approximated. The input area is mapped using simulations runs of Latin Hypercube Sampling method. The domain of the approximation polynomial is chosen so that it were possible to apply large number of simulation runs of Latin Hypercube Sampling method. The method presented also makes possible to evaluate higher-order sensitivity indices, which could not be identified in case of nonlinear FEM.
Variational problems arising in classical mechanics and nonlinear elasticity
International Nuclear Information System (INIS)
Spencer, P.
1999-01-01
In this thesis we consider two different classes of variational problems. First, one-dimensional problems arising from classical mechanics where the problem is to determine whether there is a unique function η 0 (x) which minimises the energy functional of the form I(η) = ∫ a b L(x,η(x), η'(x)) dx. We will investigate uniqueness by making a change of dependent and independent variables and showing that for a class of integrands L with a particular kind of scaling invariance the resulting integrand is completely convex. The change of variables arises by applying results from Lie group theory as applied in the study of differential equations and this work is motivated by [60] and [68]. Second, the problem of minimising energy functionals of the form E(u) = ∫ A W(∇u(x)) dx in the case of a nonlinear elastic body occupying an annular region A contains R 2 with u : A-bar → A-bar. This work is motivated by [57] (in particular the example of paragraph 4). We will consider rotationally symmetric deformations satisfying prescribed boundary conditions. We will show the existence of minimisers for stored energy functions of the form W(F) = g-tilde(vertical bar-F-vertical bar, det(F)) in a class of general rotationally symmetric deformations of a compressible annulus and for stored energy functions of the form W(F) = g-bar(vertical bar-F-vertical bar) in a class of rotationally symmetric deformations of an incompressible annulus. We will also show that in each case the minimisers are solutions of the full equilibrium equations. A model problem will be considered where the energy functional is the Dirichlet integral and it will be shown that the rotationally symmetric solution obtained is a minimiser among admissible non-rotationally symmetric deformations. In the case of an incompressible annulus, we will consider the Dirichlet integral as the energy functional and show that the rotationally symmetric equilibrium solutions in this case are weak local minimisers in
The two-capacitor problem revisited: a mechanical harmonic oscillator model approach
International Nuclear Information System (INIS)
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that exactly half the work done by a constant applied force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be exactly half the supplied energy whether that is caused by the Joule heat or by the radiation. This paper, which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem, is suitable for all undergraduate levels
Equivalent mechanical parameters of oscillating rotary motors used in transport equipment
Directory of Open Access Journals (Sweden)
A. Andziulis
2006-12-01
Full Text Available In various appliances and equipment of sundry transport means there is a lot of diverse mechanisms of periodical movement. So, the various piston or membrane pumps of fuel feeding and lubrication systems, circulation pumps, air and refrigerating coolant compressors, etc. are the typical examples of innovative and well promising application of the oscillating motors. In these cases the moving part of a motor can be directly connected to the working body of driven mechanism without the additional gears. Consequently, the drive can be simplified in design and improved in efficiency and reliability. Application of the oscillating rotary motors, if used in the aforesaid devices, strictly depends on specific properties of mechanical system of a motor aggregated with the driven mechanism and considered as the one-piece unit on the whole. So, this study analyses how the properties of mechanical system, comprised of two moving parts interconnected eccentrically or centrically, can be evaluated by the equivalent rotational inertia, equivalent mass and by equivalent mechanical power factor which, in turn, determine the operating characteristics and basic possibilities of the motor.
MECHANISM OF OPTICAL NONLINEARITY IN “LYOTROPIC LIQUID CRYSTAL — VIOLOGEN” SYSTEM
Directory of Open Access Journals (Sweden)
Hanna Bordyuh
2014-06-01
Full Text Available In the present work we analyze the characteristics of holographic grating recording and consider a mechanism of optical nonlinearity in the lyotropic liquid crystal (LLC — viologen samples. Taking into account structural and electrooptical properties of the admixture molecules it is possible to suggest that the recording is realized due to the change of polarizability of π-electron system of coloured viologen derivatives under the action of laser radiation. The main nonlinear optical parameters such as nonlinear refraction coefficient n2, cubic nonlinear susceptibility χ(3, and hyperpolarizability γ were calculated.
Weyl geometry and the nonlinear mechanics of distributed point defects
Yavari, A.
2012-09-05
The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects-where the body is stress-free-is a flat Weyl manifold, i.e. a manifold with an affine connection that has non-metricity with vanishing traceless part, but both its torsion and curvature tensors vanish. Given a spherically symmetric point defect distribution, we construct its Weyl material manifold using the method of Cartan\\'s moving frames. Having the material manifold, the anelasticity problem is transformed to a nonlinear elasticity problem and reduces the problem of computing the residual stresses to finding an embedding into the Euclidean ambient space. In the case of incompressible neo-Hookean solids, we calculate explicitly this residual stress field. We consider the example of a finite ball and a point defect distribution uniform in a smaller ball and vanishing elsewhere. We show that the residual stress field inside the smaller ball is uniform and hydrostatic. We also prove a nonlinear analogue of Eshelby\\'s celebrated inclusion problem for a spherical inclusion in an isotropic incompressible nonlinear solid. © 2012 The Royal Society.
Gompf, Florian; Pflug, Anja; Laufs, Helmut; Kell, Christian A.
2017-01-01
Functional imaging studies using BOLD contrasts have consistently reported activation of the supplementary motor area (SMA) both during motor and internal timing tasks. Opposing findings, however, have been shown for the modulation of beta oscillations in the SMA. While movement suppresses beta oscillations in the SMA, motor and non-motor tasks that rely on internal timing increase the amplitude of beta oscillations in the SMA. These independent observations suggest that the relationship between beta oscillations and BOLD activation is more complex than previously thought. Here we set out to investigate this rapport by examining beta oscillations in the SMA during movement with varying degrees of internal timing demands. In a simultaneous EEG-fMRI experiment, 20 healthy right-handed subjects performed an auditory-paced finger-tapping task. Internal timing was operationalized by including conditions with taps on every fourth auditory beat, which necessitates generation of a slow internal rhythm, while tapping to every auditory beat reflected simple auditory-motor synchronization. In the SMA, BOLD activity increased and power in both the low and the high beta band decreased expectedly during each condition compared to baseline. Internal timing was associated with a reduced desynchronization of low beta oscillations compared to conditions without internal timing demands. In parallel with this relative beta power increase, internal timing activated the SMA more strongly in terms of BOLD. This documents a task-dependent non-linear relationship between BOLD and beta-oscillations in the SMA. We discuss different roles of beta synchronization and desynchronization in active processing within the same cortical region. PMID:29249950
Gompf, Florian; Pflug, Anja; Laufs, Helmut; Kell, Christian A
2017-01-01
Functional imaging studies using BOLD contrasts have consistently reported activation of the supplementary motor area (SMA) both during motor and internal timing tasks. Opposing findings, however, have been shown for the modulation of beta oscillations in the SMA. While movement suppresses beta oscillations in the SMA, motor and non-motor tasks that rely on internal timing increase the amplitude of beta oscillations in the SMA. These independent observations suggest that the relationship between beta oscillations and BOLD activation is more complex than previously thought. Here we set out to investigate this rapport by examining beta oscillations in the SMA during movement with varying degrees of internal timing demands. In a simultaneous EEG-fMRI experiment, 20 healthy right-handed subjects performed an auditory-paced finger-tapping task. Internal timing was operationalized by including conditions with taps on every fourth auditory beat, which necessitates generation of a slow internal rhythm, while tapping to every auditory beat reflected simple auditory-motor synchronization. In the SMA, BOLD activity increased and power in both the low and the high beta band decreased expectedly during each condition compared to baseline. Internal timing was associated with a reduced desynchronization of low beta oscillations compared to conditions without internal timing demands. In parallel with this relative beta power increase, internal timing activated the SMA more strongly in terms of BOLD. This documents a task-dependent non-linear relationship between BOLD and beta-oscillations in the SMA. We discuss different roles of beta synchronization and desynchronization in active processing within the same cortical region.
Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model
Czech Academy of Sciences Publication Activity Database
Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk
2015-01-01
Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics
International Nuclear Information System (INIS)
Yang, J H; Yang, J; Kitipornchai, S
2012-01-01
This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)
Riemann-Cartan geometry of nonlinear disclination mechanics
Yavari, A.
2012-03-23
In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).
Bifurcation and Nonlinear Oscillations.
1980-09-28
Structural stability and bifurcation theory. pp. 549-560 in Dinamical Systems (Ed. MI. Peixoto), Academic Press, 1973. [211 J. Sotomayor, Generic one...Dynamical Systems Brown University ELECTP" 71, Providence, R. I. 02912 1EC 2 4 1980j //C -*)’ Septabe-4., 1980 / -A + This research was supported in...problems are discussed. The first one deals with the characterization of the flow for a periodic planar system which is the perturbation of an autonomous
Ngo, Chuong; Spagnesi, Sarah; Munoz, Carlos; Lehmann, Sylvia; Vollmer, Thomas; Misgeld, Berno; Leonhardt, Steffen
2017-08-29
There is a lack of noninvasive pulmonary function tests which can assess regional information of the lungs. Electrical impedance tomography (EIT) is a radiation-free, non-invasive real-time imaging that provides regional information of ventilation volume regarding the measurement of electrical impedance distribution. Forced oscillation technique (FOT) is a pulmonary function test which is based on the measurement of respiratory mechanical impedance over a frequency range. In this article, we introduce a new measurement approach by combining FOT and EIT, named the oscillatory electrical impedance tomography (oEIT). Our oEIT measurement system consists of a valve-based FOT device, an EIT device, pressure and flow sensors, and a computer fusing the data streams. Measurements were performed on five healthy volunteers at the frequencies 3, 4, 5, 6, 7, 8, 10, 15, and 20 Hz. The measurements suggest that the combination of FOT and EIT is a promising approach. High frequency responses are visible in the derivative of the global impedance index ΔZeit(t,fos). $\\Delta {Z_{{\\text{eit}}}}(t,{f_{{\\text{os}}}}).$ The oEIT signals consist of three main components: forced oscillation, spontaneous breathing, and heart activity. The amplitude of the oscillation component decreases with increasing frequency. The band-pass filtered oEIT signal might be a new tool in regional lung function diagnostics, since local responses to high frequency perturbation could be distinguished between different lung regions.
International Nuclear Information System (INIS)
Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.
2009-01-01
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.
Molz, F. J.; Faybishenko, B.; Jenkins, E. W.
2012-12-01
Mass and energy fluxes within the soil-plant-atmosphere continuum are highly coupled and inherently nonlinear. The main focus of this presentation is to demonstrate the results of numerical modeling of a system of 4 coupled, nonlinear ordinary differential equations (ODEs), which are used to describe the long-term, rhizosphere processes of soil microbial dynamics, including the competition between nitrogen-fixing bacteria and those unable to fix nitrogen, along with substrate concentration (nutrient supply) and oxygen concentration. Modeling results demonstrate the synchronized patterns of temporal oscillations of competing microbial populations, which are affected by carbon and oxygen concentrations. The temporal dynamics and amplitude of the root exudation process serve as a driving force for microbial and geochemical phenomena, and lead to the development of the Gompetzian dynamics, synchronized oscillations, and phase-space attractors of microbial populations and carbon and oxygen concentrations. The nonlinear dynamic analysis of time series concentrations from the solution of the ODEs was used to identify several types of phase-space attractors, which appear to be dependent on the parameters of the exudation function and Monod kinetic parameters. This phase space analysis was conducted by means of assessing the global and local embedding dimensions, correlation time, capacity and correlation dimensions, and Lyapunov exponents of the calculated model variables defining the phase space. Such results can be used for planning experimental and theoretical studies of biogeochemical processes in the fields of plant nutrition, phyto- and bio-remediation, and other ecological areas.
Ananthakrishnan, Palaniswamy
2012-11-01
The problem is of practical relevance in determining the motion response of multi-hull and air-cushion vehicles in high seas and in littoral waters. The linear inviscid problem without surface pressure has been well studied in the past. In the present work, the nonlinear wave-body interaction problem is solved using finite-difference methods based on boundary-fitted coordinates. The inviscid nonlinear problem is tackled using the mixed Eulerian-Lagrangian formulation and the solution of the incompressible Navier-Stokes equations governing the viscous problem using a fractional-step method. The pressure variation in the air cushion is modeled using the isentropic gas equation pVγ = Constant. Results show that viscosity and free-surface nonlinearity significantly affect the hydrodynamic force and the wave motion at the resonant Helmholtz frequency (at which the primary wave motion is the vertical oscillation of the mean surface in between the bodies). Air compressibility suppresses the Helmholtz oscillation and enhances the wave radiation. Work supported by the ONR under the grant N00014-98-1-0151.
Kashyap, Rahul; Westley, Alexandra; Sen, Surajit
The Duffing oscillator, a nonlinear oscillator with a potential energy with both quadratic and cubic terms, is known to show highly chaotic solutions in certain regions of its parameter space. Here, we examine the behaviors of small chains of harmonically and anharmonically coupled Duffing oscillators and show that these chains exhibit localized nonlinear excitations (LNEs) similar to the ones seen in the Fermi-Pasta-Ulam-Tsingou (FPUT) system. These LNEs demonstrate properties such as long-time energy localization, high periodicity, and slow energy leaking which rapidly accelerates upon frequency matching with the adjacent particles all of which have been observed in the FPUT system. Furthermore, by examining bifurcation diagrams, we will show that many qualitative properties of this system during the transition from weakly to strongly nonlinear behavior depend directly upon the frequencies associated with the individual Duffing oscillators.
A memristor-based third-order oscillator: beyond oscillation
Talukdar, Abdul Hafiz Ibne
2012-10-06
This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
A memristor-based third-order oscillator: beyond oscillation
Talukdar, Abdul Hafiz Ibne; Radwan, Ahmed G.; Salama, Khaled N.
2012-01-01
This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.
On non-linear dynamics of a coupled electro-mechanical system
DEFF Research Database (Denmark)
Darula, Radoslav; Sorokin, Sergey
2012-01-01
Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...
Mechanism of large optical nonlinearity in gold nanoparticle films.
Mirza, I; McCloskey, D; Blau, W J; Lunney, J G
2018-04-01
The Z-scan technique, using femtosecond (fs) laser pulses at 1480 nm laser pulses, was used to measure the nonlinear optical properties of gold (Au) nanoparticle (NP) films made by both nanosecond (ns) and fs pulsed laser deposition (PLD) in vacuum. At irradiance levels of 1×10 12 Wm -2 , the ns-PLD films displayed induced absorption with β=4×10 -5 mW -1 , and a negative lensing effect with n 2 =-4.7×10 -11 m 2 W -1 with somewhat smaller values for the fs-PLD films. These values of n 2 imply an unphysically large change in the real part of the refractive index, demonstrating the need to take account of nonlinear changes of the Fresnel coefficients and multiple beam interference in Z-scan measurements on nanoscale films. Following this approach, the Z-scan observations were analyzed to determine the effective complex refractive index of the NP film at high irradiance. It appears that at high irradiance the NP film behaves as a metal, while at low irradiance it behaves as a low-loss dielectric. Thus, it is conjectured that, for high irradiance near the waist of the Z-scan laser beam, laser driven electron tunneling between NPs gives rise to metal-like optical behavior.
Nonlinear mechanisms for drift wave saturation and induced particle transport
International Nuclear Information System (INIS)
Dimits, A.M.; Lee, W.W.
1989-12-01
A detailed theoretical study of the nonlinear dynamics of gyrokinetic particle simulations of electrostatic collisionless and weakly collisional drift waves is presented. In previous studies it was shown that, in the nonlinearly saturated phase of the evolution, the saturation levels and especially the particle fluxes have an unexpected dependence on collisionality. In this paper, the explanations for these collisionality dependences are found to be as follows: The saturation level is determined by a balance between the electron and ion fluxes. The ion flux is small for levels of the potential below an E x B-trapping threshold and increases sharply once this threshold is crossed. Due to the presence of resonant electrons, the electron flux has a much smoother dependence on the potential. In the 2-1/2-dimensional (''pseudo-3D'') geometry, the electrons are accelerated away from the resonance as they diffuse spatially, resulting in an inhibition of their diffusion. Collisions and three-dimensional effects can repopulate the resonance thereby increasing the value of the particle flux. 30 refs., 32 figs., 2 tabs
International Nuclear Information System (INIS)
Boure, J.
1967-01-01
The problem of the oscillatory behavior of heated channels is presented in terms of delay-times and a density effect model is proposed to explain the behavior. The density effect is the consequence of the physical relationship between enthalpy and density of the fluid. In the first part non-linear equations are derived from the model in a dimensionless form. A description of the mechanism of oscillations is given, based on the analysis of the equations. An inventory of the governing parameters is established. At this point of the study, some facts in agreement with the experiments can be pointed out. In the second part the start of the oscillatory behavior of heated channels is studied in terms of the density effect. The threshold equations are derived, after linearization of the equations obtained in Part I. They can be solved rigorously by numerical methods to yield: -1) a relation between the describing parameters at the onset of oscillations, and -2) the frequency of the oscillations. By comparing the results predicted by the model to the experimental behavior of actual systems, the density effect is very often shown to be the actual cause of oscillatory behaviors. (author) [fr
Coherent Dynamics of a Hybrid Quantum Spin-Mechanical Oscillator System
Lee, Kenneth William, III
A fully functional quantum computer must contain at least two important components: a quantum memory for storing and manipulating quantum information and a quantum data bus to securely transfer information between quantum memories. Typically, a quantum memory is composed of a matter system, such as an atom or an electron spin, due to their prolonged quantum coherence. Alternatively, a quantum data bus is typically composed of some propagating degree of freedom, such as a photon, which can retain quantum information over long distances. Therefore, a quantum computer will likely be a hybrid quantum device, consisting of two or more disparate quantum systems. However, there must be a reliable and controllable quantum interface between the memory and bus in order to faithfully interconvert quantum information. The current engineering challenge for quantum computers is scaling the device to large numbers of controllable quantum systems, which will ultimately depend on the choice of the quantum elements and interfaces utilized in the device. In this thesis, we present and characterize a hybrid quantum device comprised of single nitrogen-vacancy (NV) centers embedded in a high quality factor diamond mechanical oscillator. The electron spin of the NV center is a leading candidate for the realization of a quantum memory due to its exceptional quantum coherence times. On the other hand, mechanical oscillators are highly sensitive to a wide variety of external forces, and have the potential to serve as a long-range quantum bus between quantum systems of disparate energy scales. These two elements are interfaced through crystal strain generated by vibrations of the mechanical oscillator. Importantly, a strain interface allows for a scalable architecture, and furthermore, opens the door to integration into a larger quantum network through coupling to an optical interface. There are a few important engineering challenges associated with this device. First, there have been no
Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent
2017-11-01
We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.
Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent
2017-11-01
We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.
Rajesh, Asam; Bandyopadhyay, Malay; Jayannavar, Arun M.
2017-12-01
In this work, we consider two different techniques based on reservoir engineering process and quantum Zeno control method to analyze the decoherence control mechanism of a charged magneto-oscillator in contact with different type of environment. Our analysis reveals that both the control mechanisms are very much sensitive on the details of different environmental spectrum (J (ω)), and also on different system and reservoir parameters, e.g., external magnetic field (rc), confinement length (r0), temperature (T), cut-off frequency of reservoir spectrum (ωcut), and measurement interval (τ). We also demonstrate the manipulation scheme of the continuous passage from decay suppression to decay acceleration by tuning the above mentioned system or reservoir parameters, e.g., rc, r0, T and τ.
2014-12-31
frequency A/C motor. The drive chain is configured such that a belt rotates an eccentric disk and a momentum fly wheel to minimize the unsteady...b) thrust bearing for pitch oscillation. Connection Bar Movement Lever Arm Fly Wheel Eccentric Disk V-Belt 5-hp A/C Motor Flow Pulley diameter... eccentric disk and drive mechanism, and (b) thrust bearing for pitch oscillation
International Nuclear Information System (INIS)
Fang Jinqing; Yao Weiguang
1992-12-01
Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science
Elwakil, Ahmed S.; Ozoguz, Serdar; Salama, Khaled N.
2009-01-01
model for the two oscillators is derived and verified numerically. Spice simulations using AMS BiCMOS 0.35 μ model parameters and experimental results are shown. Copyright © 2009 John Wiley & Sons, Ltd.
Influences of the Control on the Nonlinear Vibrations of a Variable Compression Ratio Mechanism
Directory of Open Access Journals (Sweden)
Mănescu Bogdan
2018-01-01
Full Text Available For the mechanism described in references the study of the nonlinear vibrations is performed considering a multibody approach for the elements of the mechanism and different laws of motion for the control element. A great attention is paid to the equilibrium of the motion. The influence of different parameters of control is highlighted in the paper. The results are numerically validated.
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.
Tunable Coupling to a Mechanical Oscillator Circuit Using a Coherent Feedback Network
Directory of Open Access Journals (Sweden)
Joseph Kerckhoff
2013-06-01
Full Text Available We demonstrate a fully cryogenic microwave feedback network composed of modular superconducting devices connected by transmission lines and designed to control a mechanical oscillator that is coupled to one of the devices. The network features an electromechanical device and a tunable controller that coherently receives, processes, and feeds back continuous microwave signals that modify the dynamics and readout of the mechanical state. While previous electromechanical systems represent some compromise between efficient control and efficient readout of the mechanical state, as set by the electromagnetic decay rate, the tunable controller produces a closed-loop network that can be dynamically and continuously tuned between both extremes much faster than the mechanical response time. We demonstrate that the microwave decay rate may be modulated by at least a factor of 10 at a rate greater than 10^{4} times the mechanical response rate. The system is easy to build and suggests that some useful functions may arise most naturally at the network level of modular, quantum electromagnetic devices.
The colpitts oscillator family
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
A tutorial study of the Colpitts oscillator family defined as all oscillators based on a nonlinear amplifier and a three- terminal linear resonance circuit with one coil and two capacitors. The original patents are investigated. The eigenvalues of the linearized Jacobian for oscillators based...
Soavi, Giancarlo; Tempra, Iacopo; Pantano, Maria F; Cattoni, Andrea; Collin, Stéphane; Biagioni, Paolo; Pugno, Nicola M; Cerullo, Giulio
2016-02-23
Mechanical vibrational resonances in metal nanoparticles are intensively studied because they provide insight into nanoscale elasticity and for their potential application to ultrasensitive mass detection. In this paper, we use broadband femtosecond pump-probe spectroscopy to study the longitudinal acoustic phonons of arrays of gold nanorods with different aspect ratios, fabricated by electron beam lithography with very high size uniformity. We follow in real time the impulsively excited extensional oscillations of the nanorods by measuring the transient shift of the localized surface plasmon band. Broadband and high-sensitivity detection of the time-dependent extinction spectra enables one to develop a model that quantitatively describes the periodic variation of the plasmon extinction coefficient starting from the steady-state spectrum with only one additional free parameter. This model allows us to retrieve the time-dependent elongation of the nanorods with an ultrahigh sensitivity and to measure oscillation amplitudes of just a few picometers and plasmon energy shifts on the order of 10(-2) meV.
Characteristics and Mechanisms of Zonal Oscillation of Western Pacific Subtropical High in Summer
Guan, W.; Ren, X.; Hu, H.
2017-12-01
The zonal oscillation of the western Pacific subtropical high (WPSH) influences the weather and climate over East Asia significantly. This study investigates the features and mechanisms of the zonal oscillation of the WPSH during summer on subseasonal time scales. The zonal oscillation index of the WPSH is defined by normalized subseasonal geopotential height anomaly at 500hPa averaged over the WPSH's western edge (110° - 140°E, 10° - 30°N). The index shows a predominant oscillation with a period of 10-40 days. Large positive index indicates a strong anticyclonic anomaly over East Asia and its coastal region south of 30°N at both 850hPa and 500hPa. The WPSH stretches more westward accompanied by warmer SST anomalies beneath the western edge of the WPSH. Meanwhile, above-normal precipitation is seen over the Yangtze-Huaihe river basin and below-normal precipitation over the south of the Yangtze River. Negative index suggests a more eastward position of WPSH. The anomalies in circulation and SST for negative index are almost the mirror image of those for the positive index. In early summer, the zonal shift of the WPSH is affected by both the East Asia/Pacific (EAP) teleconnection pattern and the Silk road pattern (SRP). The positive (negative) phase of the EAP pattern is characterized by a low-level anticyclonic (cyclonic) anomaly over the subtropical western Pacific, indicating the western extension (eastward retreat) of the WPSH. Comparing with the EAP pattern, the SRP forms an upper-level anticyclonic (cyclonic) anomaly in mid-latitudes of East Asia, and then leads to the westward (eastward) movement of the WPSH. In late summer, the zonal shift of the WPSH is mainly affected by the EAP pattern, because the EAP pattern in late summer is stronger than that in early summer. The zonal shift of the WPSH is also influenced by the subseasonal air-sea interaction locally. During the early stage of WPSH's westward stretch, the local SST anomaly in late summer is
International Nuclear Information System (INIS)
Fueloep, L.
1987-10-01
The forceless mechanics of Hertz is a reformulation of the classical mechanics in a curved configuration space. The relationship between the forceless mechanics and the general relativity theory which uses curved Riemann spaces as well is investigated on the simple example of the harmonic oscillator. The mathematical similarities and differences and the different interpretations of similar formulas are discussed. Some formal constants of the Hertz mechanics have got concrete physical meanings in the general relativity. (D.Gy.)
Oscillators - a simple introduction
DEFF Research Database (Denmark)
Lindberg, Erik
2013-01-01
Oscillators are kernel components of electrical and electronic circuits. Discussion of history, mechanisms and design based on Barkhausens observation. Discussion of a Wien Bridge oscillator based on the question: Why does this circuit oscillate ?......Oscillators are kernel components of electrical and electronic circuits. Discussion of history, mechanisms and design based on Barkhausens observation. Discussion of a Wien Bridge oscillator based on the question: Why does this circuit oscillate ?...
Nonlinearity Mechanism and Correction of Sapphire Fiber Temperature Sensor on Blackbody Cavity
Directory of Open Access Journals (Sweden)
Tiejun Cao
2014-06-01
Full Text Available Based on the principle of blackbody radiation, sapphire optic fiber temperature sensor has been more widely used in recent years, and its temperature range is between 800 ~ 2000 oC, and the response time is in 10-2 magnitude, and transient temperature measurement can be high precision in harsh environments. Nonlinear constraints on sapphire fiber temperature sensor affect the accuracy and stability of the sensor. In order to solve the nonlinear problems which exist in the measurement, at first, the sapphire fiber optic temperature sensor temperature measurement principle and nonlinear generation mechanism are studied; secondly piecewise linear interpolation and spline interpolation linearization algorithm is designed with combining the nonlinear characteristics of sapphire optical fiber temperature sensor, and the program is designed on its linear and associated signal processing. Experimental results show that a good linearization of sapphire fiber optic temperature sensor can been achieved in this method.
Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations
Zhang, Yu; Jiang, Jack J.
2008-09-01
Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.
Directory of Open Access Journals (Sweden)
Gbeminiyi Sobamowo
2017-04-01
Full Text Available The development of mathematical models for describing the dynamic behaviours of fluid conveying pipes, micro-pipes and nanotubes under the influence of some thermo-mechanical parameters results into nonlinear equations that are very difficult to solve analytically. In cases where the exact analytical solutions are presented either in implicit or explicit forms, high skills and rigorous mathematical analyses were employed. It is noted that such solutions do not provide general exact solutions. Inevitably, comparatively simple, flexible yet accurate and practicable solutions are required for the analyses of these structures. Therefore, in this study, approximate analytical solutions are provided to the nonlinear equations arising in flow-induced vibration of pipes, micro-pipes and nanotubes using Galerkin-Newton-Harmonic Method (GNHM. The developed approximate analytical solutions are shown to be valid for both small and large amplitude oscillations. The accuracies and explicitness of these solutions were examined in limiting cases to establish the suitability of the method.
The quantum mechanics of the supersymmetric nonlinear sigma-model
International Nuclear Information System (INIS)
Davis, A.C.; Macfarlane, A.J.; Popat, P.C.; Holten, J.W. van
1984-01-01
The classical and quantum mechanical formalisms of the models are developed. The quantisation is done in such a way that the quantum theory can be represented explicitly in as simple a form as possible, and the problem of ordering of operators is resolved so as to maintain the supersymmetry algebra of the classical theory. (author)
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles
Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A; Wuite, Gijs J L; Roos, Wouter H; Barsegov, Valeri
The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity,
Energy Technology Data Exchange (ETDEWEB)
Yuce, C [Physics Department, Anadolu University, Eskisehir (Turkey); Kilic, A [Physics Department, Anadolu University, Eskisehir (Turkey); Coruh, A [Physics Department, Sakarya University, Sakarya (Turkey)
2006-07-15
The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wavefunction for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete, and the energy is given as a linear function of the quantum number n.
Direct Visualization of Mechanical Beats by Means of an Oscillating Smartphone
Giménez, Marcos H.; Salinas, Isabel; Monsoriu, Juan A.; Castro-Palacio, Juan C.
2017-10-01
The resonance phenomenon is widely known in physics courses. Qualitatively speaking, resonance takes place in a driven oscillating system whenever the frequency approaches the natural frequency, resulting in maximal oscillatory amplitude. Very closely related to resonance is the phenomenon of mechanical beating, which occurs when the driving and natural frequencies of the system are slightly different. The frequency of the beat is just the difference of the natural and driving frequencies. Beats are very familiar in acoustic systems. There are several works in this journal on visualizing the beats in acoustic systems. For instance, the microphone and the speaker of two mobile devices were used in previous work to analyze the acoustic beats produced by two signals of close frequencies. The formation of beats can also be visualized in mechanical systems, such as a mass-spring system or a double-driven string. Here, the mechanical beats in a smartphone-spring system are directly visualized in a simple way. The frequency of the beats is measured by means of the acceleration sensor of a smartphone, which hangs from a spring attached to a mechanical driver. This laboratory experiment is suitable for both high school and first-year university physics courses.
Ge, Li; Zhao, Nan
2018-04-01
We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.
International Nuclear Information System (INIS)
Barz, Kay
2010-01-01
In this work experimental techniques for characterization of ferroelectric nm-thin films and ferroelectric/semiconductor structures by means of nonlinear phenomena are discussed. The thin film sample is applied in a series resonant circuit. By recording time series data and amplitude-frequency-characteristics (resonance frequency shift), the nonlinear behavior can be analyzed with respect to the theoretical aspects of these effects in the framework of nonlinear dynamics. The evolving ferroelectric hysteresis is represented by the amplitude-frequency-characteristic in a very detailed form. Interpretations are presented on how transient alterations like fatigue or retention loss, affect the amplitude-frequency-characteristics. Time series analysis allows to separate the specific influence of the nonlinear components and their corresponding time constants. The work closes with suggestions for a systematic application of the presented techniques for an extended characterization of ferroelectric thin films. (orig.)
International Nuclear Information System (INIS)
Stroppe, Heribert; Streitenberger, Peter; Specht, Eckard; Zeitler, Juergen; Langer, Heinz
2017-01-01
The present book is the unification of the proved problem collections for the basic physical training of studyings of especially engineering courses at technical colleges and universities. The book contains - didactically prepared and structured in the style of a textbook as well as with increasing difficulty - a total of 960 exemplary and additional tasks from the fields mechanics, heat, electricity and magnetism, oscillations and waves, as well as atomic and nuclear physics. For the exemplary problems the whole solution path and the complete calculation process with explanation of the relevant physical laws are extensively presented, for the additional problems for the self-control only the solutions and, if necessary, intermediate calculations are given. The examples and problems with mostly practice-oriented content are selected in such a way that they largely cover the matter treated in courses and exercises and make by their didactical preparation an effective repetition and optimal examination-preparation possible.
Directory of Open Access Journals (Sweden)
Tomasz J. Wodzicki
2014-01-01
Full Text Available The proposed hypothesis concerns the transduction of auxin molecular signals arriving from the apoplast at the plasma membrane or recognized by the proteineous receptors of the responding cell, to the concentration gradients oscillating in the supracellular space, associated usually with the specific plant growth and differentiation. Acting as an agonist from outside the target cell auxin stimulates in this cell: (1 the liberation of auxin from the cytosolic pool of its conjugates directly into the basipetal efflux; (2 the synthesis of new auxin which restores the cytosolic reserve of auxin conjugates. The functioning of such a system may be effective in a series of processes initiated by the changing concentration of cytosolic calcium. The hypothesis suggests a molecular mechanism for the development and effective operation of the morphogenetic field in the supracellular space of the plant body, such as the field resulting from auxin waves discovered in cambium.
A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems
Liu, Zuolin; Xu, Jian
2018-04-01
In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.
Directory of Open Access Journals (Sweden)
Xu Fang
2018-04-01
Full Text Available High-speed, pressure-compensated variable displacement piston pumps are widely used in aircraft hydraulic systems for their high power density. The swash plate is controlled by the pressure-compensated valve, which uses pressure feedback so that the instantaneous output flow of the pump is exactly enough to maintain a presetting pressure. The oscillation of the swash plate is one of the major excitation sources in the high-speed piston pump, which may cause lower efficiency, shorter service life, and even serious damage. This paper presents an improved model to investigate the influence of the variable displacement mechanism on the swash plate oscillation and introduces some feasible ways to reduce oscillation of the swash plate. Most of the variable structural parameters of the variable displacement mechanism are taken into consideration, and their influences on swash plate oscillation are discussed in detail. The influence of the load pipe on the oscillation of the swash plate is considered in the improved model. A test rig is built and similarities between the experiments and simulated results prove that the simulation model can effectively predict the variable displacement mechanism state. The simulation results show that increasing the volume of the outlet chamber, the spring stiffness of the control valve, the action area of the actuator piston, and offset distance of the actuator piston can significantly reduce the oscillation amplitude of the swash plate. Furthermore, reducing the diameter of the control valve spool and the dead volume of the actuator piston chamber can also have a positive effect on oscillation amplitude reduction.
Alvarado-Rojas, C; Huberfeld, G; Baulac, M; Clemenceau, S; Charpier, S; Miles, R; Menendez de la Prida, L; Le Van Quyen, M
2015-01-01
Transient high-frequency oscillations (150-600 Hz) in local field potential generated by human hippocampal and parahippocampal areas have been related to both physiological and pathological processes. The cellular basis and effects of normal and abnormal forms of high-frequency oscillations (HFO) has been controversial. Here, we searched for HFOs in slices of the subiculum prepared from human hippocampal tissue resected for treatment of pharmacoresistant epilepsy. HFOs occurred spontaneously in extracellular field potentials during interictal discharges (IID) and also during pharmacologically induced preictal discharges (PID) preceding ictal-like events. While most of these events might be considered pathological since they invaded the fast ripple band (>250 Hz), others were spectrally similar to physiological ripples (150-250 Hz). Do similar cellular mechanisms underly IID-ripples and PID-ripples? Are ripple-like oscillations a valid proxy of epileptogenesis in human TLE? With combined intra- or juxta-cellular and extracellular recordings, we showed that, despite overlapping spectral components, ripple-like IID and PID oscillations were associated with different cellular and synaptic mechanisms. IID-ripples were associated with rhythmic GABAergic and glutamatergic synaptic potentials with moderate neuronal firing. In contrast, PID-ripples were associated with depolarizing synaptic inputs frequently reaching the threshold for bursting in most cells. Thus ripple-like oscillations (100-250 Hz) in the human epileptic hippocampus are associated with different mechanisms for synchrony reflecting distinct dynamic changes in inhibition and excitation during interictal and pre-ictal states. PMID:25448920
The mechanism and realization of a band-agile coaxial relativistic backward-wave oscillator
Energy Technology Data Exchange (ETDEWEB)
Ge, Xingjun; Zhang, Jun; Zhong, Huihuang; Qian, Baoliang; Wang, Haitao [College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha 410073 (China)
2014-11-03
The mechanism and realization of a band-agile coaxial relativistic backward-wave oscillator (RBWO) are presented. The operation frequency tuning can be easily achieved by merely altering the inner-conductor length. The key effects of the inner-conductor length contributing to the mechanical frequency tunability are investigated theoretically and experimentally. There is a specific inner-conductor length where the operation frequency can jump from one mode to another mode, which belongs to a different operation band. In addition, the operation frequency is tunable within each operation band. During simulation, the L-band microwave with a frequency of 1.61 GHz is radiated when the inner-conductor length is 39 cm. Meanwhile, the S-band microwave with a frequency of 2.32 GHz is radiated when the inner-conductor length is 5 cm. The frequency adjustment bandwidths of L-band and S-band are about 8.5% and 2%, respectively. Moreover, the online mechanical tunability process is described in detail. In the initial experiment, the generated microwave frequencies remain approximately 1.59 GHz and 2.35 GHz when the inner-conductor lengths are 39 cm and 5 cm. In brief, this technical route of the band-agile coaxial RBWO is feasible and provides a guide to design other types of band-agile high power microwaves sources.
A robust single-beam optical trap for a gram-scale mechanical oscillator.
Altin, P A; Nguyen, T T-H; Slagmolen, B J J; Ward, R L; Shaddock, D A; McClelland, D E
2017-11-06
Precise optical control of microscopic particles has been mastered over the past three decades, with atoms, molecules and nano-particles now routinely trapped and cooled with extraordinary precision, enabling rapid progress in the study of quantum phenomena. Achieving the same level of control over macroscopic objects is expected to bring further advances in precision measurement, quantum information processing and fundamental tests of quantum mechanics. However, cavity optomechanical systems dominated by radiation pressure - so-called 'optical springs' - are inherently unstable due to the delayed dynamical response of the cavity. Here we demonstrate a fully stable, single-beam optical trap for a gram-scale mechanical oscillator. The interaction of radiation pressure with thermo-optic feedback generates damping that exceeds the mechanical loss by four orders of magnitude. The stability of the resultant spring is robust to changes in laser power and detuning, and allows purely passive self-locking of the cavity. Our results open up a new way of trapping and cooling macroscopic objects for optomechanical experiments.
Quantum-mechanical analysis of low-gain free-electron laser oscillators
Fares, H.; Yamada, M.; Chiadroni, E.; Ferrario, M.
2018-05-01
In the previous classical theory of the low-gain free-electron laser (FEL) oscillators, the electron is described as a point-like particle, a delta function in the spatial space. On the other hand, in the previous quantum treatments, the electron is described as a plane wave with a single momentum state, a delta function in the momentum space. In reality, an electron must have statistical uncertainties in the position and momentum domains. Then, the electron is neither a point-like charge nor a plane wave of a single momentum. In this paper, we rephrase the theory of the low-gain FEL where the interacting electron is represented quantum mechanically by a plane wave with a finite spreading length (i.e., a wave packet). Using the concepts of the transformation of reference frames and the statistical quantum mechanics, an expression for the single-pass radiation gain is derived. The spectral broadening of the radiation is expressed in terms of the spreading length of an electron, the relaxation time characterizing the energy spread of electrons, and the interaction time. We introduce a comparison between our results and those obtained in the already known classical analyses where a good agreement between both results is shown. While the correspondence between our results and the classical results are shown, novel insights into the electron dynamics and the interaction mechanism are presented.
Nonlinear Fracture Mechanics and Plasticity of the Split Cylinder Test
DEFF Research Database (Denmark)
Olesen, John Forbes; Østergaard, Lennart; Stang, Henrik
2006-01-01
properties. This implies that the linear elastic interpretation of the ultimate splitting force in term of the uniaxial tensile strength of the material is only valid for special situations, e.g. for very large cylinders. Furthermore, the numerical analysis suggests that the split cylinder test is not well...... models are presented, a simple semi-analytical model based on analytical solutions for the crack propagation in a rectangular prismatic body, and a finite element model including plasticity in bulk material as well as crack propagation in interface elements. A numerical study applying these models...... demonstrates the influence of varying geometry or constitutive properties. For a split cylinder test in load control it is shown how the ultimate load is either plasticity dominated or fracture mechanics dominated. The transition between the two modes is related to changes in geometry or constitutive...
International Nuclear Information System (INIS)
Kretzschmar, Martin
1999-01-01
When a Penning trap is operated with an additional quadrupole driving field with a frequency that equals a suitable combination (sum or difference) of the frequencies of the fundamental modes of motion (modified cyclotron, magnetron and axial frequency), then a periodic conversion of the participating modes into each other is observed, strongly resembling the Rabi oscillations in a 2-level atom driven by a laser field tuned to the transition frequency. This investigation attempts to understand on a fundamental level how and why the motion of a classical particle in a macroscopic apparatus can be truely analogous to the oscillations of states of quantum mechanical 2-level systems (2-level atom or magnetic resonance). Ion motion in a Penning trap with an additional quadrupole driving field is described in a quantum mechanical frame work. The Heisenberg equations of motion for the creation and annihilation operators of the interacting oscillators have been explicitly solved, the time development operator of the Schroedinger picture has been determined. The driving field provides for two types of intermode interaction: Type I preserves the total number of excitation quanta present in the two interacting modes, the system oscillates between the modes with a frequency corresponding to the Rabi frequency in two-level systems. Type II preserves the difference of the numbers of excitation quanta present in the two interacting modes, it causes the ion motion to become unbounded. The two types of interaction are associated in a natural way with a SU(2) and a SU(1,1) Lie algebra. The three generators of these algebras form a vector operator that we denote as the Bloch vector operator. The Hilbert space decomposes in a natural way into invariant subspaces, finite dimensional in the case of type I interaction (SU(2)-algebra) and infinite dimensional in the case of type II interaction (SU(1,1)-algebra). The physics of the 2-level atom in the laser field can be described in the 2
Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox
Polchinski, Joseph
1991-01-01
The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.
Nonlinear electro-magneto-mechanical constitutive modelling of monolayer graphene
Sfyris, D.; Sfyris, G. I.; Bustamante, R.
2016-04-01
Using the classical theory of invariants for the specific class of graphene's symmetry, we constitutively characterize electro-magneto-mechanical interactions of graphene at continuum level. Graphene's energy depends on five arguments: the Finger strain tensor, the curvature tensor, the shift vector, the effective electric field intensity and the effective magnetic induction. The Finger strain tensor describes in- surface phenomena, the curvature tensor is responsible for the out-of-surface motions, while the shift vector is used due to the fact that graphene is a multilattice. The electric and the magnetic fields are described by the effective electric field intensity and the effective magnetic induction, respectively. An energy with the above arguments that also respects graphene's symmetries is found to have 42 invariants. Using these invariants, we evaluate all relevant measures by finding derivatives of the energy with respect to the five arguments of the energy. We also lay down the field equations that should be satisfied. These are the Maxwell equations, the momentum equation, the moment of momentum equation and the equation ruling the shift vector. Our framework is general enough to capture fully coupled processes in the finite deformation regime.
Liu, Yang; He, Shengping; Li, Fei; Wang, Huijun; Zhu, Yali
2017-12-01
Based on long-term reanalysis datasets, this study revealed that the relationship between the Arctic Oscillation (AO) and the East Asian jet stream (EAJS) is significant negative during 1925-1945 and 1985-2005 (significant periods; hereafter SPs) whereas insignificant during 1900-1920 and 1955-1975 (insignificant periods; ISPs). The unstable AO-EAJS relationship might be related to the interdecadal change of AO's spatial structure. During SPs winters, anomalous positive AO events are characterized by atmospheric negative anomalies in the Arctic with two anomalous positive centers located in the extratropical Atlantic and Pacific, exhibiting a quasi-barotropic structure. By contrast, the anomalous center in the North Pacific is barely observed during ISPs winters. Further analysis indicated that such interdecadal change might be attributed to change of troposphere-stratosphere coupling and the North Pacific air-sea interaction. On the one hand, anomalous AO at surface is closely related to obvious planetary waves downward from the stratosphere during SPs, which favors the subtropics-Arctic teleconnection. On the other hand, the Interdecadal Pacific Oscillation (IPO) shows warm phase during SPs, which induces larger variance of the Aleutian Low and more intensive divergence anomalies at upper level troposphere. Due to the advection of vorticity induced by stronger divergence is favorable for stronger Rossby wave source, the Rossby wave activity is much stronger and could further propagate eastward to the North Atlantic during SPs, resulting in the Pacific-Atlantic teleconnection. Such a mechanism is supported by the numerical simulations from two individual models that are perturbed by warm/cold IPO sea surface temperature anomalies.
Structural, Linear, and Nonlinear Optical and Mechanical Properties of New Organic L-Serine Crystal
Directory of Open Access Journals (Sweden)
K. Rajesh
2014-01-01
Full Text Available Nonlinear optical single crystal of organic amino acid L-Serine (LS was grown by slow evaporation technique. Solubility study of the compound was measured and metastable zone width was found. Single crystal X-ray diffraction study was carried out for the grown crystal. The linear and nonlinear optical properties of the crystal were confirmed by UV-Vis analysis and powder SHG tester. FT-IR spectrum was recorded and functional groups were analyzed. Vickers’ microhardness studies showed the mechanical strength of the grown crystal. Laser damage threshold value of the crystal was calculated. Photoconductivity studies reveal the conductivity of the crystal.
Experimental Searches for Exotic Short-Range Forces Using Mechanical Oscillators
Weisman, Evan
Experimental searches for forces beyond gravity and electromagnetism at short range have attracted a great deal of attention over the last decade. In this thesis I describe the test mass development for two new experiments searching for forces below 1 mm. Both modify a previous experiment that used 1 kHz mechanical oscillators as test masses with a stiff conducting shield between them to suppress backgrounds, a promising technique for probing exceptionally small distances at the limit of instrumental thermal noise. To further reduce thermal noise, one experiment will use plated silicon test masses at cryogenic temperatures. The other experiment, which searches for spin-dependent interactions, will apply the spin-polarizable material Dy3Fe5O 12 to the test mass surfaces. This material exhibits orbital compensation of the magnetism associated with its intrinsic electron spin, minimizing magnetic backgrounds. Several plated silicon test mass prototypes were fabricated using photolithography (useful in both experiments), and spin-dependent materials were synthesized with a simple chemical recipe. Both silicon and spin-dependent test masses demonstrate the mechanical and magnetic properties necessary for sensitive experiments. I also describe sensitivity calculations of another proposed spin-dependent experiment, based on a modified search for the electron electric dipole moment, which show unprecedented sensitivity to exotic monopole-dipole forces. Inspired by a finite element model, a study attempting to maximize detector quality factor versus geometry is also presented, with experimental results so far not explained by the model.
International Nuclear Information System (INIS)
Ji, J.C.; Zhang, N.
2009-01-01
Non-resonant bifurcations of codimension two may appear in the controlled van der Pol-Duffing oscillator when two critical time delays corresponding to a double Hopf bifurcation have the same value. With the aid of centre manifold theorem and the method of multiple scales, the non-resonant response and two types of primary resonances of the forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. It is shown that the non-resonant response of the forced oscillator may exhibit quasi-periodic motions on a two- or three-dimensional (2D or 3D) torus. The primary resonant responses admit single and mixed solutions and may exhibit periodic motions or quasi-periodic motions on a 2D torus. Illustrative examples are presented to interpret the dynamics of the controlled system in terms of two dummy unfolding parameters and exemplify the periodic and quasi-periodic motions. The analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation.
International Nuclear Information System (INIS)
DePuit, Ryan J; Squires, Todd M
2012-01-01
Active and nonlinear microrheology experiments involve a colloidal probe that is forced to move within a material, with the goal of recovering the nonlinear rheological response properties of the material. Various mechanisms cause discrepancies between the nonlinear rheology measured microrheologically and macroscopically, including direct probe-bath collisions, the Lagrangian unsteadiness experienced by the material elements, and the spatially inhomogeneous and rheologically mixed strain field set up around the probe. Here, we perform computational nonlinear microrheology experiments, in which a colloidal probe translates through a dilute suspension of Brownian ellipsoids, whose results we compare against analogous computational experiments on the macroscopic shear rheology of the same model material. The quantitative impact of each of the mechanisms for micro-macro-discrepancy can thus be computed directly, with additional computational experiments performed where the processes in question are ‘turned off’. We show that all three discrepancy mechanisms impact the microrheological measurement quantitatively, and that none can be neglected. This motivates a search for microrheological probes whose geometry or forcing is optimized to minimize these impacts, which we present in a companion article.
A novel auto-tuning PID control mechanism for nonlinear systems.
Cetin, Meric; Iplikci, Serdar
2015-09-01
In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith
2017-05-01
In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.
Single-nary philosophy for non-linear study of mechanics of materials
International Nuclear Information System (INIS)
Tran, C.
2005-01-01
Non-linear study of mechanics of materials is formulated in this paper as a problem of meta-intelligent system analysis. Non-linearity will be singled out as an important concept for understanding of high-order complex systems. Through single-nary thinking, which will be represented in this work, we introduce a modification of Aristotelian philosophy using modal logic and multi-valued logic (these logics we call 'high-order' logic). Next, non-linear cause - effect relations are expressed through non-additive measures and multiple-information aggregation principles based on fuzzy integration. The study of real time behaviors, required experiences and intuition, will be realized using truth measures (non-additive measures) and a procedure for information processing in intelligence levels. (author)
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Energy Technology Data Exchange (ETDEWEB)
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
Nonlinear mechanical response of the extracellular matrix: learning from articular cartilage
Kearns, Sarah; Das, Moumita
2015-03-01
We study the mechanical structure-function relations in the extracellular matrix (ECM) with focus on nonlinear shear and compression response. As a model system, our study focuses on the ECM in articular cartilage tissue which has two major mechanobiological components: a network of the biopolymer collagen that acts as a stiff, reinforcing matrix, and a flexible aggrecan network that facilitates deformability. We model this system as a double network hydrogel made of interpenetrating networks of stiff and flexible biopolymers respectively. We study the linear and nonlinear mechanical response of the model ECM to shear and compression forces using a combination of rigidity percolation theory and energy minimization approaches. Our results may provide useful insights into the design principles of the ECM as well as biomimetic hydrogels that are mechanically robust and can, at the same time, easily adapt to cues in their surroundings.
Laursen, Tod A
2003-01-01
This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis, as well as for engineers and scientists dealing with technologies in which tribological response must be characterized, the book includes an introductory but detailed overview of nonlinear finite element formulations before dealing with contact and impact specifically. Topics encompassed include the continuum mechanics, mathematical structure, variational framework, and finite element implementations associated with contact/impact interaction. Additionally, important and currently emerging research topics in computational contact mechanics are introduced, encompassing such topics as tribological complexity, conservative treatment of inelastic impact interaction, and novel spatial discretization strategies.
Features and states of microscopic particles in nonlinear quantum-mechanics systems
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can
International Nuclear Information System (INIS)
Kovacic, Ivana
2009-01-01
An analytical approach to determine the approximate solution for the periodic motion of non-conservative oscillators with a fractional-order restoring force and slowly varying parameters is presented. The solution has the form of the first-order differential equation for the amplitude and phase of motion. The method used is based on the combination of the Krylov-Bogoliubov method with Hamilton's variational principle with the uncommutative rule for the variation of velocity. The conservative systems with slowly varying parameters are also considered. The corresponding adiabatic invariant is obtained. Two examples are given to illustrate derived theoretical results.
Nonlinear mechanics of non-rigid origami: an efficient computational approach
Liu, K.; Paulino, G. H.
2017-10-01
Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on `bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.
Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.
Shang, Xituan; Yen, Michael R T; Gaber, M Waleed
2010-06-01
The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.
The mechanism by which nonlinearity sustains turbulence in plane Couette flow
Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.
2018-04-01
Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.
Wave Physics Oscillations - Solitons - Chaos
Nettel, Stephen
2009-01-01
This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.
Sequential Modular Position and Momentum Measurements of a Trapped Ion Mechanical Oscillator
Flühmann, C.; Negnevitsky, V.; Marinelli, M.; Home, J. P.
2018-04-01
The noncommutativity of position and momentum observables is a hallmark feature of quantum physics. However, this incompatibility does not extend to observables that are periodic in these base variables. Such modular-variable observables have been suggested as tools for fault-tolerant quantum computing and enhanced quantum sensing. Here, we implement sequential measurements of modular variables in the oscillatory motion of a single trapped ion, using state-dependent displacements and a heralded nondestructive readout. We investigate the commutative nature of modular variable observables by demonstrating no-signaling in time between successive measurements, using a variety of input states. Employing a different periodicity, we observe signaling in time. This also requires wave-packet overlap, resulting in quantum interference that we enhance using squeezed input states. The sequential measurements allow us to extract two-time correlators for modular variables, which we use to violate a Leggett-Garg inequality. Signaling in time and Leggett-Garg inequalities serve as efficient quantum witnesses, which we probe here with a mechanical oscillator, a system that has a natural crossover from the quantum to the classical regime.
Quantum Correlations of Light from a Room-Temperature Mechanical Oscillator
Sudhir, V.; Schilling, R.; Fedorov, S. A.; Schütz, H.; Wilson, D. J.; Kippenberg, T. J.
2017-07-01
When an optical field is reflected from a compliant mirror, its intensity and phase become quantum-correlated due to radiation pressure. These correlations form a valuable resource: the mirror may be viewed as an effective Kerr medium generating squeezed states of light, or the correlations may be used to erase backaction from an interferometric measurement of the mirror's position. To date, optomechanical quantum correlations have been observed in only a handful of cryogenic experiments, owing to the challenge of distilling them from thermomechanical noise. Accessing them at room temperature, however, would significantly extend their practical impact, with applications ranging from gravitational wave detection to chip-scale accelerometry. Here, we observe broadband quantum correlations developed in an optical field due to its interaction with a room-temperature nanomechanical oscillator, taking advantage of its high-cooperativity near-field coupling to an optical microcavity. The correlations manifest as a reduction in the fluctuations of a rotated quadrature of the field, in a frequency window spanning more than an octave below mechanical resonance. This is due to coherent cancellation of the two sources of quantum noise contaminating the measured quadrature—backaction and imprecision. Supplanting the backaction force with an off-resonant test force, we demonstrate the working principle behind a quantum-enhanced "variational" force measurement.
Cheng, Yu; Muroski, Megan E; Petit, Dorothée C M C; Mansell, Rhodri; Vemulkar, Tarun; Morshed, Ramin A; Han, Yu; Balyasnikova, Irina V; Horbinski, Craig M; Huang, Xinlei; Zhang, Lingjiao; Cowburn, Russell P; Lesniak, Maciej S
2016-02-10
Magnetic particles that can be precisely controlled under a magnetic field and transduce energy from the applied field open the way for innovative cancer treatment. Although these particles represent an area of active development for drug delivery and magnetic hyperthermia, the in vivo anti-tumor effect under a low-frequency magnetic field using magnetic particles has not yet been demonstrated. To-date, induced cancer cell death via the oscillation of nanoparticles under a low-frequency magnetic field has only been observed in vitro. In this report, we demonstrate the successful use of spin-vortex, disk-shaped permalloy magnetic particles in a low-frequency, rotating magnetic field for the in vitro and in vivo destruction of glioma cells. The internalized nanomagnets align themselves to the plane of the rotating magnetic field, creating a strong mechanical force which damages the cancer cell structure inducing programmed cell death. In vivo, the magnetic field treatment successfully reduces brain tumor size and increases the survival rate of mice bearing intracranial glioma xenografts, without adverse side effects. This study demonstrates a novel approach of controlling magnetic particles for treating malignant glioma that should be applicable to treat a wide range of cancers. Copyright © 2015 Elsevier B.V. All rights reserved.
Gonzalez-Burgos, Guillermo; Lewis, David A
2008-09-01
Synchronization of neuronal activity in the neocortex may underlie the coordination of neural representations and thus is critical for optimal cognitive function. Because cognitive deficits are the major determinant of functional outcome in schizophrenia, identifying their neural basis is important for the development of new therapeutic interventions. Here we review the data suggesting that phasic synaptic inhibition mediated by specific subtypes of cortical gamma-aminobutyric acid (GABA) neurons is essential for the production of synchronized network oscillations. We also discuss evidence indicating that GABA neurotransmission is altered in schizophrenia and propose mechanisms by which such alterations can decrease the strength of inhibitory connections in a cell-type-specific manner. We suggest that some alterations observed in the neocortex of schizophrenia subjects may be compensatory responses that partially restore inhibitory synaptic efficacy. The findings of altered neural synchrony and impaired cognitive function in schizophrenia suggest that such compensatory responses are insufficient and that interventions aimed at augmenting the efficacy of GABA neurotransmission might be of therapeutic value.
Demekhov, A. G.
2017-03-01
By using numerical simulations we generalize certain relationships between the parameters of quasimonochromatic whistler-mode waves generated at the linear and nonlinear stages of the cyclotron instability in the backward-wave oscillator regime. One of these relationships is between the wave amplitude at the nonlinear stage and the linear growth rate of the cyclotron instability. It was obtained analytically by V.Yu.Trakhtengerts (1984) for a uniform medium under the assumption of constant frequency and amplitude of the generated wave. We show that a similar relationship also holds for the signals generated in a nonuniform magnetic field and having a discrete structure in the form of short wave packets (elements) with fast frequency drift inside each element. We also generalize the formula for the linear growth rate of absolute cyclotron instability in a nonuniform medium and analyze the relationship between the frequency drift rate in the discrete elements and the wave amplitude. These relationships are important for analyzing the links between the parameters of chorus emissions in the Earth's and planetary magnetospheres and the characteristics of the energetic charged particles generating these signals.
Energy Technology Data Exchange (ETDEWEB)
Hagedorn, R
1957-03-07
A mechanical system of two degrees of freedom is considered which can be described by a system of canonical differential equations. The Hamiltonian is assumed to be explicitly time-dependent with period 2. The aim is to bring this system by a sequence of canonical and periodical transformations into a form where the new Hamiltonian is constant and as simple as possible. The general theory is then brought to a stage where it becomes immediately applicable to given particular cases, particularly to circular particle accelerators. More general results are given on exciting strengths of different subresonance lines of equal order, on symmetry relations and on the one-dimensional case. An example is also given where the theory is overstressed and its predictions become wrong.
Directory of Open Access Journals (Sweden)
Ingrid Almeida Miranda
Full Text Available BACKGROUND: Pulmonary complications are the most common cause of death and morbidity in systemic sclerosis (SSc. The forced oscillation technique (FOT offers a simple and detailed approach to investigate the mechanical properties of the respiratory system. We hypothesized that SSc may introduce changes in the resistive and reactive properties of the respiratory system, and that FOT may help the diagnosis of these abnormalities. METHODOLOGY/PRINCIPAL FINDINGS: We tested these hypotheses in controls (n = 30 and patients with abnormalities classified using spirometry (n = 52 and pulmonary volumes (n = 29. Resistive data were interpreted with the zero-intercept resistance (Ri and the slope of the resistance (S as a function of frequency. Reactance changes were evaluated by the mean reactance between 4 and 32 Hz (Xm and the dynamic compliance (Crs,dyn. The mechanical load was evaluated using the absolute value of the impedance in 4 Hz (Z4Hz. A compartmental model was used to obtain central (R and peripheral (Rp resistances, and alveolar compliance (C. The clinical usefulness was evaluated by investigating the area under the receiver operating characteristic curve (AUC. The presence of expiratory flow limitation (EFL was also evaluated. For the groups classified using spirometry, SSc resulted in increased values in Ri, R, Rp and Z4Hz (p0.90. In groups classified by pulmonary volume, SSc resulted in reductions in S, Xm, C and Crs,dyn (p0.80. It was also observed that EFL is not common in patients with SSc. CONCLUSIONS/SIGNIFICANCE: This study provides evidence that the respiratory resistance and reactance are changed in SSc. This analysis provides a useful description that is of particular significance for understanding respiratory pathophysiology and to ease the diagnosis of respiratory abnormalities in these patients.
Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint
Bullock, S. J.; Peterson, L. D.
1994-01-01
The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.
Resolving the mystery of milliwatt-threshold opto-mechanical self-oscillation in dual-nanoweb fiber
Directory of Open Access Journals (Sweden)
J. R. Koehler
2016-08-01
Full Text Available It is interesting to pose the question: How best to design an optomechanical device, with no electronics, optical cavity, or laser gain, that will self-oscillate when pumped in a single pass with only a few mW of single-frequency laser power? One might begin with a mechanically resonant and highly compliant system offering very high optomechanical gain. Such a system, when pumped by single-frequency light, might self-oscillate at its resonant frequency. It is well-known, however, that this will occur only if the group velocity dispersion of the light is high enough so that phonons causing pump-to-Stokes conversion are sufficiently dissimilar to those causing pump-to-anti-Stokes conversion. Recently it was reported that two light-guiding membranes 20 μm wide, ∼500 nm thick and spaced by ∼500 nm, suspended inside a glass fiber capillary, oscillated spontaneously at its mechanical resonant frequency (∼6 MHz when pumped with only a few mW of single-frequency light. This was surprising, since perfect Raman gain suppression would be expected. In detailed measurements, using an interferometric side-probing technique capable of resolving nanoweb movements as small as 10 pm, we map out the vibrations along the fiber and show that stimulated intermodal scattering to a higher-order optical mode frustrates gain suppression, permitting the structure to self-oscillate. A detailed theoretical analysis confirms this picture. This novel mechanism makes possible the design of single-pass optomechanical oscillators that require only a few mW of optical power, no electronics nor any optical resonator. The design could also be implemented in silicon or any other suitable material.
International Nuclear Information System (INIS)
Kobayashi, Akira; Ohnishi, Yuzo
1986-01-01
The nonlinearity of material properties used in the coupled mechanical-hydraulic-thermal analysis is investigated from the past literatures. Some nonlinearity that is respectively effective for the system is introduced into our computer code for analysis such a coupling problem by using finite element method. And the effects of nonlinearity of each material property on the coupled behavior in rock mass are examined for simple model and Stripa project model with the computer code. (author)
Chen, Chun-Wei; Khoo, Iam Choon; Zhao, Shuo; Lin, Tsung-Hsien; Ho, Tsung-Jui
2015-10-01
We have investigated the mechanisms responsible for nonlinear optical processes occurring in azobenzene-doped blue phase liquid crystals (BPLC), which exhibit two thermodynamically stable BPs: BPI and BPII. In coherent two wave-mixing experiments, a slow (minutes) and a fast (few milliseconds) side diffractions are observed. The underlying mechanisms were disclosed by monitoring the dynamics of grating formation and relaxation as well as by some supplementary experiments. We found the photothermal indexing and dye/LC intermolecular torque leading to lattice distortion to be the dominant mechanisms for the observed nonlinear response in BPLC. Moreover, the response time of the nonlinear optical process varied with operating phase. The rise time of the thermal indexing process was in good agreement with our findings on the temperature dependence of BP refractive index: τ(ISO) > τ(BPI) > τ(BPII). The relaxation time of the torque-induced lattice distortion was analogue to its electrostriction counterpart: τ'(BPI) > τ'(BPII). In a separate experiment, lattice swelling with selective reflection of direction changed from green to red was also observed. This was attributable to the isomerization-induced change in cholesteric pitch, which directly affects the lattice spacing. The phenomenon was confirmed by measuring the optical rotatory power of the BPLC.
On the New Scenario of Annihilation of the Cross-Well Chaotic Attractor in a Nonlinear Oscillator
International Nuclear Information System (INIS)
Szemplinska, W.; Zubrzycki, A.; Tyrkiel, E.
1999-01-01
The twin-well potential Duffing oscillator is considered and the investigations are focused on a new scenario of destruction of the cross-well chaotic attractor. The new phenomenon belongs to the category of subduction bifurcation and consists in replacement of the cross-well chaotic attractor by a pair of unsymmetric 2T-periodic attractors. It is shown that the new scenario forms a transition zone in the system control parameter plane, the zone, which separates the two known scenarios of annihilation of the cross-well chaotic attractor: the boundary crisis, and the subduction in which the two single-well T-periodic attractors are born in a saddle-node bifurcation. (author)
Interactions between neural networks: a mechanism for tuning chaos and oscillations.
Wang, Lipo
2007-06-01
We show that chaos and oscillations in a higher-order binary neural network can be tuned effectively using interactions between neural networks. Our results suggest that network interactions may be useful as a means of adjusting the level of dynamic activities in systems that employ chaos and oscillations for information processing, or as a means of suppressing oscillatory behaviors in systems that require stability.
Avdyushev, Victor A.
2017-12-01
Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the
Haimovich, Ory; Oron, Alexander
2013-05-01
The nonlinear dynamics of a thin axisymmetric liquid film on a horizontal cylindrical substrate subjected to an axial double-frequency forcing that consists of two components of different amplitudes and frequencies and a possible phase shift is considered in this paper. A nonlinear evolution equation governing the spatiotemporal dynamics of the film interface has been derived in the long-wave limit. Similar to the case of a single-frequency forcing considered in our earlier work, there exists a critical forcing amplitude below which the film undergoes a long-time capillary rupture typical for a static cylinder, whereas above it the film remains continuous. We find that it is possible to arrest the rupture even if the forcing parameters of each of the two components correspond separately to the domain where rupture takes place. It is shown that the critical forcing amplitude is easily determined via a single-frequency case when the two forcing frequencies are equal. In the case of different forcing amplitudes and frequencies, the variation of the critical forcing amplitude as a function of the frequency ratio exhibits a unique behavior displaying the emergence of spikes. A related case of an amplitude-modulated single-frequency forcing is also addressed here. For a sufficiently small frequency of the amplitude modulation, a significant increase of the pattern amplitude is observed. In the case of commensurate forcing frequencies, the flow is found to be quasiperiodic.
Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?
Gadelha, H.
2010-05-12
Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.
Nonlinear finite element analysis of the plantar fascia due to the windlass mechanism.
Cheng, Hsin-Yi Kathy; Lin, Chun-Li; Chou, Shih-Wei; Wang, Hsien-Wen
2008-08-01
Tightening of plantar fascia by passively dorsiflexing the toes during walking has functional importance. The purpose of this research was to evaluate the influence of big toe dorsiflexion angles upon plantar fascia tension (the windlass effect) with a nonlinear finite element approach. A two-dimensional finite element model of the first ray was constructed for biomechanical analysis. In order to imitate the windlass effect and to evaluate the mechanical responses of the plantar fascia under various conditions, 12 model simulations--three dorsiflexion angles of the big toe (45 degrees, 30 degrees, and 15 degrees), two plantar fascia properties (linear, nonlinear), and two weightbearing conditions (with body weight, without body weight)--were designed and analyzed. Our results demonstrated that nonlinear modeling of the plantar fascia provides a more sophisticated representation of experimental data than the linear one. Nonlinear plantar fascia setting also predicted a higher stress distribution along the fiber directions especially with larger toe dorsiflexion angles (45 degrees>30 degrees>15 degrees). The plantar fascia stress was found higher near the metatarsal insertion and faded as it moved toward the calcaneal insertion. Passively dorsiflexing the big toe imposes tension onto the plantar fascia. Windlass mechanism also occurs during stance phase of walking while the toes begin to dorsiflex. From a biomechanical standpoint, the plantar fascia tension may help propel the body upon its release at the point of push off. A controlled stretch via dorsiflexing the big toe may have a positive effect on treating plantar fasciitis by providing proper guidance for collagen regeneration. The windlass mechanism is also active during the stance phase of walking when the toes begin to dorsiflex.
Jones, M.; Emmert, J. T.; Drob, D. P.; Picone, J. M.; Meier, R. R.
2018-01-01
We demonstrate how Earth's obliquity generates the global thermosphere-ionosphere (T-I) semiannual oscillation (SAO) in mass density and electron density primarily through seasonally varying large-scale advection of neutral thermospheric constituents, sometimes referred to as the "thermospheric spoon" mechanism (TSM). The National Center for Atmospheric Research thermosphere-ionosphere-mesosphere-electrodynamics general circulation model (TIME-GCM) is used to isolate the TSM forcing of this prominent intraannual variation (IAV) and to elucidate the contributions of other processes to the T-I SAO. An ˜30% SAO in globally averaged mass density (relative to its global annual average) at 400 km is reproduced in the TIME-GCM in the absence of seasonally varying eddy diffusion, tropospheric tidal forcing, and gravity wave breaking. Artificially, decreasing the tilt of Earth's rotation axis with respect to the ecliptic plane to 11.75° reduces seasonal variations in insolation and weakens interhemispheric pressure differences at the solstices, thereby damping the global-scale, interhemispheric transport of atomic oxygen (O) and molecular nitrogen in the thermosphere and reducing the simulated global mass density SAO amplitude to ˜10%. Simulated T-I IAVs in mass density and electron density have equinoctial maxima at all latitudes near the F2 region peak; this phasing and its latitude dependence agree well with empirically inferred climatologies. When tropospheric tides and gravity waves are included, simulated IAV amplitudes and their latitudinal dependence also agree well with empirically inferred climatologies. Simulated meridional and vertical transport of O due to the TSM couples to the upper mesospheric circulation, which also contributes to the T-I SAO through O chemistry.
Huang, Xian-Rong; Peng, Ru-Wen
2010-04-01
Interactions between light and conducting microstructures or nanostructures can result in a variety of novel phenomena, but their underlying mechanisms have not been completely understood. From calculations of surface charge density waves on conducting gratings and by comparing them with classical surface plasmons, we revealed a general yet concrete picture regarding the coupling of light to free electron oscillation on structured conducting surfaces that can lead to oscillating subwavelength charge patterns (i.e., structured surface plasmons). New wavelets emitted from these light sources then destructively interfere to form evanescent waves. This principle, usually combined with other mechanisms, is mainly a geometrical effect that can be universally involved in light scattering from all periodic and non-periodic structures containing free electrons. This picture may provide clear guidelines for developing conductor-based nano-optical devices.
Mode competition and hopping in optomechanical nano-oscillators
Zhang, Xingwang; Lin, Tong; Tian, Feng; Du, Han; Zou, Yongchao; Chau, Fook Siong; Zhou, Guangya
2018-04-01
We investigate the inter-mode nonlinear interaction in the multi-mode optomechanical nano-oscillator which consists of coupled silicon nanocantilevers, where the integrated photonic crystal nanocavities provide the coupling between the optical and mechanical modes. Due to the self-saturation and cross-saturation of the mechanical gain, the inter-mode competition is observed, which leads to the bistable operation of the optomechanical nano-oscillator: only one of the mechanical modes can oscillate at any one time, and the oscillation of one mode extremely suppresses that of the other with a side mode suppression ratio (SMSR) up to 40 dB. In the meantime, mode hopping, i.e., the optomechanical oscillation switches from one mode to the other, is also observed and found to be able to be provoked by excitation laser fluctuations.
Vaughan, O. H., Jr.; Hung, R. J.
1975-01-01
Skylab 4 crew members performed a series of demonstrations showing the oscillations, rotations, as well as collision coalescence of water droplets which simulate various physical models of fluids under low gravity environment. The results from Skylab demonstrations provide information and illustrate the potential of an orbiting space-oriented research laboratory for the study of more sophisticated fluid mechanic experiments. Experiments and results are discussed.
Chen, Shu-Peng; He, Ling-Yun
2010-04-01
Based on Partition Function and Multifractal Spectrum Analysis, we investigated the nonlinear dynamical mechanisms in China’s agricultural futures markets, namely, Dalian Commodity Exchange (DCE for short) and Zhengzhou Commodity Exchange (ZCE for short), where nearly all agricultural futures contracts are traded in the two markets. Firstly, we found nontrivial multifractal spectra, which are the empirical evidence of the existence of multifractal features, in 4 representative futures markets in China, that is, Hard Winter wheat (HW for short) and Strong Gluten wheat (SG for short) futures markets from ZCE and Soy Meal (SM for short) futures and Soy Bean No.1 (SB for short) futures markets from DCE. Secondly, by shuffling the original time series, we destroyed the underlying nonlinear temporal correlation; thus, we identified that long-range correlation mechanism constitutes major contributions in the formation in the multifractals of the markets. Thirdly, by tracking the evolution of left- and right-half spectra, we found that there exist critical points, between which there are different behaviors, in the left-half spectra for large price fluctuations; but for the right-hand spectra for small price fluctuations, the width of those increases slowly as the delay t increases in the long run. Finally, the dynamics of large fluctuations is significantly different from that of the small ones, which implies that there exist different underlying mechanisms in the formation of multifractality in the markets. Our main contributions focus on that we not only provided empirical evidence of the existence of multifractal features in China agricultural commodity futures markets; but also we pioneered in investigating the sources of the multifractality in China’s agricultural futures markets in current literature; furthermore, we investigated the nonlinear dynamical mechanisms based on spectrum analysis, which offers us insights into the underlying dynamical mechanisms in
On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere
Directory of Open Access Journals (Sweden)
I. P. Chunchuzov
2009-11-01
Full Text Available The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.
Mechanical nonlinearity elimination with a micromechanical clamped-free semicircular beams resonator
Chen, Dongyang; Chen, Xuying; Wang, Yong; Liu, Xinxin; Guan, Yangyang; Xie, Jin
2018-04-01
This paper reports a micro-machined clamped-free semicircular beam resonator aiming to eliminate the nonlinearity that widely exists in traditional mechanical resonators. Cubic coefficients over vibration displacement due to axial extension of the beams are analyzed through theoretical modelling, and the corresponding frequency effect is demonstrated. With the device working in the elastic vibration mode, the cubic coefficients are eliminated by using a free end to release the nonlinear extension of beams and thus the inside axial stress. The amplitude-frequency (A-f) effect is overcome in a large region of source power, and the coefficient of frequency softening is linearized in a large region of polarization voltage. As a result, the resonator can be driven at larger vibration amplitude to achieve a high signal to noise ratio and power handling performance.
Development of Nonlinear Flight Mechanical Model of High Aspect Ratio Light Utility Aircraft
Bahri, S.; Sasongko, R. A.
2018-04-01
The implementation of Flight Control Law (FCL) for Aircraft Electronic Flight Control System (EFCS) aims to reduce pilot workload, while can also enhance the control performance during missions that require long endurance flight and high accuracy maneuver. In the development of FCL, a quantitative representation of the aircraft dynamics is needed for describing the aircraft dynamics characteristic and for becoming the basis of the FCL design. Hence, a 6 Degree of Freedom nonlinear model of a light utility aircraft dynamics, also called the nonlinear Flight Mechanical Model (FMM), is constructed. This paper shows the construction of FMM from mathematical formulation, the architecture design of FMM, the trimming process and simulations. The verification of FMM is done by analysis of aircraft behaviour in selected trimmed conditions.
Eleiwi, Fadi
2015-07-01
This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
Rudra, Shubhobrata; Maitra, Madhubanti
2017-01-01
This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The math...
Modeling of Nonlinear Mechanical Response in CFRP Angle-Ply Laminates
Ogihara, Shinji
2014-03-01
It is known that the failure process in angle-ply laminate involves matrix cracking and delamination and that they exhibit nonlinear stress-strain relation. There may be a significant effect of the constituent blocked ply thickness on the mechanical behavior of angle-ply laminates. These days, thin prepregs whose thickness is, for example 50 micron, are developed and commercially available. Therefore, we can design wide variety of laminates with various constituent ply thicknesses. In this study, effects of constituent ply thickness on the nonlinear mechanical behavior and the damage behavior of CFRP angle-ply laminates are investigated experimentally. Based on the experimental results, the mechanical response in CFRP angle-ply laminates is modeled by using the finite strain viscoplasticity model. We evaluated the mechanical behavior and damage behavior in CFRP angle-ply laminates with different constituent ply thickness under tensile loading experimentally. It was found that as the constituent ply thickness decreases, the strength and failure strain increases. We also observed difference in damage behavior. The preliminary results of finite strain viscoplasticity model considering the damage effect for laminated composites are shown. A qualitative agreement is obtained.
Grace Chao, Pen-hsiu; Hsu, Hsiang-Yi; Tseng, Hsiao-Yun
2014-09-01
Fiber structure and order greatly impact the mechanical behavior of fibrous materials. In biological tissues, the nonlinear mechanics of fibrous scaffolds contribute to the functionality of the material. The nonlinear mechanical properties of the wavy structure (crimp) in collagen allow tissue flexibility while preventing over-extension. A number of approaches have tried to recreate this complex mechanical functionality. We generated microcrimped fibers by briefly heating electrospun parallel fibers over the glass transition temperature or by ethanol treatment. The crimp structure is similar to those of collagen fibers found in native aorta, intestines, or ligaments. Using poly-L-lactic acid fibers, we demonstrated that the bulk materials exhibit changed stress-strain behaviors with a significant increase in the toe region in correlation to the degree of crimp, similar to those observed in collagenous tissues. In addition to mimicking the stress-strain behavior of biological tissues, the microcrimped fibers are instructive in cell morphology and promote ligament phenotypic gene expression. This effect can be further enhanced by dynamic tensile loading, a physiological perturbation in vivo. This rapid and economical approach for microcrimped fiber production provides an accessible platform to study structure-function relationships and a novel functional scaffold for tissue engineering and cell mechanobiology studies.
International Nuclear Information System (INIS)
Grace Chao, Pen-hsiu; Hsu, Hsiang-Yi; Tseng, Hsiao-Yun
2014-01-01
Fiber structure and order greatly impact the mechanical behavior of fibrous materials. In biological tissues, the nonlinear mechanics of fibrous scaffolds contribute to the functionality of the material. The nonlinear mechanical properties of the wavy structure (crimp) in collagen allow tissue flexibility while preventing over-extension. A number of approaches have tried to recreate this complex mechanical functionality. We generated microcrimped fibers by briefly heating electrospun parallel fibers over the glass transition temperature or by ethanol treatment. The crimp structure is similar to those of collagen fibers found in native aorta, intestines, or ligaments. Using poly-L-lactic acid fibers, we demonstrated that the bulk materials exhibit changed stress–strain behaviors with a significant increase in the toe region in correlation to the degree of crimp, similar to those observed in collagenous tissues. In addition to mimicking the stress–strain behavior of biological tissues, the microcrimped fibers are instructive in cell morphology and promote ligament phenotypic gene expression. This effect can be further enhanced by dynamic tensile loading, a physiological perturbation in vivo. This rapid and economical approach for microcrimped fiber production provides an accessible platform to study structure–function relationships and a novel functional scaffold for tissue engineering and cell mechanobiology studies. (papers)
Directory of Open Access Journals (Sweden)
Wenwen Sui
Full Text Available Abstract Nonlinear dynamic analysis of an axially moving telescopic mechanism for truss structure bridge inspection vehicle under pedestrian excitation is carried out. A biomechanically inspired inverted-pendulum model is utilized to simplify the pedestrian. The nonlinear equations of motion for the beam-pedestrian system are derived using the Hamilton's principle. The equations are transformed into two ordinary differential equations by applying the Galerkin's method at the first two orders. The solutions to the equations are acquired by using the Newmark-β method associated with the Newton-Raphson method. The time-dependent feature of the eigenfunctions for the two beams are taken into consideration in the solutions. Accordingly, the equations of motion for a simplified system, in which the pedestrian is regarded as moving cart, are given. In the numerical examples, dynamic responses of the telescopic mechanism in eight conditions of different beam-telescoping and pedestrian-moving directions are simulated. Comparisons between the vibrations of the beams under pedestrian excitation and corresponding moving cart are carried out to investigate the influence of the pedestrian excitation on the telescopic mechanism. The results show that the displacement of the telescopic mechanism under pedestrian excitation is smaller than that under moving cart especially when the pedestrian approaches the beams end. Additionally, compared with moving cart, the pedestrian excitation can effectively strengthen the vibration when the beam extension is small or when the pedestrian is close to the beams end.
Nonlinear Entanglement and its Application to Generating Cat States
Shen, Y.; Assad, S. M.; Grosse, N. B.; Li, X. Y.; Reid, M. D.; Lam, P. K.
2015-03-01
The Einstein-Podolsky-Rosen (EPR) paradox, which was formulated to argue for the incompleteness of quantum mechanics, has since metamorphosed into a resource for quantum information. The EPR entanglement describes the strength of linear correlations between two objects in terms of a pair of conjugate observables in relation to the Heisenberg uncertainty limit. We propose that entanglement can be extended to include nonlinear correlations. We examine two driven harmonic oscillators that are coupled via third-order nonlinearity can exhibit quadraticlike nonlinear entanglement which, after a projective measurement on one of the oscillators, collapses the other into a cat state of tunable size.
Directory of Open Access Journals (Sweden)
Bin Guo
2016-03-01
Full Text Available Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960–2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD. Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years and inter-decadal scale (quasi-12 and quasi-23 years. Moreover, the 2–3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements.
Guo, Bin; Chen, Zhongsheng; Guo, Jinyun; Liu, Feng; Chen, Chuanfa; Liu, Kangli
2016-03-21
Changes in precipitation could have crucial influences on the regional water resources in arid regions such as Xinjiang. It is necessary to understand the intrinsic multi-scale variations of precipitation in different parts of Xinjiang in the context of climate change. In this study, based on precipitation data from 53 meteorological stations in Xinjiang during 1960-2012, we investigated the intrinsic multi-scale characteristics of precipitation variability using an adaptive method named ensemble empirical mode decomposition (EEMD). Obvious non-linear upward trends in precipitation were found in the north, south, east and the entire Xinjiang. Changes in precipitation in Xinjiang exhibited significant inter-annual scale (quasi-2 and quasi-6 years) and inter-decadal scale (quasi-12 and quasi-23 years). Moreover, the 2-3-year quasi-periodic fluctuation was dominant in regional precipitation and the inter-annual variation had a considerable effect on the regional-scale precipitation variation in Xinjiang. We also found that there were distinctive spatial differences in variation trends and turning points of precipitation in Xinjiang. The results of this study indicated that compared to traditional decomposition methods, the EEMD method, without using any a priori determined basis functions, could effectively extract the reliable multi-scale fluctuations and reveal the intrinsic oscillation properties of climate elements.
Response to a pure tone in a nonlinear mechanical-electrical-acoustical model of the cochlea.
Meaud, Julien; Grosh, Karl
2012-03-21
In this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Boure, J [Commissariat a l' Energie Atomique, Centre d' Etudes Nucleaires de Grenoble, 38 (France)
1967-07-01
The problem of the oscillatory behavior of heated channels is presented in terms of delay-times and a density effect model is proposed to explain the behavior. The density effect is the consequence of the physical relationship between enthalpy and density of the fluid. In the first part non-linear equations are derived from the model in a dimensionless form. A description of the mechanism of oscillations is given, based on the analysis of the equations. An inventory of the governing parameters is established. At this point of the study, some facts in agreement with the experiments can be pointed out. In the second part the start of the oscillatory behavior of heated channels is studied in terms of the density effect. The threshold equations are derived, after linearization of the equations obtained in Part I. They can be solved rigorously by numerical methods to yield: -1) a relation between the describing parameters at the onset of oscillations, and -2) the frequency of the oscillations. By comparing the results predicted by the model to the experimental behavior of actual systems, the density effect is very often shown to be the actual cause of oscillatory behaviors. (author) [French] Premiere partie: mecanisme (equations non linearisees). On expose le probleme du comportement oscillatoire des canaux chauffes en mettant l'accent sur la presence de retards dans le systeme et on propose un modele a 'effet de densite' pour expliquer ce comportement. L'effet de densite est la consequence de la relation physique entre l'enthalpie et la masse volumique du fluide. Les equations non lineaires du schema mathematique correspondant sont etablies et mises sous forme adimensionnelle. L'analyse de ces equations conduit a une description du mecanisme des oscillations. On donne la liste des parametres dont depend le comportement du modele. A ce stade de l'etude, on peut deja relever dans ce comportement plusieurs faits conformes a l'experience. Deuxieme partie: seuils d'oscillation
Vorotnikov, K.; Starosvetsky, Y.
2018-01-01
The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.
Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics
International Nuclear Information System (INIS)
Czachor, M.
1996-01-01
Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)
The use of the J* integral for non-linear fracture mechanics
International Nuclear Information System (INIS)
Hellen, T.K.
1976-09-01
The Griffith energy balance criterion, first postulated over 50 years ago, is still the basis of linear elastic fracture mechanics. From this, accurate numerical methods for establishing stress intensity factors and energy release rates have been developed. One such method involves path independent contour integrals about the crack tip. An improved contour integral, designated J* is discussed, and shown to have distinct advantages over others in non-linear strain situations. A number of examples are shown including fractures in thermo-plastic and creep situations. (author)
Fault Diagnosis for Nonlinear Hydraulic-Mechanical Drilling Pipe Handling System
DEFF Research Database (Denmark)
Choux, Martin; Blanke, Mogens
2011-01-01
Leakage and increased friction are common faults in hydraulic cylinders that can have serious consequences if they are not detected at early stage. In this paper, the design of a fault detector for a nonlinear hydraulic mechanical system is presented. By considering the system in steady state, two...... residual signals are generated and analysed with a composite hypothesis test which accommodates for unknown parameters. The resulting detector is able to detect abrupt changes in leakage or friction given the noisy pressure and position measurements. Test rig measurements validate the properties...
Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies
Sozio, Fabio; Yavari, Arash
2017-01-01
In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.
Measurement and control of a mechanical oscillator at its thermal decoherence rate
Wilson, D. J.; Sudhir, V.; Piro, N.; Schilling, R.; Ghadimi, A.; Kippenberg, T. J.
2014-01-01
In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen highly successful applications in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. By contrast, the ability to stabilize the quantum state of a tangibly massive object, such as a nanomechanical oscillator, remains a difficult challenge: The main obstacle is environmental decoherence, which places s...
Czech Academy of Sciences Publication Activity Database
Jiruška, Přemysl; Alvarado-Rojas, C.; Schevon, C.A.; Staba, R.; Stacey, W.; Wendling, F.; Avoli, M.
2017-01-01
Roč. 58, č. 8 (2017), s. 1330-1339 ISSN 0013-9580 R&D Projects: GA MZd(CZ) NV15-29835A; GA ČR(CZ) GA14-02634S Institutional support: RVO:67985823 Keywords : high-frequency oscillations * epilepsy * ripples * fast ripples * ictogenesis * epileptogenesis * seizures * interneurons * computer models Subject RIV: FH - Neurology OBOR OECD: Neurosciences (including psychophysiology Impact factor: 5.295, year: 2016