WorldWideScience

Sample records for nonlinear electron oscillations

  1. 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

  2. Nonlinear oscillations

    CERN Document Server

    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

  3. Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

    Science.gov (United States)

    Osherovich, V. A.; Fainberg, J.

    2018-01-01

    We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

  4. Phase mixing of transverse oscillations in the linear and nonlinear regimes for IFR relativistic electron beam propagation

    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

  5. 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.)

  6. Modeling nonlinearities in MEMS oscillators.

    Science.gov (United States)

    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.

  7. 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.

  8. Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits

    KAUST Repository

    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.

  9. Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits

    KAUST Repository

    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.

  10. Nonlinearity induced synchronization enhancement in mechanical oscillators

    Science.gov (United States)

    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.

  11. 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.

  12. Self-excited nonlinear plasma series resonance oscillations in geometrically symmetric capacitively coupled radio frequency discharges

    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

  13. Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

    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.

  14. 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.

  15. 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....

  16. 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.

  17. 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

  18. 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.

  19. Coupled nonlinear oscillators

    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.

  20. 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)

  1. Relaxation oscillations induced by amplitude-dependent frequency in dissipative trapped electron mode turbulence

    International Nuclear Information System (INIS)

    Terry, P.W.; Ware, A.S.; Newman, D.E.

    1994-01-01

    A nonlinear frequency shift in dissipative trapped electron mode turbulence is shown to give rise to a relaxation oscillation in the saturated power density spectrum. A simple non-Markovian closure for the coupled evolution of ion momentum and electron density response is developed to describe the oscillations. From solutions of a nonlinear oscillator model based on the closure, it is found that the oscillation is driven by the growth rate, as modified by the amplitude-dependent frequency shift, with inertia provided by the memory of the growth rate of prior amplitudes. This memory arises from time-history integrals common to statistical closures. The memory associated with a finite time of energy transfer between coupled spectrum components does not sustain the oscillation in the simple model. Solutions of the model agree qualitatively with the time-dependent numerical solutions of the original dissipative trapped electron model, yielding oscillations with the proper phase relationship between the fluctuation energy and the frequency shift, the proper evolution of the wave number spectrum shape and particle flux, and a realistic period

  2. 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.

  3. 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...

  4. Nonlinear analysis of ring oscillator circuits

    KAUST Repository

    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.

  5. Nonlinear analysis of ring oscillator circuits

    KAUST Repository

    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.

  6. On the nonlinear modeling of ring oscillators

    KAUST Repository

    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.

  7. On the nonlinear modeling of ring oscillators

    KAUST Repository

    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.

  8. 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

  9. Oscillations in nonlinear systems

    CERN Document Server

    Hale, Jack K

    2015-01-01

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

  10. Aeroelastic Limit-Cycle Oscillations resulting from Aerodynamic Non-Linearities

    NARCIS (Netherlands)

    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

  11. Applied nonlinear optics in the journal 'Quantum Electronics'

    International Nuclear Information System (INIS)

    Grechin, Sergei G; Dmitriev, Valentin G; Chirkin, Anatolii S

    2011-01-01

    A brief historical review of the experimental and theoretical works on nonlinear optical frequency conversion (generation of harmonics, up- and down-conversion, parametric oscillation), which have been published in the journal 'Quantum Electronics' for the last 40 years, is presented.

  12. 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.

  13. 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...

  14. Analytical solution of strongly nonlinear Duffing oscillators

    OpenAIRE

    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...

  15. 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 ...

  16. 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 ...

  17. Oscillators from nonlinear realizations

    Science.gov (United States)

    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.

  18. 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)

  19. Deep saturated Free Electron Laser oscillators and frozen spikes

    Energy Technology Data Exchange (ETDEWEB)

    Ottaviani, P.L. [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Pagnutti, S., E-mail: simonetta.pagnutti@enea.it [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Dattoli, G., E-mail: giuseppe.dattoli@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Sabia, E., E-mail: elio.sabia@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Petrillo, V., E-mail: vittoria.petrillo@mi.infn.it [Universita' degli Studi di Milano, via Celoria 16, IT 20133, Milano (Italy); INFN - Mi, via Celoria 16, IT 20133, Milano (Italy); Slot, P.J.M. van der, E-mail: p.j.m.vanderslot@utwente.nl [Mesa+ Institute for Nanotechnology, University of Twente, P.O.Box 217, 7500 AE, Enschede (Netherlands); Biedron, S., E-mail: sandra.biedron@colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States); Milton, S., E-mail: milton@engr.colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States)

    2016-10-21

    We analyze the behavior of Free Electron Laser (FEL) oscillators operating in the deep saturated regime and point out the formation of sub-peaks of the optical pulse. These are very stable configurations and the sub-peaks are found to have a duration corresponding to the coherence length. We speculate on the physical mechanisms underlying their growth and attempt an identification with natural mode-locked structures in FEL oscillators. Their impact on the intra-cavity nonlinear harmonic generation is also discussed along with the possibility of exploiting them as cavity out-coupler.

  20. Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

    Science.gov (United States)

    Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

    2017-01-01

    Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

  1. 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

  2. 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 ...

  3. 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.

  4. 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

  5. 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)

  6. Runaway relativistic electron scattering on the plazma oscillations in tokamak

    International Nuclear Information System (INIS)

    Krasovitskij, V.B.; Razdorski, V.G.

    1980-01-01

    The dynamics of fast electrons in a tolamak plasma with the presence of the constant external electric field have been inveatigated. It is shown that the occurrence of the relativistic electrons ''tail'' of the distribution function is followed by an intensive plasma oscillation swinging under conditions of the anomalous Doppler effect and their large angle scattering in the momentum space. A part of scattered electrons is captured by tokamak inhomogeneous magnetic field and causes the occurrence of a new low frequency alfven instability under conditions of magnetic drift resonance followed by quasilinear diffusion of relativistic electrons along the small radius of the torus. The flux of runaway electrons scattered on plasma oscillations has been found. A nonlinear diffusion equation has been derived for the flux of captured electrons. The equation defines the carrying out of fast particles from the plasma filament center to its periphery depending on the external magnetic field and plasma parameters

  7. 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.

  8. Flavor Oscillations in the Supernova Hot Bubble Region: Nonlinear Effects of Neutrino Background

    Science.gov (United States)

    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.

  9. 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...

  10. Nonlinear transport behavior of low dimensional electron systems

    Science.gov (United States)

    Zhang, Jingqiao

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

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

    International Nuclear Information System (INIS)

    Oberman, C.

    1972-01-01

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

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÖDINGER

    Directory of Open Access Journals (Sweden)

    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 Schrödinger 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 can’t be normalized.   Keywords : harmonic oscillator, nonlinear Schrödinger.

  17. 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.

  18. 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.

  19. 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.

  20. Multisynchronization of chaotic oscillators via nonlinear observer approach.

    Science.gov (United States)

    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.

  1. 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.

  2. Numerical study of chaotic oscillations in the electron beam with virtual cathode in the external non-uniform magnetic fields

    Energy Technology Data Exchange (ETDEWEB)

    Hramov, Alexander E., E-mail: aeh@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Koronovskii, Alexey A., E-mail: alkor@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation); Kurkin, Semen, E-mail: KurkinSA@nonlin.sgu.r [Faculty of Nonlinear Processes, Saratov State University, 83, Astrakhanskaya, Saratov, 410012 (Russian Federation)

    2010-07-05

    In this Letter the results of theoretical investigations of the chaotic microwave oscillator based on the electron beam with a virtual cathode are presented. Nonlinear non-stationary processes in these electron systems are studied by means of numerical analysis of 2.5D model. It was discovered that the non-uniform external magnetic field value controls the dynamical regime of oscillations in the virtual cathode oscillator. The processes of the chaotization of output microwave radiation are described and interpreted from the point of view of the formation and interaction of electron structures (bunches) in the electron beams. The numerical results have shown that the investigated electron system with virtual cathode could be considered as a promising controlled source of wideband chaotic oscillations in the microwave range.

  3. A Static and Dynamic Investigation of Quantum Nonlinear Transport in Highly Dense and Mobile 2D Electron Systems

    Science.gov (United States)

    Dietrich, Scott

    Heterostructures made of semiconductor materials may be one of most versatile environments for the study of the physics of electron transport in two dimensions. These systems are highly customizable and demonstrate a wide range of interesting physical phenomena. In response to both microwave radiation and DC excitations, strongly nonlinear transport that gives rise to non-equilibrium electron states has been reported and investigated. We have studied GaAs quantum wells with a high density of high mobility two-dimensional electrons placed in a quantizing magnetic field. This study presents the observation of several nonlinear transport mechanisms produced by the quantum nature of these materials. The quantum scattering rate, 1tau/q, is an important parameter in these systems, defining the width of the quantized energy levels. Traditional methods of extracting 1tau/q involve studying the amplitude of Shubnikov-de Haas oscillations. We analyze the quantum positive magnetoresistance due to the cyclotron motion of electrons in a magnetic field. This method gives 1tau/q and has the additional benefit of providing access to the strength of electron-electron interactions, which is not possible by conventional techniques. The temperature dependence of the quantum scattering rate is found to be proportional to the square of the temperature and is in very good agreement with theory that considers electron-electron interactions in 2D systems. In quantum wells with a small scattering rate - which corresponds to well-defined Landau levels - quantum oscillations of nonlinear resistance that are independent of magnetic field strength have been observed. These oscillations are periodic in applied bias current and are connected to quantum oscillations of resistance at zero bias: either Shubnikov-de Haas oscillations for single subband systems or magnetointersubband oscillations for two subband systems. The bias-induced oscillations can be explained by a spatial variation of electron

  4. 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

  5. Spin–orbit coupling induced magnetoresistance oscillation in a dc biased two-dimensional electron system

    International Nuclear Information System (INIS)

    Wang, C M; Lei, X L

    2014-01-01

    We study dc-current effects on the magnetoresistance oscillation in a two-dimensional electron gas with Rashba spin-orbit coupling, using the balance-equation approach to nonlinear magnetotransport. In the weak current limit the magnetoresistance exhibits periodical Shubnikov-de Haas oscillation with changing Rashba coupling strength for a fixed magnetic field. At finite dc bias, the period of the oscillation halves when the interbranch contribution to resistivity dominates. With further increasing current density, the oscillatory resistivity exhibits phase inversion, i.e., magnetoresistivity minima (maxima) invert to maxima (minima) at certain values of the dc bias, which is due to the current-induced magnetoresistance oscillation. (paper)

  6. 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.

  7. Downshift of electron plasma oscillations in the electron foreshock region

    International Nuclear Information System (INIS)

    Fuselier, S.A.

    1984-01-01

    Electron plasma oscillations in the Earth's electron foreshock region are observed to shift above and below the local electron plasma frequency. As plasma oscillations shift from the plasma frequency, their bandwidth increases and their wavelength decreases. Observations of plasma oscillations well below the plasma frequency are correlated with times when ISEE-I is far downstream of the electron foreshock boundary. Although wavelengths of plasma oscillations below the plasma frequency satisfy klambda/sub De/ approx. = 1, the Doppler shift due to the motion of the solar wind is not sufficient to produce the observed frequency shifts. A beam-plasma interaction with beam velocities on the order of the electron thermal velocity is suggested as an explanation for plasma oscillations above and below the plasma frequency. Frequency, bandwidth, and wavelength changes predicted from the beam-plasma interaction are in good agreement with the observed characteristics of plasma oscillations in the foreshock region

  8. Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

    Science.gov (United States)

    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.

  9. Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

    Science.gov (United States)

    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.

  10. 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.

  11. Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

    Science.gov (United States)

    Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

    2015-05-21

    In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

  12. Downshift of electron plasma oscillations in the electron foreshock region

    International Nuclear Information System (INIS)

    Fuselier, S.A.; Gurnett, D.A.; Fitzenreiter, R.J.; NASA, Goddard Space Flight Center, Greenbelt, MD)

    1985-01-01

    Electron plasma oscillations in the earth's electron foreshock region are observed to shift above and below the local electron plasma frequency. As plasma oscillations shift downward from the plasma frequency, their bandwidth increases and their wavelength decreases. Observations of plasma oscillations well below the plasma frequency are correlated with times when ISEE 1 is far downstream of the electron foreshock boundary. Although wavelengths of plasma oscillations below the plasma frequency satisfy k x lambda-De approximately 1 the Doppler shift due to the motion of the solar wind is not sufficient to produce the observed frequency shifts. A beam-plasma interaction with beam velocities on the order of the electron thermal velocity is suggested as an explanation for plasma oscillations above and below the plasma frequency. Frequency, bandwidth, and wavelength changes predicted from the beam-plasma interaction are in good agreement with the observed characteristics of plasma oscillations in the foreshock region. 28 references

  13. Third harmonic generation by Bloch-oscillating electrons in a quasioptical array

    International Nuclear Information System (INIS)

    Ghosh, A.W.; Wanke, M.C.; Allen, S.J.; Wilkins, J.W.

    1999-01-01

    We compute the third harmonic field generated by Bloch-oscillating electrons in a quasioptical array of superlattices under THz irradiation. The third harmonic power transmitted oscillates with the internal electric field, with nodes associated with Bessel functions in eEd/ℎω. The nonlinear response of the array causes the output power to be a multivalued function of the incident laser power. The output can be optimized by adjusting the frequency of the incident pulse to match one of the Fabry-Pacute erot resonances in the substrate. Within the transmission-line model of the array, the maximum conversion efficiency is 0.1%. copyright 1999 American Institute of Physics

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

    Science.gov (United States)

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

    2017-06-12

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

  15. 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

  16. Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

    Science.gov (United States)

    Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

    2016-06-01

    This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

  17. Nonlinear wavenumber of an electron plasma wave

    International Nuclear Information System (INIS)

    Vidmar, P.J.; Malmberg, J.H.; Starke, T.P.

    1976-01-01

    The wavenumber of a large-amplitude electron plasma wave propagating on a collisionless plasma column is measured. The wavenumber is shifted from that of a small-amplitude wave of the same frequency. This nonlinear wavenumber shift, deltak/subr/, depends on position, frequency, and initial wave amplitude, Phi. The observed spatial oscillations of deltak/subr/ agree qualitatively with recent theories. Experimentally deltak/subr/proportionalk/subi/S (Phi) rootPhi where k/subi/ is the linear Landau damping coefficient, S (Phi) equivalentk/subi/(Phi)/k/subi/, and k/subi/(Phi) is the initial damping coefficient which depends on Phi

  18. Nonlinear dynamics in micromechanical and nanomechanical resonators and oscillators

    Science.gov (United States)

    Dunn, Tyler

    dynamics in passive resonators, self-sustained MEMS are becoming increasingly prevalent in both research and technology for crucial objectives, such as measurement of time. Despite some effort, much work remains in order to understand phase noise and stability for an oscillator based upon a nonlinear resonator. With the eventual goal of making comprehensive measurements of such a nonlinear oscillator with controlled amplitude and phase, this work describes the realization of a micromechanical phase feedback oscillator.

  19. 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

  20. Sinusoidal oscillators with lower gain requirements at higher frequencies based on an explicit tanh(x) nonlinearity

    KAUST Repository

    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.

  1. 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...

  2. Controlling nonlinear longitudinal space charge oscillations for high peak current bunch train generation

    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.

  3. 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

  4. Quantum electronics maser amplifiers and oscillators

    CERN Document Server

    Fain, V M; Sanders, J H

    2013-01-01

    Quantum Electronics, Volume 2: Maser Amplifiers and Oscillators deals with the experimental and theoretical aspects of maser amplifiers and oscillators which are based on the principles of quantum electronics. It shows how the concepts and equations used in quantum electronics follow from the basic principles of theoretical physics.Comprised of three chapters, this volume begins with a discussion on the elements of the theory of quantum oscillators and amplifiers working in the microwave region, along with the practical achievements in this field. Attention is paid to two-level paramagnetic ma

  5. Quantum Nonlinear Optics

    CERN Document Server

    Hanamura, Eiichi; Yamanaka, Akio

    2007-01-01

    This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

  6. Nonlinear optics in germanium mid-infrared fiber material: Detuning oscillations in femtosecond mid-infrared spectroscopy

    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.

  7. 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.

  8. Complex behavior in chains of nonlinear oscillators.

    Science.gov (United States)

    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.

  9. Sensitivity and Nonlinearity of Thermoacoustic Oscillations

    Science.gov (United States)

    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.

  10. Flutter and limit cycle oscillation suppression using linear and nonlinear tuned vibration absorbers

    OpenAIRE

    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...

  11. Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

    Science.gov (United States)

    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.

  12. 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...

  13. 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

  14. 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...

  15. Nonlinear transient waves in coupled phase oscillators with inertia.

    Science.gov (United States)

    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.

  16. 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.

  17. 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 ...

  18. 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.

  19. Discrete oscillator design linear, nonlinear, transient, and noise domains

    CERN Document Server

    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

  20. The Two-Beam Free Electron Laser Oscillator

    CERN Document Server

    Thompson, Neil R

    2004-01-01

    A one-dimensional model of a free-electron laser operating simultaneously with two electron beams of different energies [1] is extended to an oscillator configuration. The electron beam energies are chosen so that an harmonic of the lower energy beam is at the fundamental radiation wavelength of the higher energy beam. Potential benefits over a single-beam free-electron laser oscillator are discussed.

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

    Science.gov (United States)

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

    2018-01-01

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

  2. Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators

    KAUST Repository

    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.

  3. Electronegative nonlinear oscillating modes in plasmas

    Science.gov (United States)

    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.

  4. Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

    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

  5. Nonlinear dynamics of a magnetically driven Duffing-type spring–magnet oscillator in the static magnetic field of a coil

    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)

  6. 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.

  7. Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

    CERN Document Server

    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. .

  8. 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)

  9. 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.

  10. Discontinuous Spirals of Stable Periodic Oscillations

    DEFF Research Database (Denmark)

    Sack, Achim; Freire, Joana G.; Lindberg, Erik

    2013-01-01

    We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase...

  11. 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.

  12. Oscillation criteria for first-order forced nonlinear difference equations

    OpenAIRE

    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.

  13. Electromagnetic Radiation Originating from Unstable Electron Oscillations

    DEFF Research Database (Denmark)

    Juul Rasmussen, Jens; Pécseli, Hans

    1975-01-01

    Electromagnetic oscillations in the range 300 – 700 MHz were observed from an unmagnetized argon discharge with an unstable electron velocity distribution function.......Electromagnetic oscillations in the range 300 – 700 MHz were observed from an unmagnetized argon discharge with an unstable electron velocity distribution function....

  14. Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.

    Science.gov (United States)

    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.

  15. Two-oscillator model of trapped-modes interaction in a nonlinear bilayer fish-scale metamaterial

    OpenAIRE

    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...

  16. Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator

    Directory of Open Access Journals (Sweden)

    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.

  17. Closed-loop suppression of chaos in nonlinear driven oscillators

    Science.gov (United States)

    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.

  18. 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.

  19. Propagation of a femtosecond laser pulse with duration of several optical oscillation periods in a medium with a quadratic nonlinearity

    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)

  20. Experimental Observation of Chaotic Beats in Oscillators Sharing Nonlinearity

    Science.gov (United States)

    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.

  1. The Downshift of Electron Plasma Oscillations in the Electron Foreshock Region.

    Science.gov (United States)

    1984-10-10

    Ii D-Ai50 52 THE DOWNSHIFT OF ELECTRON PLASMA OSCILLATIONS IN THE i/1. ELECTRON FORESHOCK R.. (U) I0MM UNIV 10MM CITY DEPT OF PHYSICS AND ASTRONOMY 5...OSCILLATIONS 0 IN THE ELECTRON FORESHOCK REGION In by S. A. Fuselierl, D. A. Gurnett 1 , Ace NTI 0. and R. J. Fitzenreiter 2 DTI I ,3WERSflY o. 06UNDED ISAI...geleasel Ditibto Unlimited 02 1 16 U. of Iowa 84-21 THE DOWNSHIFT OF ELECTRON PLASMA OSCILLATIONSJ / IN THE ELECTRON FORESHOCK REGION t - by Z I S. A

  2. Nonstandard conserved Hamiltonian structures in dissipative/damped systems: Nonlinear generalizations of damped harmonic oscillator

    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.

  3. Neutrino oscillations and neutrino-electron scattering

    International Nuclear Information System (INIS)

    Kayser, B.; Rosen, S.P.

    1980-10-01

    Neutrino flavor oscillations can significantly alter the cross section for neutrino-electron scattering. As a result, such oscillations can affect the comparison between existing reactor data and theories of neutral-current processes. They may also lead to strikingly large effects in high-energy accelerator experiments

  4. 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

  5. Non-linear frequency and amplitude modulation of a nano-contact spin torque oscillator

    OpenAIRE

    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.

  6. 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.

  7. Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane

    Science.gov (United States)

    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

  8. Hall field-induced magnetoresistance oscillations of a two-dimensional electron system

    International Nuclear Information System (INIS)

    Kunold, A.; Torres, M.

    2008-01-01

    We develop a model of the nonlinear response to a dc electrical current of a two-dimensional electron system (2DES) placed on a magnetic field. Based on the exact solution to the Schroedinger equation in arbitrarily strong electric and magnetic fields, and separating the relative and guiding center coordinates, a Kubo-like formula for the current is worked out as a response to the impurity scattering. Self-consistent expressions determine the longitudinal and Hall components of the electric field in terms of the dc current. The differential resistivity displays strong Hall field-induced oscillations, in agreement with the main features of the phenomenon observed in recent experiments

  9. Pure odd-order oscillators with constant excitation

    Science.gov (United States)

    Cveticanin, L.

    2011-02-01

    In this paper the excited vibrations of a truly nonlinear oscillator are analyzed. The excitation is assumed to be constant and the nonlinearity is pure (without a linear term). The mathematical model is a second-order nonhomogeneous differential equation with strong nonlinear term. Using the first integral, the exact value of period of vibration i.e., angular frequency of oscillator described with a pure nonlinear differential equation with constant excitation is analytically obtained. The closed form solution has the form of gamma function. The period of vibration depends on the value of excitation and of the order and coefficient of the nonlinear term. For the case of pure odd-order-oscillators the approximate solution of differential equation is obtained in the form of trigonometric function. The solution is based on the exact value of period of vibration. For the case when additional small perturbation of the pure oscillator acts, the so called 'Cveticanin's averaging method' for a truly nonlinear oscillator is applied. Two special cases are considered: one, when the additional term is a function of distance, and the second, when damping acts. To prove the correctness of the method the obtained results are compared with those for the linear oscillator. Example of pure cubic oscillator with constant excitation and linear damping is widely discussed. Comparing the analytically obtained results with exact numerical ones it is concluded that they are in a good agreement. The investigations reported in the paper are of special interest for those who are dealing with the problem of vibration reduction in the oscillator with constant excitation and pure nonlinear restoring force the examples of which can be found in various scientific and engineering systems. For example, such mechanical systems are seats in vehicles, supports for machines, cutting machines with periodical motion of the cutting tools, presses, etc. The examples can be find in electronics

  10. 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

  11. Two-electron Rabi oscillations in real-time time-dependent density-functional theory

    International Nuclear Information System (INIS)

    Habenicht, Bradley F.; Tani, Noriyuki P.; Provorse, Makenzie R.; Isborn, Christine M.

    2014-01-01

    We investigate the Rabi oscillations of electrons excited by an applied electric field in several simple molecular systems using time-dependent configuration interaction (TDCI) and real-time time-dependent density-functional theory (RT-TDDFT) dynamics. While the TDCI simulations exhibit the expected single-electron Rabi oscillations at a single resonant electric field frequency, Rabi oscillations in the RT-TDDFT simulations are a two-electron process. The existence of two-electron Rabi oscillations is determined both by full population inversion between field-free molecular orbitals and the behavior of the instantaneous dipole moment during the simulations. Furthermore, the Rabi oscillations in RT-TDDFT are subject to an intensity threshold of the electric field, below which Rabi oscillations do not occur and above which the two-electron Rabi oscillations occur at a broad range of frequencies. It is also shown that at field intensities near the threshold intensity, the field frequency predicted to induce Rabi oscillations by linear response TDDFT only produces detuned Rabi oscillations. Instead, the field frequency that yields the full two-electron population inversion and Rabi oscillation behavior is shown to be the average of single-electron transition frequencies from the ground S 0 state and the doubly-excited S 2 state. The behavior of the two-electron Rabi oscillations is rationalized via two possible models. The first model is a multi-photon process that results from the electric field interacting with the three level system such that three level Rabi oscillations may occur. The second model suggests that the mean-field nature of RT-TDDFT induces paired electron propagation

  12. 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...

  13. Electronically tunable RC sinusoidal oscillators

    International Nuclear Information System (INIS)

    Florescu, Valeriu

    2008-01-01

    This paper presents two types of active configurations for realizing electronically tunable RC sinusoidal oscillators. The type-1 network employs two grounded scaled resistances KR 1 and KR 2 , where K is scaling factor. The frequency of oscillation W 0 is controlled conveniently by adjusting K, since W 0 appears in the form W 0 =1/K √ R 1 C 1 R 2 C 2 . For realizing the scaled resistances, an active configuration is proposed, which realizes KR 1 =R 1 /(1+f(V B )), where f(V B ) denotes a function of a controlling voltage V B . Thus the frequency tuning can be effected by controlling a voltage V B . The type-2 oscillator uses two periodically switched conductances. It is shown that the tuning of oscillation frequency can be done by varying the pulse width-to-period ratio (t/T) of the periodically switched conductances. (author)

  14. Reactor oscillator - I - III, Part III - Electronic device

    International Nuclear Information System (INIS)

    Lolic, B.; Jovanovic, S.

    1961-12-01

    This report describes functioning of the reactor oscillator electronic system. Two methods of oscillator operation were discussed. The first method is so called method of amplitude modulation of the reactor power, and the second newer method is phase method. Both methods are planned for the present reactor oscillator

  15. Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

    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.

  16. Nonlinear Effects in Three-minute Oscillations of the Solar Chromosphere. I. An Analytical Nonlinear Solution and Detection of the Second Harmonic

    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.

  17. 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

  18. 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

  19. Effects produced by oscillations applied to nonlinear dynamic systems: a general approach and examples

    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...

  20. Large time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics

    OpenAIRE

    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...

  1. An Apparatus to Demonstrate Linear and Nonlinear Oscillations of a Pendulum

    Science.gov (United States)

    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.…

  2. 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)

  3. 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

  4. Electron diode oscillators for high-power RF generation

    International Nuclear Information System (INIS)

    Humphries, S.

    1989-01-01

    Feedback oscillators have been used since the invention of the vacuum tube. This paper describes the extension of these familiar circuits to the regime of relativistic electron beam diodes. Such devices have potential application for the generation of high power RF radiation in the range 50-250 MHz, 1-10 GW with 20-60% conversion efficiency. This paper reviews the theory of the oscillator and the results of a design study. Calculations for the four-electrode diode with EGUN and EBQ show that good modulations of 30 kA electron beam at 600 kV can be achieved with moderate field stress on the electrodes. Conditions for oscillation have been studied with an in-house transmission line code. A design for a 7.5 GW oscillator at 200 MHz with 25% conversion efficiency is presented

  5. Nonreciprocal acoustics and dynamics in the in-plane oscillations of a geometrically nonlinear lattice.

    Science.gov (United States)

    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

  6. 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)

  7. 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

  8. Signatures of nonlinearity in single cell noise-induced oscillations.

    Science.gov (United States)

    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.

  9. Nonlinear Dynamics in Spear Wigglers

    International Nuclear Information System (INIS)

    2002-01-01

    BL11, the most recently installed wiggler in the SPEAR storage ring at SSRL, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and with closed orbit shifts were used to characterize the nonlinear fields of the SPEAR insertion devices (IDs). Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different than the flip coil measurements made along a straight line. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Corrector magnets to cancel the BL11 nonlinear fields are presently under construction

  10. Higher-Order Approximations of Motion of a Nonlinear Oscillator Using the Parameter Expansion Technique

    Science.gov (United States)

    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.

  11. An electronically tunable current-mode quadrature oscillator using PCAs

    OpenAIRE

    Herencsár, Norbert; Lahiri, Abhirup; Vrba, Kamil; Koton, Jaroslav

    2012-01-01

    The paper presents a new realization of active RC sinusoidal oscillator with electronically tunable condition and frequency of oscillation. As compared to the class of three resistors, two capacitors (3R-2C) based canonic oscillators, the proposed circuit here uses only two resistors and two capacitors as the passive components and still provides non-interactive tuning laws for the condition of oscillation (CO) and the frequency of oscillation (FO). The proposed circuit employs new bipolar pr...

  12. 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)

  13. 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)

  14. Robust nonlinear model predictive control for nuclear power plants in load following operations with bounded xenon oscillations

    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.

  15. Reactor oscillator - I - III, Part III - Electronic device; Reaktorski oscilator - I-III, III Deo - Elektronski uredjaj

    Energy Technology Data Exchange (ETDEWEB)

    Lolic, B; Jovanovic, S [Institute of Nuclear Sciences Boris Kidric, Laboratorija za fiziku reaktora, Vinca, Beograd (Serbia and Montenegro)

    1961-12-15

    This report describes functioning of the reactor oscillator electronic system. Two methods of oscillator operation were discussed. The first method is so called method of amplitude modulation of the reactor power, and the second newer method is phase method. Both methods are planned for the present reactor oscillator.

  16. A nonlinear bounce kinetic equation for trapped electrons

    International Nuclear Information System (INIS)

    Gang, F.Y.

    1990-03-01

    A nonlinear bounce averaged drift kinetic equation for trapped electrons is derived. This equation enables one to compute the nonlinear response of the trapped electron distribution function in terms of the field-line projection of a potential fluctuation left-angle e -inqθ φ n right-angle b . It is useful for both analytical and computational studies of the nonlinear evolution of short wavelength (n much-gt 1) trapped electron mode-driven turbulence. 7 refs

  17. Damping of electron center-of-mass oscillation in ultracold plasmas

    International Nuclear Information System (INIS)

    Chen, Wei-Ting; Witte, Craig; Roberts, Jacob L.

    2016-01-01

    Applying a short electric field pulse to an ultracold plasma induces an electron plasma oscillation. This manifests itself as an oscillation of the electron center of mass around the ion center of mass in the ultracold plasma. In general, the oscillation can damp due to either collisionless or collisional mechanisms, or a combination of the both. To investigate the nature of oscillation damping in ultracold plasmas, we developed a molecular dynamics model of the ultracold plasma electrons. Through this model, we found that depending on the neutrality of the ultracold plasma and the size of an applied DC electric field, there are some parameter ranges where the damping is primarily collisional and some primarily collisionless. We conducted experiments to compare the measured damping rate with theory predictions and found them to be in good agreement. Extension of our measurements to different parameter ranges should enable studies for strong-coupling influence on electron-ion collision rates.

  18. A search for oscillations of muon-neutrinos to electron-neutrinos

    CERN Document Server

    Procario, Michael

    1986-01-01

    The author has searched in the heavy liquid bubble chamber BEBC for electron neutrino charge current events which could arise from oscillation of the muon neutrinos (average energy ∼1.5 GeV) obtained with a low energy proton beam at the CERN PS targeted 825 m upstream from BEBC. The appearance of electron neutrino CC interactions provides a sensitive indication of nu/sub μ/ → nu/sub e/ oscillation. The author observed 460 muon neutrino CC events and 4 electron neutrino CC events with an estimated background of 3.5 electron neutrino CC events. Using the likelihood ratio method to test the oscillation hypothesis, the author finds no evidence for nu/sub μ/ → nu/sub e/ oscillation and set the limits δm2 ≤ 0.13 eV2 (maximal mixing) and sin22theta ≤ 0.018 for δm2 = 3 eV2 at 90% confidence level

  19. 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$.

  20. Synchronizing a single-electron shuttle to an external drive

    Science.gov (United States)

    Moeckel, Michael J.; Southworth, Darren R.; Weig, Eva M.; Marquardt, Florian

    2014-04-01

    The nanomechanical single-electron shuttle is a resonant system in which a suspended metallic island oscillates between and impacts at two electrodes. This setup holds promise for one-by-one electron transport and the establishment of an absolute current standard. While the charge transported per oscillation by the nanoscale island will be quantized in the Coulomb blockade regime, the frequency of such a shuttle depends sensitively on many parameters, leading to drift and noise. Instead of considering the nonlinearities introduced by the impact events as a nuisance, here we propose to exploit the resulting nonlinear dynamics to realize a highly precise oscillation frequency via synchronization of the shuttle self-oscillations to an external signal. We link the established phenomenological description of synchronization based on the Adler equation to the microscopic nonlinear dynamics of the electron shuttle by calculating the effective Adler constant analytically in terms of the microscopic parameters.

  1. Synchronizing a single-electron shuttle to an external drive

    International Nuclear Information System (INIS)

    Moeckel, Michael J; Southworth, Darren R; Weig, Eva M; Marquardt, Florian

    2014-01-01

    The nanomechanical single-electron shuttle is a resonant system in which a suspended metallic island oscillates between and impacts at two electrodes. This setup holds promise for one-by-one electron transport and the establishment of an absolute current standard. While the charge transported per oscillation by the nanoscale island will be quantized in the Coulomb blockade regime, the frequency of such a shuttle depends sensitively on many parameters, leading to drift and noise. Instead of considering the nonlinearities introduced by the impact events as a nuisance, here we propose to exploit the resulting nonlinear dynamics to realize a highly precise oscillation frequency via synchronization of the shuttle self-oscillations to an external signal. We link the established phenomenological description of synchronization based on the Adler equation to the microscopic nonlinear dynamics of the electron shuttle by calculating the effective Adler constant analytically in terms of the microscopic parameters

  2. Electronic oscillations in a hot plasma due the non-Maxwellian velocity distributions

    International Nuclear Information System (INIS)

    Dias, L.A.V.; Nakamura, Y.

    1977-01-01

    In a completely ionized hot plasma, with a non-Maxwellian electron velocity distribution, it is shown that, depending on the electron temperature, oscillations may occur at the elctron plasma and gyro frequencies. For three different electron velocity distributions, it is shown the oscillations dependency on the temperature. This situation occurs in the ionospheric plasma when artificially heated by HF radio waves. If the distribution is Maxwellian, the oscillation only occur near the electron plasma frequency [pt

  3. Nonlinear oscillations of the FitzHugh-Nagumo equations under combined external and two-frequency parametric excitations

    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.

  4. Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems

    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.

  5. 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

  6. An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

    Science.gov (United States)

    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.

  7. Electron acoustic nonlinear structures in planetary magnetospheres

    Science.gov (United States)

    Shah, K. H.; Qureshi, M. N. S.; Masood, W.; Shah, H. A.

    2018-04-01

    In this paper, we have studied linear and nonlinear propagation of electron acoustic waves (EAWs) comprising cold and hot populations in which the ions form the neutralizing background. The hot electrons have been assumed to follow the generalized ( r , q ) distribution which has the advantage that it mimics most of the distribution functions observed in space plasmas. Interestingly, it has been found that unlike Maxwellian and kappa distributions, the electron acoustic waves admit not only rarefactive structures but also allow the formation of compressive solitary structures for generalized ( r , q ) distribution. It has been found that the flatness parameter r , tail parameter q , and the nonlinear propagation velocity u affect the propagation characteristics of nonlinear EAWs. Using the plasmas parameters, typically found in Saturn's magnetosphere and the Earth's auroral region, where two populations of electrons and electron acoustic solitary waves (EASWs) have been observed, we have given an estimate of the scale lengths over which these nonlinear waves are expected to form and how the size of these structures would vary with the change in the shape of the distribution function and with the change of the plasma parameters.

  8. Conductance oscillation in graphene-nanoribbon-based electronic Fabry-Perot resonators

    International Nuclear Information System (INIS)

    Zhang Yong; Han Mei; Shen Linjiang

    2010-01-01

    By using the tight-binding approximation and the Green's function method, the quantum conductance of the Fabry-Perot-like electronic resonators composed of zigzag and metallic armchair edge graphene nanoribbons (GNRs) was studied numerically. Obtained results show that due to Fabry-Perot-like electronic interference, the conductance of the GNR resonators oscillates periodically with the Fermi energy. The effects of disorders and coupling between the electrodes and the GNR on conductance oscillations were explored. It is found that the conductance oscillations appear at the strong coupling and become resonant peaks as the coupling is very weak. It is also found that the strong disorders in the GNR can smear the conductance oscillation periods. In other words, the weak coupling and the strong disorders all can blur the conductance oscillations, making them unclearly distinguished.

  9. Oscillation of Nonlinear Delay Differential Equation with Non-Monotone Arguments

    Directory of Open Access Journals (Sweden)

    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.

  10. Nonlinear Oscillations in Biology and Chemistry

    CERN Document Server

    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...

  11. particle simulation for electrostatic oscillation of virtual cathode in relativistic electron beams

    International Nuclear Information System (INIS)

    Chen Deming; Wang Min

    1990-01-01

    The virtual cathode oscillation in relativistic electron beams is studied by a 1-D electrostatic particle simulation code with finite-size-particle model. When injection current is less than the space charge limiting current, electron beam propagates stably and transsmits completely. When injection current exceeds the space charge limit, its propagation is unstable, a part of electrons reflect and the other electrons transsmit. The position and potential of the virtual cathode caused by space charge effects oscillate periodically. When the beam current increases, the virtual cathode position closer to the injection plane and its oscillating region gets narrower, the virtual cathode potential decreases and its amplitude increases, the oscillation frequency increases above the beam plasma frequency

  12. Cardiovascular oscillations: in search of a nonlinear parametric model

    Science.gov (United States)

    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.

  13. 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.

  14. 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.

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

    International Nuclear Information System (INIS)

    Wang Jinzhi; Duan Zhisheng; Huang Lin

    2006-01-01

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

  16. 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.

  17. Nonlinear electron-acoustic rogue waves in electron-beam plasma system with non-thermal hot electrons

    Science.gov (United States)

    Elwakil, S. A.; El-hanbaly, A. M.; Elgarayh, A.; El-Shewy, E. K.; Kassem, A. I.

    2014-11-01

    The properties of nonlinear electron-acoustic rogue waves have been investigated in an unmagnetized collisionless four-component plasma system consisting of a cold electron fluid, non-thermal hot electrons obeying a non-thermal distribution, an electron beam and stationary ions. It is found that the basic set of fluid equations is reduced to a nonlinear Schrodinger equation. The dependence of rogue wave profiles on the electron beam and energetic population parameter are discussed. The results of the present investigation may be applicable in auroral zone plasma.

  18. Suppression and revival of oscillation in indirectly coupled limit cycle oscillators

    International Nuclear Information System (INIS)

    Sharma, P.R.; Kamal, N.K.; Verma, U.K.; Suresh, K.; Thamilmaran, K.; Shrimali, M.D.

    2016-01-01

    Highlights: • The phenomena of suppression and revival of oscillations are studied in indirectly coupled nonlinear oscillators. • The decay parameter and a feedback factor play a crucial role in emergent dynamical behavior of oscillators. • The critical curves for different dynamical regions are obtained analytically using linear stability analysis. • Electronic circuit experiments demonstrate these emergent dynamical states. - Abstract: We study the phenomena of suppression and revival of oscillations in a system of limit cycle oscillators coupled indirectly via a dynamic local environment. The dynamics of the environment is assumed to decay exponentially with time. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). We also show that introducing a feedback factor in the diffusion term revives the oscillations in this system. The critical curves for the regions of different emergent states as a function of coupling strength, decay parameter of the environment and feedback factor in the coupling are obtained analytically using linear stability analysis. These results are found to be consistent with the numerics and are also observed experimentally.

  19. Sinusoidal oscillators and waveform generators using modern electronic circuit building blocks

    CERN Document Server

    Senani, Raj; Singh, V K; Sharma, R K

    2016-01-01

    This book serves as a single-source reference to sinusoidal oscillators and waveform generators, using classical as well as a variety of modern electronic circuit building blocks. It provides a state-of-the-art review of a large variety of sinusoidal oscillators and waveform generators and includes a catalogue of over 600 configurations of oscillators and waveform generators, describing their relevant design details and salient performance features/limitations. The authors discuss a number of interesting, open research problems and include a comprehensive collection of over 1500 references on oscillators and non-sinusoidal waveform generators/relaxation oscillators. Offers readers a single-source reference to everything connected to sinusoidal oscillators and waveform generators, using classical as well as modern electronic circuit building blocks; Provides a state-of-the-art review of a large variety of sinusoidal oscillators and waveform generators; Includes a catalog of over 600 configurations of oscillato...

  20. Effect of state-dependent delay on a weakly damped nonlinear oscillator.

    Science.gov (United States)

    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.

  1. Nonlinear theory of the free-electron laser

    International Nuclear Information System (INIS)

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

    1984-01-01

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

  2. Weakly nonlinear electron plasma waves in collisional plasmas

    DEFF Research Database (Denmark)

    Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.

    1986-01-01

    The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...

  3. 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.

  4. Nonlinear electrostatic solitary waves in electron-positron plasmas

    Science.gov (United States)

    Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.

    2016-02-01

    The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.

  5. Hamiltonian formulation and statistics of an attracting system of nonlinear oscillators

    International Nuclear Information System (INIS)

    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.)

  6. A memristor-based third-order oscillator: beyond oscillation

    KAUST Repository

    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.

  7. A memristor-based third-order oscillator: beyond oscillation

    KAUST Repository

    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.

  8. Nonlinear dust-acoustic structures in space plasmas with superthermal electrons, positrons, and ions

    Energy Technology Data Exchange (ETDEWEB)

    Saberian, E., E-mail: e.saberian@neyshabur.ac.ir [University of Neyshabur, Department of Physics, Faculty of Basic Sciences (Iran, Islamic Republic of); Esfandyari-Kalejahi, A.; Afsari-Ghazi, M. [Azarbaijan Shahid Madani University, Department of Physics, Faculty of Sciences (Iran, Islamic Republic of)

    2017-01-15

    Some features of nonlinear dust-acoustic (DA) structures are investigated in a space plasma consisting of superthermal electrons, positrons, and positive ions in the presence of negatively charged dust grains with finite-temperature by employing a pseudo-potential technique in a hydrodynamic model. For this purpose, it is assumed that the electrons, positrons, and ions obey a kappa-like (κ) distribution in the background of adiabatic dust population. In the linear analysis, it is found that the dispersion relation yield two positive DA branches, i.e., the slow and fast DA waves. The upper branch (fast DA waves) corresponds to the case in which both (negatively charged) dust particles and (positively charged) ion species oscillate in phase with electrons and positrons. On the other hand, the lower branch (slow DA waves) corresponds to the case in which only dust particles oscillate in phase with electrons and positrons, while ion species are in antiphase with them. On the other hand, the fully nonlinear analysis shows that the existence domain of solitons and their characteristics depend strongly on the dust charge, ion charge, dust temperature, and the spectral index κ. It is found that the minimum/maximum Mach number increases as the spectral index κ increases. Also, it is found that only solitons with negative polarity can propagate and that their amplitudes increase as the parameter κ increases. Furthermore, the domain of Mach number shifts to the lower values, when the value of the dust charge Z{sub d} increases. Moreover, it is found that the Mach number increases with an increase in the dust temperature. Our analysis confirms that, in space plasmas with highly charged dusts, the presence of superthermal particles (electrons, positrons, and ions) may facilitate the formation of DA solitary waves. Particularly, in two cases of hydrogen ions H{sup +} (Z{sub i} = 1) and doubly ionized Helium atoms He{sup 2+} (Z{sub i} = 2), the mentioned results are the same

  9. Nature's Autonomous Oscillators

    Science.gov (United States)

    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.

  10. Nonlinear charge transport in bipolar semiconductors due to electron heating

    International Nuclear Information System (INIS)

    Molina-Valdovinos, S.; Gurevich, Yu.G.

    2016-01-01

    It is known that when strong electric field is applied to a semiconductor sample, the current voltage characteristic deviates from the linear response. In this letter, we propose a new point of view of nonlinearity in semiconductors which is associated with the electron temperature dependence on the recombination rate. The heating of the charge carriers breaks the balance between generation and recombination, giving rise to nonequilibrium charge carriers concentration and nonlinearity. - Highlights: • A new mechanism of nonlinearity of current-voltage characteristic (CVC) is proposed. • The hot electron temperature violates the equilibrium between electrons and holes. • This violation gives rise to nonequilibrium concentration of electrons and holes. • This leads to nonlinear CVC (along with the heating nonlinearity).

  11. Nonlinear charge transport in bipolar semiconductors due to electron heating

    Energy Technology Data Exchange (ETDEWEB)

    Molina-Valdovinos, S., E-mail: sergiom@fisica.uaz.edu.mx [Universidad Autónoma de Zacatecas, Unidad Académica de Física, Calzada Solidaridad esq. Paseo, La Bufa s/n, CP 98060, Zacatecas, Zac, México (Mexico); Gurevich, Yu.G. [Centro de Investigación y de Estudios Avanzados del IPN, Departamento de Física, Av. IPN 2508, México D.F., CP 07360, México (Mexico)

    2016-05-27

    It is known that when strong electric field is applied to a semiconductor sample, the current voltage characteristic deviates from the linear response. In this letter, we propose a new point of view of nonlinearity in semiconductors which is associated with the electron temperature dependence on the recombination rate. The heating of the charge carriers breaks the balance between generation and recombination, giving rise to nonequilibrium charge carriers concentration and nonlinearity. - Highlights: • A new mechanism of nonlinearity of current-voltage characteristic (CVC) is proposed. • The hot electron temperature violates the equilibrium between electrons and holes. • This violation gives rise to nonequilibrium concentration of electrons and holes. • This leads to nonlinear CVC (along with the heating nonlinearity).

  12. Electronically Tunable Current-Mode Quadrature Oscillator Using Single MCDTA

    Directory of Open Access Journals (Sweden)

    Y. Li

    2010-12-01

    Full Text Available This paper presents a modified current differencing transconductance amlpifier (MCDTA and the MCDTA based quadrature oscillator. The oscillator is current-mode and provides current output from high output impedance terminals. The circuit uses only one MCDTA and two grounded capacitors, and is easy to be integrated. Its oscillation frequency can be tuned electronically by tuning bias currents of MCDTA. Finally, frequency error is analyzed. The results of circuit simulations are in agreement with theory.

  13. Classical plasma dynamics of Mie-oscillations in atomic clusters

    Science.gov (United States)

    Kull, H.-J.; El-Khawaldeh, A.

    2018-04-01

    Mie plasmons are of basic importance for the absorption of laser light by atomic clusters. In this work we first review the classical Rayleigh-theory of a dielectric sphere in an external electric field and Thomson’s plum-pudding model applied to atomic clusters. Both approaches allow for elementary discussions of Mie oscillations, however, they also indicate deficiencies in describing the damping mechanisms by electrons crossing the cluster surface. Nonlinear oscillator models have been widely studied to gain an understanding of damping and absorption by outer ionization of the cluster. In the present work, we attempt to address the issue of plasmon relaxation in atomic clusters in more detail based on classical particle simulations. In particular, we wish to study the role of thermal motion on plasmon relaxation, thereby extending nonlinear models of collective single-electron motion. Our simulations are particularly adopted to the regime of classical kinetics in weakly coupled plasmas and to cluster sizes extending the Debye-screening length. It will be illustrated how surface scattering leads to the relaxation of Mie oscillations in the presence of thermal motion and of electron spill-out at the cluster surface. This work is intended to give, from a classical perspective, further insight into recent work on plasmon relaxation in quantum plasmas [1].

  14. On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

    Science.gov (United States)

    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.

  15. Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring

    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

  16. 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

  17. 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.

  18. Oscillating two-stream instability of laser wakefield-driven plasma ...

    Indian Academy of Sciences (India)

    on electrons, driving the low-frequency mode, i.e., causing local density depression n (ω, k). This density perturbation in conjunction with the oscillating electron velocity v0 at (ω0, k0) produces nonlinear density perturbations nNL. 1,2 at (ω1,2, k1,2) that drive the sidebands. In §2, the local theory of OTSI of laser ...

  19. Nonlinear Electron Waves in Strongly Magnetized Plasmas

    DEFF Research Database (Denmark)

    Pécseli, Hans; Juul Rasmussen, Jens

    1980-01-01

    Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....

  20. Nonlinear bounce resonances between magnetosonic waves and equatorially mirroring electrons

    Science.gov (United States)

    Chen, Lunjin; Maldonado, Armando; Bortnik, Jacob; Thorne, Richard M.; Li, Jinxing; Dai, Lei; Zhan, Xiaoya

    2015-08-01

    Equatorially mirroring energetic electrons pose an interesting scientific problem, since they generally cannot resonate with any known plasma waves and hence cannot be scattered down to lower pitch angles. Observationally it is well known that the flux of these equatorial particles does not simply continue to build up indefinitely, and so a mechanism must necessarily exist that transports these particles from an equatorial pitch angle of 90° down to lower values. However, this mechanism has not been uniquely identified yet. Here we investigate the mechanism of bounce resonance with equatorial noise (or fast magnetosonic waves). A test particle simulation is used to examine the effects of monochromatic magnetosonic waves on the equatorially mirroring energetic electrons, with a special interest in characterizing the effectiveness of bounce resonances. Our analysis shows that bounce resonances can occur at the first three harmonics of the bounce frequency (nωb, n = 1, 2, and 3) and can effectively reduce the equatorial pitch angle to values where resonant scattering by whistler mode waves becomes possible. We demonstrate that the nature of bounce resonance is nonlinear, and we propose a nonlinear oscillation model for characterizing bounce resonances using two key parameters, effective wave amplitude à and normalized wave number k~z. The threshold for higher harmonic resonance is more strict, favoring higher à and k~z, and the change in equatorial pitch angle is strongly controlled by k~z. We also investigate the dependence of bounce resonance effects on various physical parameters, including wave amplitude, frequency, wave normal angle and initial phase, plasma density, and electron energy. It is found that the effect of bounce resonance is sensitive to the wave normal angle. We suggest that the bounce resonant interaction might lead to an observed pitch angle distribution with a minimum at 90°.

  1. Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators.

    Science.gov (United States)

    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.

  2. Synchronization of delay-coupled nonlinear oscillators : an approach based on the stability analysis of synchronized equilibria

    NARCIS (Netherlands)

    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

  3. 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.

  4. Control electron beam oscillation regimes in Pierce diode with overcritical current

    International Nuclear Information System (INIS)

    Rempen, I.S.; Khramov, A.E.

    2001-01-01

    The effect of the delayed feedback on the complex oscillation regimes in the electron flux with the overcritical current in the Pierce diode is studied. The possibility of controlling the oscillation regimes through changing the feedback parameters is shown. The finite-dimensional model, describing the behavior of the electron flux in the Pierce diode hydrodynamic model, is constructed. Its behavior under the effect of the delayed feedback is studied [ru

  5. Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling.

    Science.gov (United States)

    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.

  6. Oscillators and Eigenvalues

    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....

  7. Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

    Science.gov (United States)

    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.

  8. Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.

    Science.gov (United States)

    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

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

    Science.gov (United States)

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

    2017-05-01

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

  10. Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators

    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)

  11. Patterns of patterns of synchronization: Noise induced attractor switching in rings of coupled nonlinear oscillators

    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.

  12. 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.

  13. XXIII International Conference on Nonlinear Dynamics of Electronic Systems

    CERN Document Server

    Stoop, Ruedi; Stramaglia, Sebastiano

    2017-01-01

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

  14. Electromagnetic drift modes in an inhomogeneous electron gas

    DEFF Research Database (Denmark)

    Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens

    1986-01-01

    A pair of nonlinear equations is derived which describes the dynamics of the electromagnetic drift oscillations in a nonuniform magnetized electron gas. It is shown that the nonlinear electromagnetic drift modes can propagate in the form of dipole vortices...

  15. Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities.

    Science.gov (United States)

    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.

  16. Nonlinear response and bistability of driven ion acoustic waves

    Science.gov (United States)

    Akbari-Moghanjoughi, M.

    2017-08-01

    The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

  17. Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

    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.

  18. Applicability of Time-Averaged Holography for Micro-Electro-Mechanical System Performing Non-Linear Oscillations

    Science.gov (United States)

    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

  19. Applicability of time-averaged holography for micro-electro-mechanical system performing non-linear oscillations.

    Science.gov (United States)

    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.

  20. Image processing with a cellular nonlinear network

    International Nuclear Information System (INIS)

    Morfu, S.

    2005-01-01

    A cellular nonlinear network (CNN) based on uncoupled nonlinear oscillators is proposed for image processing purposes. It is shown theoretically and numerically that the contrast of an image loaded at the nodes of the CNN is strongly enhanced, even if this one is initially weak. An image inversion can be also obtained without reconfiguration of the network whereas a gray levels extraction can be performed with an additional threshold filtering. Lastly, an electronic implementation of this CNN is presented

  1. Non-linear spin transport in magnetic semiconductor superlattices

    International Nuclear Information System (INIS)

    Bejar, Manuel; Sanchez, David; Platero, Gloria; MacDonald, A.H.

    2004-01-01

    The electronic spin dynamics in DC-biased n-doped II-VI semiconductor multiquantum wells doped with magnetic impurities is presented. Under certain range of electronic doping, conventional semiconductor superlattices present self-sustained oscillations. Magnetically doped wells (Mn) present large spin splittings due to the exchange interaction. The interplay between non-linear interwell transport, the electron-electron interaction and the exchange between electrons and the magnetic impurities produces interesting time-dependent features in the spin polarization current tuned by an external magnetic field

  2. A new analytical approach for limit cycles and quasi-periodic solutions of nonlinear oscillators: the example of the forced Van der Pol Duffing oscillator

    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)

  3. Nonlinear features of the electron temperature gradient mode and electron thermal transport in tokamaks

    International Nuclear Information System (INIS)

    Kaw, P.K.; Singh, R.; Weiland, J.G.

    2001-01-01

    Analytical investigations of several linear and nonlinear features of ETG turbulence are reported. The linear theory includes effects such as finite beta induced electromagnetic shielding, coupling to electron magnetohydrodynamic modes like whistlers etc. It is argued that nonlinearly, turbulence and transport are dominated by radially extended modes called 'streamers'. A nonlinear mechanism generating streamers based on a modulational instability theory of the ETG turbulence is also presented. The saturation levels of the streamers using a Kelvin Helmholtz secondary instability mechanism are calculated and levels of the electron thermal transport due to streamers are estimated. (author)

  4. Nonlinearity in structural and electronic materials

    International Nuclear Information System (INIS)

    Bishop, A.R.; Beardmore, K.M.; Ben-Naim, E.

    1997-01-01

    This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project strengthens a nonlinear technology base relevant to a variety of problems arising in condensed matter and materials science, and applies this technology to those problems. In this way the controlled synthesis of, and experiments on, novel electronic and structural materials provide an important focus for nonlinear science, while nonlinear techniques help advance the understanding of the scientific principles underlying the control of microstructure and dynamics in complex materials. This research is primarily focused on four topics: (1) materials microstructure: growth and evolution, and porous media; (2) textures in elastic/martensitic materials; (3) electro- and photo-active polymers; and (4) ultrafast photophysics in complex electronic materials. Accomplishments included the following: organization of a ''Nonlinear Materials'' seminar series and international conferences including ''Fracture, Friction and Deformation,'' ''Nonequilibrium Phase Transitions,'' and ''Landscape Paradigms in Physics and Biology''; invited talks at international conference on ''Synthetic Metals,'' ''Quantum Phase Transitions,'' ''1996 CECAM Euroconference,'' and the 1995 Fall Meeting of the Materials Research Society; large-scale simulations and microscopic modeling of nonlinear coherent energy storage at crack tips and sliding interfaces; large-scale simulation and microscopic elasticity theory for precursor microstructure and dynamics at solid-solid diffusionless phase transformations; large-scale simulation of self-assembling organic thin films on inorganic substrates; analysis and simulation of smoothing of rough atomic surfaces; and modeling and analysis of flux pattern formation in equilibrium and nonequilibrium Josephson junction arrays and layered superconductors

  5. Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

    Science.gov (United States)

    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.

  6. Weiss oscillations in the electronic structure of modulated graphene

    International Nuclear Information System (INIS)

    Tahir, M; Sabeeh, K; MacKinnon, A

    2007-01-01

    We present a theoretical study of the electronic structure of modulated graphene in the presence of a perpendicular magnetic field. The density of states and the bandwidth for the Dirac electrons in this system are determined. The appearance of unusual Weiss oscillations in the bandwidth and density of states is the main focus of this work

  7. FREQUENCY CATASTROPHE AND CO-EXISTING ATTRACTORS IN A CELL Ca2+ NONLINEAR OSCILLATION MODEL WITH TIME DELAY*

    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.

  8. Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Wang, C., E-mail: cwang@mail.sim.ac.cn; Wang, F.; Cao, J. C., E-mail: jccao@mail.sim.ac.cn [Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050 (China)

    2014-09-01

    Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

  9. Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field

    International Nuclear Information System (INIS)

    Wang, C.; Wang, F.; Cao, J. C.

    2014-01-01

    Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation

  10. Terahertz radiation induced chaotic electron transport in semiconductor superlattices with a tilted magnetic field.

    Science.gov (United States)

    Wang, C; Wang, F; Cao, J C

    2014-09-01

    Chaotic electron transport in semiconductor superlattice induced by terahertz electric field that is superimposed on a dc electric field along the superlattice axis are studied using the semiclassical motion equations including the effect of dissipation. A magnetic field that is tilted relative to the superlattice axis is also applied to the system. Numerical simulation shows that electrons in superlattice miniband exhibit complicate nonlinear oscillating modes with the influence of terahertz radiation. Transitions between frequency-locking and chaos via pattern forming bifurcations are observed with the varying of terahertz amplitude. It is found that the chaotic regions gradually contract as the dissipation increases. We attribute the appearance of complicate nonlinear oscillation in superlattice to the interaction between terahertz radiation and internal cooperative oscillating mode relative to Bloch oscillation and cyclotron oscillation.

  11. Self-excitation of microwave oscillations in plasma-assisted slow-wave oscillators by an electron beam with a movable focus

    Science.gov (United States)

    Bliokh, Yu. P.; Nusinovich, G. S.; Shkvarunets, A. G.; Carmel, Y.

    2004-10-01

    Plasma-assisted slow-wave oscillators (pasotrons) operate without external magnetic fields, which makes these devices quite compact and lightweight. Beam focusing in pasotrons is provided by ions, which appear in the device due to the impact ionization of a neutral gas by beam electrons. Typically, the ionization time is on the order of the rise time of the beam current. This means that, during the rise of the current, beam focusing by ions becomes stronger. Correspondingly, a beam of electrons, which was initially diverging radially due to the self-electric field, starts to be focused by ions, and this focus moves towards the gun as the ion density increases. This feature makes the self-excitation of electromagnetic (em) oscillations in pasotrons quite different from practically all other microwave sources where em oscillations are excited by a stationary electron beam. The process of self-excitation of em oscillations has been studied both theoretically and experimentally. It is shown that in pasotrons, during the beam current rise the amount of current entering the interaction space and the beam coupling to the em field vary. As a result, the self-excitation can proceed faster than in conventional microwave sources with similar operating parameters such as the operating frequency, cavity quality-factor and the beam current and voltage.

  12. Research on nonlinearity effect of secondary electron multiplier

    International Nuclear Information System (INIS)

    Wei Xingjian; Liao Junsheng; Deng Dachao; Yu Chunrong; Yuan Li

    2007-01-01

    The nonlinearity of secondary electron multiplier (SEM) of a thermal ionization mass spectrometer has been researched by using UTB-500 uranium isotope reference material and multi-collecting technique. The results show that the nonlinearity effect of SEM exists in the whole ion counting range, and there is an extreme point of the nonlinearity when the ion counting rate is about 20000 cps. The deviation between measured value of the extreme point and the reference value of the reference sample can be up to 3%, and the nonlinearity obeys logarithm linearity law on both sides of extreme point. A kind of mathematics model of nonlinearity calibration has been put forward. Using this model, the nonlinearity of SEM of TIMS can be calibrated. (authors)

  13. Oscillating patterns in image processing and nonlinear evolution equations the fifteenth Dean Jacqueline B. Lewis memorial lectures

    CERN Document Server

    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...

  14. Existence of periodic orbits in nonlinear oscillators of Emden–Fowler form

    Energy Technology Data Exchange (ETDEWEB)

    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.

  15. 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

  16. Study of nonlinear electron-acoustic solitary and shock waves in a dissipative, nonplanar space plasma with superthermal hot electrons

    Energy Technology Data Exchange (ETDEWEB)

    Han, Jiu-Ning, E-mail: hanjiuning@126.com; He, Yong-Lin; Luo, Jun-Hua; Nan, Ya-Gong; Han, Zhen-Hai; Dong, Guang-Xing [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China); Duan, Wen-Shan [College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 (China); Li, Jun-Xiu [College of Civil Engineering, Hexi University, Zhangye 734000 (China)

    2014-01-15

    With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significant effects on the properties of nonlinear waves and collision-induced nonlinear structure.

  17. Electron beam modification of vanadium dioxide oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Belyaev, Maksim; Velichko, Andrey; Putrolaynen, Vadim; Perminov, Valentin; Pergament, Alexander [Petrozavodsk State University, Petrozavodsk (Russian Federation)

    2017-03-15

    The paper presents the results of a study of electron-beam modification (EBM) of VO{sub 2}-switch I-V curve threshold parameters and the self-oscillation frequency of a circuit containing such a switching device. EBM in vacuum is reversible and the parameters are restored when exposed to air at pressure of 150 Pa. At EBM with a dose of 3 C cm{sup -2}, the voltages of switching-on (V{sub th}) and off (V{sub h}), as well as the OFF-state resistance R{sub off}, decrease down to 50% of the initial values, and the oscillation frequency increases by 30% at a dose of 0.7 C cm{sup -2}. Features of physics of EBM of an oscillator are outlined considering the contribution of the metal and semiconductor phases of the switching channel. Controlled modification allows EBM forming of switches with preset parameters. Also, it might be used in artificial oscillatory neural networks for pattern recognition based on frequency shift keying. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  18. Generation of “gigantic” ultra-short microwave pulses based on passive mode-locking effect in electron oscillators with saturable absorber in the feedback loop

    International Nuclear Information System (INIS)

    Ginzburg, N. S.; Denisov, G. G.; Vilkov, M. N.; Zotova, I. V.; Sergeev, A. S.

    2016-01-01

    A periodic train of powerful ultrashort microwave pulses can be generated in electron oscillators with a non-linear saturable absorber installed in the feedback loop. This method of pulse formation resembles the passive mode-locking widely used in laser physics. Nevertheless, there is a specific feature in the mechanism of pulse amplification when consecutive energy extraction from different fractions of a stationary electron beam takes place due to pulse slippage over the beam caused by the difference between the wave group velocity and the electron axial velocity. As a result, the peak power of generated “gigantic” pulses can exceed not only the level of steady-state generation but also, in the optimal case, the power of the driving electron beam.

  19. Nonlinear longitudinal dynamics studies at the ALS

    International Nuclear Information System (INIS)

    Byrd, J.M.; Cheng, W.-H.; De Santis, S.; Li, D.; Stupakov, G.; Zimmermann, F.

    1999-01-01

    We present a summary of results for a variety of studies of nonlinear longitudinal dynamics in the Advanced Light Source, an electron storage ring. These include observation of decoherence at injection, decay of an injected beam, forced synchrotron oscillations and diffusion from one bunch to the next. All of the measurements were made using a dual-scan streak camera which allowed the real-time observation of the longitudinal distribution of the electron beam

  20. Bound-Electron Nonlinearity Beyond the Ionization Threshold

    Science.gov (United States)

    Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

    2018-05-01

    We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

  1. Electron acceleration during the decay of nonlinear Whistler waves in low-beta electron-ion plasma

    International Nuclear Information System (INIS)

    Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro

    2014-01-01

    Relativistic electron acceleration through dissipation of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave in low-beta plasma is investigated by utilizing a one-dimensional fully relativistic electromagnetic particle-in-cell code. The nonlinear (large-amplitude) parent whistler wave decays through the parametric instability which enhances electrostatic ion acoustic waves and electromagnetic whistler waves. These waves satisfy the condition of three-wave coupling. Through the decay instability, the energy of electron bulk velocity supporting the parent wave is converted to the thermal energy perpendicular to the background magnetic field. Increase of the perpendicular temperature triggers the electron temperature anisotropy instability which generates broadband whistler waves and heats electrons in the parallel direction. The broadband whistler waves are inverse-cascaded during the relaxation of the electron temperature anisotropy. In lower-beta conditions, electrons with a pitch angle of about 90° are successively accelerated by inverse-cascaded whistler waves, and selected electrons are accelerated to over a Lorentz factor of 10. The result implies that the nonlinear dissipation of a finite-amplitude and short-wavelength whistler wave plays an important role in producing relativistic nonthermal electrons over a few MeV especially at lower beta plasmas.

  2. 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...

  3. Oscillating molecular dipoles require strongly correlated electronic and nuclear motion

    International Nuclear Information System (INIS)

    Chang, Bo Y; Shin, Seokmin; Palacios, Alicia; Martín, Fernando; Sola, Ignacio R

    2015-01-01

    To create an oscillating electric dipole in an homonuclear diatomic cation without an oscillating driver one needs (i) to break the symmetry of the system and (ii) to sustain highly correlated electronic and nuclear motion. Based on numerical simulations in H 2 + we present results for two schemes. In the first one (i) is achieved by creating a superposition of symmetric and antisymmetric electronic states freely evolving, while (ii) fails. In a second scheme, by preparing the system in a dressed state of a strong static field, both conditions hold. We then analyze the robustness of this scheme with respect to features of the nuclear wave function and its intrinsic sources of decoherence. (tutorial)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-09-01

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

  5. Adiabatic and non-adiabatic electron oscillations in a static electric field

    International Nuclear Information System (INIS)

    Wahlberg, C.

    1977-03-01

    The influence of a static electric field on the oscillations of a one-dimensional stream of electrons is investigated. In the weak field limit the oscillations are adiabatic and mode coupling negligible, but becomes significant if the field is tronger. The latter effect is believed to be of importance for the stability of e.g. potential double layers

  6. Electronically Tunable Quadrature Sinusoidal Oscillator with Equal Output Amplitudes during Frequency Tuning Process

    Directory of Open Access Journals (Sweden)

    Den Satipar

    2017-01-01

    Full Text Available A new configuration of voltage-mode quadrature sinusoidal oscillator is proposed. The proposed oscillator employs two voltage differencing current conveyors (VDCCs, two resistors, and two grounded capacitors. In this design, the use of multiple/dual output terminal active building block is not required. The tuning of frequency of oscillation (FO can be done electronically by adjusting the bias current of active device without affecting condition of oscillation (CO. The electronic tuning can be done by controlling the bias current using a digital circuit. The amplitude of two sinusoidal outputs is equal when the frequency of oscillation is tuned. This makes the sinusoidal output voltages meet good total harmonic distortions (THD. Moreover, the proposed circuit can provide the sinusoidal output current with high impedance which is connected to external load or to another circuit without the use of buffer device. To confirm that the oscillator can generate the quadrature sinusoidal output signal, the experimental results using VDCC constructed from commercially available ICs are also included. The experimental results agree well with theoretical anticipation.

  7. Small systems of Duffing oscillators and the Fermi-Pasta-Ulam-Tsingou system An examination of the possible reasons for the unusual stability of localized nonlinear excitations in these systems

    Science.gov (United States)

    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.

  8. Electron dynamics with radiation and nonlinear wigglers

    International Nuclear Information System (INIS)

    Jowett, J.M.

    1986-06-01

    The physics of electron motion in storage rings is described by supplementing the Hamiltonian equations of motion with fluctuating radiation reaction forces to describe the effects of synchrotron radiation. This leads to a description of radiation damping and quantum diffusion in single-particle phase-space by means of Fokker-Planck equations. For practical purposes, most storage rings remain in the regime of linear damping and diffusion; this is discussed in some detail with examples, concentrating on longitudinal phase space. However special devices such as nonlinear wigglers may permit the new generation of very large rings to go beyond this into regimes of nonlinear damping. It is shown how a special combined-function wiggler can be used to modify the energy distribution and current profile of electron bunches

  9. Charged particle emission effects on the characteristics of glow discharges with oscillating electrons

    CERN Document Server

    Nikulin, S P

    2001-01-01

    One discusses the effect of selection of charged particles on conditions to maintain and the characteristics of a glow discharge with oscillating electrons. It is shown that there is a pressure dependent optimal level of ion selection when the energy efficiency of ion source reaches its maximum value. It is determined that departure of fast ionizing electrons affects negatively the discharge maintenance wile emission of slow plasma electrons may promote maintenance of a discharge high current shape. It is shown that high efficient electron emission without violation of a discharge stability may take place in a magnetic field due to different nature of spatial distributions of fast and slow particles in discharges with electron oscillation

  10. Power-level regulation and simulation of nonlinear pressurized water reactor core with xenon oscillation using H-infinity loop shaping control

    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.

  11. 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

  12. Design of an electronically tunable millimeter wave Gyrotron Backward Wave Oscillator

    International Nuclear Information System (INIS)

    Caplan, M.

    1987-01-01

    A non-linear self-consistent computer simulation code is used to analyze the saturated output of the Gyrotron Backward Wave Oscillator (Gyro BWO) which can be used as a tunable driver for a 250 GHz FEL amplifier. Simulations show that the Gyrotron BWO using a Pierce/Wiggler gun configuration can produce at least 10 kW of microwave power over the range 249 GHz to 265 GHz by varying beam voltage alone

  13. State space modeling of Memristor-based Wien oscillator

    KAUST Repository

    Talukdar, Abdul Hafiz Ibne; Radwan, Ahmed G.; Salama, Khaled N.

    2011-01-01

    State space modeling of Memristor based Wien 'A' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.

  14. State space modeling of Memristor-based Wien oscillator

    KAUST Repository

    Talukdar, Abdul Hafiz Ibne

    2011-12-01

    State space modeling of Memristor based Wien \\'A\\' oscillator has been demonstrated for the first time considering nonlinear ion drift in Memristor. Time dependant oscillating resistance of Memristor is reported in both state space solution and SPICE simulation which plausibly provide the basis of realizing parametric oscillation by Memristor based Wien oscillator. In addition to this part Memristor is shown to stabilize the final oscillation amplitude by means of its nonlinear dynamic resistance which hints for eliminating diode in the feedback network of conventional Wien oscillator. © 2011 IEEE.

  15. The effect of the dust’s electric dipole moment on transverse oscillations of the one dimensional dusty crystals

    Directory of Open Access Journals (Sweden)

    S Karimi

    2013-10-01

    Full Text Available In this paper, we investigated the effect of dipole-dipole interaction between the dust particles on the transverse oscillation of one dimensional dusty crystal. We used the Boltzmann distribution for the electrons and ions density and assumed that dust particles are negatively charged. The equation of motion for dust particles in this one dimensional chain was obtained. It is shown that the direction of dipoles plays an important role in the motion of dusts and significantly changes the oscillation frequency. Also, in the long wavelength approximation, a nonlinear Schrödinger equation for the evolution of the amplitude of the nonlinear oscillations was derived, showing that both the bright solitons and the dark solitons could exist.

  16. Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

    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.

  17. Electron plasma oscillations in the Venus foreshock

    Science.gov (United States)

    Crawford, G. K.; Strangeway, R. J.; Russell, C. T.

    1990-01-01

    Plasma waves are observed in the solar wind upstream of the Venus bow shock by the Pioneer Venus Orbiter. These wave signatures occur during periods when the interplanetary magnetic field through the spacecraft position intersects the bow shock, thereby placing the spacecraft in the foreshock region. The electron foreshock boundary is clearly evident in the data as a sharp onset in wave activity and a peak in intensity. Wave intensity is seen to drop rapidly with increasing penetration into the foreshock. The peak wave electric field strength at the electron foreshock boundary is found to be similar to terrestrial observations. A normalized wave spectrum was constructed using measurements of the electron plasma frequency and the spectrum was found to be centered about this value. These results, along with polarization studies showing the wave electric field to be field aligned, are consistent with the interpretation of the waves as electron plasma oscillations.

  18. Electron plasma oscillations in the Venus foreshock

    International Nuclear Information System (INIS)

    Crawford, G.K.; Strangeway, R.J.; Russell, C.T.

    1990-01-01

    Plasma waves are observed in the solar wind upstream of the Venus bow shock by the Pioneer Venus Orbiter. These wave signatures occur during periods when the interplanetary magnetic field through the spacecraft position intersects the bow shock, thereby placing the spacecraft in the foreshock region. The electron foreshock boundary is clearly evident in the data as a sharp onset in wave activity and a peak in intensity. Wave intensity is seen to drop rapidly with increasing penetration into the foreshock. The peak wave electric field strength at the electron foreshock boundary is found to be similar to terrestrial observations. A normalized wave spectrum was constructed using measurements of the electron plasma frequency and the spectrum was found to be centered about this value. These results, along with polarization studies showing the wave electric field to be field aligned, are consistent with the interpretation of the waves as electron plasma oscillations

  19. Nonlinear ion-mixing-mode particle transport in the dissipative trapped electron regime

    International Nuclear Information System (INIS)

    Ware, A.S.; Terry, P.W.

    1993-09-01

    The nonlinear particle transport arising from the convection of nonadiabatic electron density by ion temperature gradient driven turbulence is examined for trapped electron collisionality regimes. The renormalized dissipative nonadiabatic trapped electron phase space density response is derived and used to calculate the nonlinear particle flux along with an ansatz for the turbulently broadened frequency spectrum. In the lower temperature end of this regime, trapped electrons are collisional and all components of the quasilinear particle flux are outward (i.e., in the direction of the gradients). Nonlinear effects can alter the phase between the nonadiabatic trapped electron phase space density and the electrostatic potential, producing inward components in the particle flux. Specifically, both turbulent shifting of the peak of the frequency spectrum and nonlinear source terms in the trapped electron response can give rise to inward components. However, in the dissipative regime these terms are small and the trapped electron response remains dominantly laminar. When the trapped electrons are collisionless, there is a temperature threshold above which the electron temperature gradient driven component of the quasilinear particle flux changes sign and becomes inward. For finite amplitude turbulence, however, turbulent broadening of both the electron collisional resonance and the frequency spectrum removes tills threshold., and the temperature gradient driven component remains outward

  20. Numerical simulation of electron beam welding with beam oscillations

    Science.gov (United States)

    Trushnikov, D. N.; Permyakov, G. L.

    2017-02-01

    This research examines the process of electron-beam welding in a keyhole mode with the use of beam oscillations. We study the impact of various beam oscillations and their parameters on the shape of the keyhole, the flow of heat and mass transfer processes and weld parameters to develop methodological recommendations. A numerical three-dimensional mathematical model of electron beam welding is presented. The model was developed on the basis of a heat conduction equation and a Navier-Stokes equation taking into account phase transitions at the interface of a solid and liquid phase and thermocapillary convection (Marangoni effect). The shape of the keyhole is determined based on experimental data on the parameters of the secondary signal by using the method of a synchronous accumulation. Calculations of thermal and hydrodynamic processes were carried out based on a computer cluster, using a simulation package COMSOL Multiphysics.

  1. Collective oscillations of electrons when simulating first principles and nature of anomalous drift along the power axis

    International Nuclear Information System (INIS)

    Majorov, S.A.; Tkachev, A.N.; Yakovlenko, S.I.

    1996-01-01

    A hypothesis is proposed that a metastable supercooled state of a classic Coulomb particle system can be conditioned by a quasiresonance interaction of bound electrons with the collective oscillations of plasma electrons. This interaction is especially important when the Kepler frequency is of the order of Langmuir oscillation frequency (which takes place when the electron orbit radius is of the order of average distance between the charges). Based on the simulation it is shown that the typical time of the Coulomb particle system dipole moment oscillations appears to be of the order of the Langmuir oscillation frequency. 10 refs.; 3 figs

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

    CERN Document Server

    Ginoux, Jean-Marc

    2017-01-01

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

  3. The role of nonlinear torsional contributions on the stability of flexural-torsional oscillations of open-cross section beams

    Science.gov (United States)

    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.

  4. Rayleigh-type parametric chemical oscillation

    Energy Technology Data Exchange (ETDEWEB)

    Ghosh, Shyamolina; Ray, Deb Shankar, E-mail: pcdsr@iacs.res.in [Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032 (India)

    2015-09-28

    We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

  5. Rayleigh-type parametric chemical oscillation.

    Science.gov (United States)

    Ghosh, Shyamolina; Ray, Deb Shankar

    2015-09-28

    We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

  6. Modeling paraxial wave propagation in free-electron laser oscillators

    NARCIS (Netherlands)

    Karssenberg, J.G.; van der Slot, Petrus J.M.; Volokhine, I.; Verschuur, Jeroen W.J.; Boller, Klaus J.

    2006-01-01

    Modeling free-electron laser (FEL) oscillators requires calculation of both the light-beam interaction within the undulator and the light propagation outside the undulator. We have developed a paraxial optical propagation code that can be combined with various existing models of gain media, for

  7. Tracing the transition of a macro electron shuttle into nonlinear response

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Chulki [Sensor System Research Center, Korea Institute of Science and Technology, Seoul 136791 (Korea, Republic of); Prada, Marta [I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstr. 9, Hamburg 20355 (Germany); Qin, Hua [Key Laboratory of Nanodevices, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, 398 Ruoshui Road, Industrial Park, Suzhou City, Jiangsu 215123 (China); Kim, Hyun-Seok [Division of Electronics and Electrical Engineering, Dongguk University-Seoul, 100715 Seoul (Korea, Republic of); Blick, Robert H., E-mail: rblick@physnet.uni-hamburg.de [Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin-53706 (United States); Center for Hybrid Nanostructures, Universität Hamburg, Jungiusstr. 11c, Hamburg 20355 (Germany); Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1415 Engineering Dr. Madison, Wisconsin-53706 (United States)

    2015-02-09

    We present a study on a macroscopic electron shuttle in the transition from linear to nonlinear response. The shuttle consists of a classical mechanical pendulum situated between two capacitor plates. The metallic pendulum enables mechanical transfer of electrons between the plates, hence allowing to directly trace electron shuttling in the time domain. By applying a high voltage to the plates, we drive the system into a controlled nonlinear response, where we observe period doubling.

  8. Chimera regimes in a ring of oscillators with local nonlinear interaction

    Science.gov (United States)

    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.

  9. Coupled oscillators with parity-time symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Tsoy, Eduard N., E-mail: etsoy@uzsci.net

    2017-02-05

    Different models of coupled oscillators with parity-time (PT) symmetry are studied. Hamiltonian functions for two and three linear oscillators coupled via coordinates and accelerations are derived. Regions of stable dynamics for two coupled oscillators are obtained. It is found that in some cases, an increase of the gain-loss parameter can stabilize the system. A family of Hamiltonians for two coupled nonlinear oscillators with PT-symmetry is obtained. An extension to high-dimensional PT-symmetric systems is discussed. - Highlights: • A generalization of a Hamiltonian system of linear coupled oscillators with the parity-time (PT) symmetry is suggested. • It is found that an increase of the gain-loss parameter can stabilize the system. • A family of Hamiltonian functions for two coupled nonlinear oscillators with PT-symmetry is obtained.

  10. Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

    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.

  11. Effect of boundary on controlled memristor-based oscillator

    KAUST Repository

    Fouda, Mohamed E.

    2012-10-01

    Recently, the applications of memristors have spread into many fields and especially in the circuit theory. Many models have been proposed for the HP-memristor based on the window functions. In this paper, we introduce a complete mathematical analysis of the controlled reactance-less oscillator for two different window functions of Joglekar\\'s model (linear and nonlinear dopant drift) to discuss the effect of changing the window function on the oscillator\\'s behavior. The generalized necessary and sufficient conditions based on the circuit elements and control voltages for both the linear and nonlinear models are introduced. Moreover, closed form expressions for the oscillation frequency and duty cycle are derived for these models and verified using PSPICE simulations showing an excellent matching. Finally a comparison between the linear and nonlinear models which shows their effect on the oscillation frequency and conditions of oscillation is introduced. © 2012 IEEE.

  12. 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.

  13. Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

    Science.gov (United States)

    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.

  14. 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

  15. One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator.

    Science.gov (United States)

    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.

  16. Non-linear oscillations of fluid in a container

    NARCIS (Netherlands)

    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

  17. Modified Legendre Wavelets Technique for Fractional Oscillation Equations

    Directory of Open Access Journals (Sweden)

    Syed Tauseef Mohyud-Din

    2015-10-01

    Full Text Available Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinear fractional order oscillation equation into a fractional order recurrence relation and then Legendre wavelets method is applied on the converted problem. In order to check the efficiency and accuracy of the suggested modification, we have considered three problems namely: fractional order force-free Duffing–van der Pol oscillator, forced Duffing–van der Pol oscillator and higher order fractional Duffing equations. The obtained results are compared with the results obtained via other techniques.

  18. 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)

  19. Extreme Nonlinear Optics An Introduction

    CERN Document Server

    Wegener, Martin

    2005-01-01

    Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...

  20. Nonlinear Waves in Complex Systems

    DEFF Research Database (Denmark)

    2007-01-01

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

  1. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

    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

  2. Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic 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 [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.

  3. OnWien Bridge Oscillators as Modified Multi-vibrators

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2014-01-01

    A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals......A tutorial introduction to electrical oscilla- tors. Investigating Wien bridge oscillators as modified multi-vibrators. Introducing chaotic behavior into a Wien bridge oscillator by means of adding a simple nonlinear cir- cuit as a load of one of the amplifier input terminals...

  4. Period doubling of azimuthal oscillations on a non-neutral magnetized electron column

    International Nuclear Information System (INIS)

    Boswell, R.W.

    1985-01-01

    The low-frequency azimuthal oscillations on a non-neutral magnetized electron column of very low density are investigated. A perturbation analysis of the slow mode of the rigid rotator equilibrium is developed to illustrate the nature of large-amplitude fundamental-mode oscillations. The results of this theoretical analysis show two important characteristics: firstly, as the perturbation amplitude is increased the wave form ceases to be purely sinusoidal and shows period doubling. Secondly, above a certain threshold, all harmonics of the wave grow and the wave breaks. The results of the former are compared with a simple electron beam experiment and are found to be in good qualitative agreement. (author)

  5. Symmetries in Hall-like systems: microwave and nonlinear transport effects

    International Nuclear Information System (INIS)

    Torres, Manuel; Kunold, Alejandro

    2008-01-01

    In this work, we present a model to describe the nonlinear response to a dc electrical current of a two-dimensional electron system subjected to magnetic and microwave fields. Considering the separation of the electron coordinates into the non-commuting relative and guiding center coordinates, we obtain a unitary transformation that exactly solves the time-dependent Schroedinger equation in the presence of arbitrarily strong electric, magnetic and microwave fields. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We discuss results related to the recently discovered zero-resistance states and to the microwave-induced resistivity oscillations and the Hall-induced resistivity oscillations

  6. Phase-mixing of Langmuir oscillations in cold electron-positron-ion plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Maity, Chandan [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)

    2014-07-15

    Space-time evolution of Langmuir oscillations in a cold homogeneous electron-positron-ion plasma has been analyzed by employing a straightforward perturbation expansion method, showing phase-mixing and, thus, wave-breaking of excited oscillations at arbitrary amplitudes. Within an assumption of infinitely massive ions, an approximate phase-mixing time is found to scale as ω{sub pe}t{sub mix}∼[(6/δ{sup 2})((2−α){sup 5/2}/(1−α))]{sup 1/3}, where “δ” and “α” (= n{sub 0i}/n{sub 0e}) are the amplitude of perturbation and the ratio of equilibrium ion density to equilibrium electron density, respectively, and ω{sub pe}∼√(4πn{sub 0e}e{sup 2}/m) is the electron plasma frequency. The results presented on phase-mixing of Langmuir modes in multispecies plasmas are expected to be relevant to laboratory and astrophysical environments.

  7. Nonlinear electron transport in magnetized laser plasmas

    International Nuclear Information System (INIS)

    Kho, T.H.; Haines, M.G.

    1986-01-01

    Electron transport in a magnetized plasma heated by inverse bremsstrahlung is studied numerically using a nonlinear Fokker--Planck model with self-consistent E and B fields. The numerical scheme is described. Nonlocal transport is found to alter many of the transport coefficients derived from linear transport theory, in particular, the Nernst and Righi--Leduc effects, in addition to the perpendicular heat flux q/sub perpendicular/, are substantially reduced near critical surface. The magnetic field, however, remains strongly coupled to the nonlinear q/sub perpendicular/ and, as has been found in hydrosimulations, convective amplification of the magnetic field occurs in the overdense plasma

  8. On nonlinear control design for autonomous chaotic systems of integer and fractional orders

    International Nuclear Information System (INIS)

    Ahmad, Wajdi M.; Harb, Ahmad M.

    2003-01-01

    In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

  9. Nonlinear screening effect in an ultrarelativistic degenerate electron-positron gas

    International Nuclear Information System (INIS)

    Tsintsadze, N. L.; Rasheed, A.; Shah, H. A.; Murtaza, G.

    2009-01-01

    Nonlinear screening process in an ultrarelativistic degenerate electron-positron gas has been investigated by deriving a generalized nonlinear Poisson equation for the electrostatic potential. In the simple one-dimensional case, the nonlinear Poisson equation leads to Debye-like (Coulomb-like) solutions at distances larger (less) than the characteristic length. When the electrostatic energy is larger than the thermal energy, this nonlinear Poisson equation converts into the relativistic Thomas-Fermi equation whose asymptotic solution in three dimensions shows that the potential field goes to zero at infinity much more slowly than the Debye potential. The possibility of the formation of a bound state in electron-positron plasma is also indicated. Further, it is investigated that the strong spatial fluctuations of the potential field may reduce the screening length and that the root mean square of this spatial fluctuating potential goes to zero for large r rather slowly as compared to the case of the Debye potential.

  10. 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

  11. Nu shifts in betatron oscillations from uniform perturbations in the presence of non-linear magnetic guide fields

    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

  12. Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

    Science.gov (United States)

    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

  13. Nonlinearity, Viscosity and Air-Compressibility Effects on the Helmholtz Resonant Wave Motion Generated by an Oscillating Twin Body in a Free Surface

    Science.gov (United States)

    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.

  14. Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

    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

  15. Nonlinear oscillations of inviscid free drops

    Science.gov (United States)

    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.

  16. Neutrino oscillations in dense neutrino gases

    International Nuclear Information System (INIS)

    Samuel, S.

    1993-01-01

    We consider oscillations of neutrinos under conditions in which the neutrino density is sufficiently large that neutrino-neutrino interactions cannot be neglected. A formalism is developed to treat this highly nonlinear system. Numerical analysis reveals a rich array of phenomena. In certain gases, a self-induced Mikheyev-Smirnov-Wolfenstein effect occurs in which electron neutrinos are resonantly converted into muon neutrinos. In another relatively low-density gas, an unexpected parametric resonant conversion takes place. Finally, neutrino-neutrino interactions maintain coherence in one system for which a priori one expected decoherence

  17. Nonlinear interaction of powerful short electromagnetic pulses with an electron plasma

    International Nuclear Information System (INIS)

    Rao, N.N.; Yu, M.Y.; Shukla, P.K.

    1990-01-01

    The nonlinear interaction of powerful short electromagnetic pulses with a plasma consisting of two groups of electrons and immobile ions has been studied. It is shown that the interaction is governed by a nonlinear equation for the electromagnetic wave envelope and a driven nonlinear equation for the low-frequency electron fluctuations. The driver for the latter depends explicitly on the spatio-temporal evolution of the electromagnetic wave flux. It is found that, depending on the cold-to-hot electron density ratio, the localized pulse can propagate with sub- as well as supersonic velocities accompanied by compressional or rarefactional density perturbations. The conditions of existence for the different types of solitary pulses are obtained. The present investigation may be relevant to the study of wave-plasma interaction devices such as inertial fusion confinement as well as to ionospheric modification experiments. (author)

  18. Electron screening and kinetic-energy oscillations in a strongly coupled plasma

    International Nuclear Information System (INIS)

    Chen, Y.C.; Simien, C.E.; Laha, S.; Gupta, P.; Martinez, Y.N.; Mickelson, P.G.; Nagel, S.B.; Killian, T.C.

    2004-01-01

    We study equilibration of strongly coupled ions in an ultracold neutral plasma produced by photoionizing laser-cooled and trapped atoms. By varying the electron temperature, we show that electron screening modifies the equilibrium ion temperature. Even with few electrons in a Debye sphere, the screening is well described by a model using a Yukawa ion-ion potential. We also observe damped oscillations of the ion kinetic energy that are a unique feature of equilibration of a strongly coupled plasma

  19. Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma

    International Nuclear Information System (INIS)

    Wang Yunliang; Shukla, P. K.; Eliasson, B.

    2013-01-01

    We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schrödinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.

  20. David Shoenberg and the beauty of quantum oscillations

    Science.gov (United States)

    Pudalov, V. M.

    2011-01-01

    The quantum oscillation effect was discovered in Leiden in 1930, by W. J. de Haas and P. M. van Alphen when measuring magnetization, and by L. W. Shubnikov and de Haas when measuring magnetoresistance. Studying single crystals of bismuth, they observed oscillatory variations in the magnetization and magnetoresistance with magnetic field. Shoenberg, whose first research in Cambridge had been on bismuth, found that much stronger oscillations are observed when a bismuth sample is cooled to liquid helium temperature rather than liquid hydrogen, which had been used by de Haas. In 1938 Shoenberg went from Cambridge to Moscow to study these oscillations at Kapitza's Institute where liquid helium was available at that time. In 1947, J. Marcus observed similar oscillations in zinc and that persuaded Schoenberg to return to this research. After that, the dHvA effect became one of his main research topics. In particular, he developed techniques for quantitative measurement of this effect in many metals. A theoretical explanation of quantum oscillations was given by L. Onsager in 1952, and an analytical quantitative theory by I. M. Lifshitz and A. M. Kosevich in 1955. These theoretical advances seemed to provide a comprehensive description of the effect. Since then, quantum oscillations have been widely used as a tool for measuring Fermi surface extremal cross-sections and all-angle electron scattering times. In his pioneering experiments of the 1960's, Shoenberg revealed the richness and deep essence of the quantum oscillation effect and showed how the beauty of the effect is disclosed under nonlinear conditions imposed by interactions in the system under study. It was quite surprising that "magnetic interaction" conditions could cause the apparently weak quantum oscillation effect to have such strong consequences as breaking the sample into magnetic (now called "Shoenberg") domains and forming an inhomogeneous magnetic state. With his contributions to the field of quantum

  1. David Schoenberg and the beauty of quantum oscillations

    International Nuclear Information System (INIS)

    Pudalov, V.M.

    2012-01-01

    The quantum oscillation effect was discovered in Leiden, in 1930, by W.J. de Haas and P.M. van Alphen in magnetization measurement, and by L.W. Shubnikov and de Haas - in magnetoresistance. Studying single crystals of bismuth, they observed oscillatory variations of magnetization and magnetoresistance with magnetic field. Shoenberg, whose first research in Cambridge had been on bismuth, found that much stronger oscillations are observed when a bismuth sample is cooled to liquid helium rather than to liquid hydrogen, which had been used by de Haas. In 1938 Shoenberg came from Cambridge to Moscow to study these oscillations at Kapitza Institute where liquid helium was available at that time. In 1947, J. Marcus observed similar oscillations in zinc, that persuaded Shoenberg to return to this research, and, since then, the dHvA effect had been one of his main research topic. In particular, he developed techniques for quantitative measurements of the effect in many metals. Theoretical explanation of quantum oscillations was given by L. Onsager in 1952, and the analytical quantitative theory by I.M. Lifshitz and A.M. Kosevich in 1955. These theoretical advancements seemed to provide a comprehensive description of the effect. Since then, quantum oscillations were commonly considered as a tool for measuring Fermi surface extremal cross-sections and all-angle electron scattering times. However, in his pioneering experiments in 1960s, Shoenberg revealed the richness and deep essence of the quantum oscillation effect and showed how the beauty of the effect is disclosed under nonlinear conditions imposed by interactions in the system under study. It was quite unexpected, that under 'magnetic interaction' conditions, the apparently weak effect of quantum oscillations may lead to such strong consequences as breaking the sample into magnetic (now called 'Shoenberg') domains and the formation of an inhomogeneous magnetic state. Owing to his contribution to the field of quantum

  2. 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.

  3. Observation of a new plasma regime with stationary electron temperature oscillations on Tore Supra

    International Nuclear Information System (INIS)

    Artaud, J.F.; Giruzzi, G.; Imbeaux, F.; Segui, J.L.; Garbet, X.

    2003-01-01

    This document is a copy of the slides presented on the 9. joint US-European Transport Task Force meeting. The first part is devoted to the experimental observations of a new tokamak plasma regime with stationary electron temperature oscillations. The oscillations appear on ECE spontaneously, sometimes associated with a transition to the LHEP regime. The second part presents an interpretation of these oscillations by analogy with a predator-prey system. (A.L.B.)

  4. Nonlinear and Nonsymmetric Single-Molecule Electronic Properties Towards Molecular Information Processing.

    Science.gov (United States)

    Tamaki, Takashi; Ogawa, Takuji

    2017-09-05

    This review highlights molecular design for nonlinear and nonsymmetric single-molecule electronic properties such as rectification, negative differential resistance, and switching, which are important components of future single-molecule information processing devices. Perspectives on integrated "molecular circuits" are also provided. Nonlinear and nonsymmetric single-molecule electronics can be designed by utilizing (1) asymmetric molecular cores, (2) asymmetric anchoring groups, (3) an asymmetric junction environment, and (4) asymmetric electrode materials. This review mainly focuses on the design of molecular cores.

  5. Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

    Science.gov (United States)

    Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul

    2012-09-01

    In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

  6. Model-independent quantitative measurement of nanomechanical oscillator vibrations using electron-microscope linescans

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Huan; Fenton, J. C.; Chiatti, O. [London Centre for Nanotechnology, University College London, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Warburton, P. A. [London Centre for Nanotechnology, University College London, 17–19 Gordon Street, London WC1H 0AH (United Kingdom); Department of Electronic and Electrical Engineering, University College London, Torrington Place, London WC1E 7JE (United Kingdom)

    2013-07-15

    Nanoscale mechanical resonators are highly sensitive devices and, therefore, for application as highly sensitive mass balances, they are potentially superior to micromachined cantilevers. The absolute measurement of nanoscale displacements of such resonators remains a challenge, however, since the optical signal reflected from a cantilever whose dimensions are sub-wavelength is at best very weak. We describe a technique for quantitative analysis and fitting of scanning-electron microscope (SEM) linescans across a cantilever resonator, involving deconvolution from the vibrating resonator profile using the stationary resonator profile. This enables determination of the absolute amplitude of nanomechanical cantilever oscillations even when the oscillation amplitude is much smaller than the cantilever width. This technique is independent of any model of secondary-electron emission from the resonator and is, therefore, applicable to resonators with arbitrary geometry and material inhomogeneity. We demonstrate the technique using focussed-ion-beam–deposited tungsten cantilevers of radius ∼60–170 nm inside a field-emission SEM, with excitation of the cantilever by a piezoelectric actuator allowing measurement of the full frequency response. Oscillation amplitudes approaching the size of the primary electron-beam can be resolved. We further show that the optimum electron-beam scan speed is determined by a compromise between deflection of the cantilever at low scan speeds and limited spatial resolution at high scan speeds. Our technique will be an important tool for use in precise characterization of nanomechanical resonator devices.

  7. Comparative analysis of gyrotron backward-wave oscillators operating at different cyclotron harmonics

    International Nuclear Information System (INIS)

    Yeh, Y.S.; Chang, T.H.; Wu, T.S.

    2004-01-01

    A comparative analysis between the fundamental and second cyclotron harmonics of gyrotron backward-wave oscillators (gyro-BWOs) is presented. The simulation results reveal that nonlinear field contraction is a common feature for both harmonic interactions. Besides, the electron transit angle, used to characterize the axial modes of the fundamental harmonic TE 11 mode at the start-oscillation conditions, is found to be applicable even for the second harmonic TE 21 mode. Each axial mode of either the fundamental harmonic TE 11 or the second harmonic TE 21 modes is maintained at a constant value of the electron transit angle while changing the operating parameters, such as magnetic field and beam voltage. Extensive numerical calculations are conducted for the start-oscillation currents and tuning properties. Moreover, single-mode operating regimes are suggested where the second harmonic TE 21 gyro-BWO could generate a considerable output power, comparing with the fundamental harmonic TE 11 gyro-BWO

  8. Electronically induced nuclear transitions - temperature dependence and Rabi oscillations

    International Nuclear Information System (INIS)

    Niez, J.J.

    2002-01-01

    This paper deals with a nucleus electromagnetically coupled with the bound states of its electronic surroundings. It describes the temperature dependence of its dynamics and the onset of potential Rabi oscillations by means of a Master Equation. The latter is generalized in order to account for possible strong resonances. Throughout the paper the approximation schemes are discussed and tested. (authors)

  9. An application of nonlinear supratransmission to the propagation of binary signals in weakly damped, mechanical systems of coupled oscillators

    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

  10. Nonlinear Dynamics of a Magnetically Driven Duffing-Type Spring-Magnet Oscillator in the Static Magnetic Field of a Coil

    Science.gov (United States)

    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…

  11. Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

    Science.gov (United States)

    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.

  12. Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

    Science.gov (United States)

    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.

  13. Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

    Science.gov (United States)

    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.

  14. 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 ?...

  15. Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

    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.

  16. Suppression of chaos by weak resonant excitations in a non-linear oscillator with a non-symmetric potential

    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

  17. Nonlinear asteroseismology: insight from amplitude and frequency modulations of oscillation modes in compact pulsators from Kepler photometry

    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.

  18. Neuromorphic computing with nanoscale spintronic oscillators.

    Science.gov (United States)

    Torrejon, Jacob; Riou, Mathieu; Araujo, Flavio Abreu; Tsunegi, Sumito; Khalsa, Guru; Querlioz, Damien; Bortolotti, Paolo; Cros, Vincent; Yakushiji, Kay; Fukushima, Akio; Kubota, Hitoshi; Yuasa, Shinji; Stiles, Mark D; Grollier, Julie

    2017-07-26

    Neurons in the brain behave as nonlinear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behaviour to realize high-density, low-power neuromorphic computing will require very large numbers of nanoscale nonlinear oscillators. A simple estimation indicates that to fit 10 8 oscillators organized in a two-dimensional array inside a chip the size of a thumb, the lateral dimension of each oscillator must be smaller than one micrometre. However, nanoscale devices tend to be noisy and to lack the stability that is required to process data in a reliable way. For this reason, despite multiple theoretical proposals and several candidates, including memristive and superconducting oscillators, a proof of concept of neuromorphic computing using nanoscale oscillators has yet to be demonstrated. Here we show experimentally that a nanoscale spintronic oscillator (a magnetic tunnel junction) can be used to achieve spoken-digit recognition with an accuracy similar to that of state-of-the-art neural networks. We also determine the regime of magnetization dynamics that leads to the greatest performance. These results, combined with the ability of the spintronic oscillators to interact with each other, and their long lifetime and low energy consumption, open up a path to fast, parallel, on-chip computation based on networks of oscillators.

  19. 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.

  20. 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.

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

    International Nuclear Information System (INIS)

    Zhu Hongjun; Xiong Shijie

    2010-01-01

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

  2. Probing collective oscillation of d-orbital electrons at the nanoscale

    Science.gov (United States)

    Dhall, Rohan; Vigil-Fowler, Derek; Houston Dycus, J.; Kirste, Ronny; Mita, Seiji; Sitar, Zlatko; Collazo, Ramon; LeBeau, James M.

    2018-02-01

    Here, we demonstrate that high energy electrons can be used to explore the collective oscillation of s, p, and d orbital electrons at the nanometer length scale. Using epitaxial AlGaN/AlN quantum wells as a test system, we observe the emergence of additional features in the loss spectrum with the increasing Ga content. A comparison of the observed spectra with ab-initio theory reveals that the origin of these spectral features lies in excitations of 3d-electrons contributed by Ga. We find that these modes differ in energy from the valence electron plasmons in Al1-xGaxN due to the different polarizabilities of the d electrons. Finally, we study the dependence of observed spectral features on the Ga content, lending insights into the origin of these spectral features, and their coupling with electron-hole excitations.

  3. Response of a core coherent density oscillation on electron cyclotron resonance heating in Heliotron J plasma

    Science.gov (United States)

    Kobayashi, T.; Kobayashi, S.; Lu, X. X.; Kenmochi, N.; Ida, K.; Ohshima, S.; Yamamoto, S.; Kado, S.; Kokubu, D.; Nagasaki, K.; Okada, H.; Minami, T.; Otani, Y.; Mizuuchi, T.

    2018-01-01

    We report properties of a coherent density oscillation observed in the core region and its response to electron cyclotron resonance heating (ECH) in Heliotron J plasma. The measurement was performed using a multi-channel beam emission spectroscopy system. The density oscillation is observed in a radial region between the core and the half radius. The poloidal mode number is found to be 1 (or 2). By modulating the ECH power with 100 Hz, repetition of formation and deformation of a strong electron temperature gradient, which is likely ascribed to be an electron internal transport barrier, is realized. Amplitude and rotation frequency of the coherent density oscillation sitting at the strong electron temperature gradient location are modulated by the ECH, while the poloidal mode structure remains almost unchanged. The change in the rotation velocity in the laboratory frame is derived. Assuming that the change of the rotation velocity is given by the background E × B velocity, a possible time evolution of the radial electric field was deduced.

  4. Electron-beam driven relaxation oscillations in ferroelectric nanodisks

    Energy Technology Data Exchange (ETDEWEB)

    Ng, Nathaniel; Ahluwalia, Rajeev [Institute of High Performance Computing, Singapore 138632 (Singapore); Kumar, Ashok [CSIR-National Physical Laboratory, Delhi 110012 (India); Srolovitz, David J. [Department of Materials Science and Engineering and Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States); Chandra, Premala [Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854 (United States); Scott, James F. [Department of Physics, Cavendish Laboratory, J. J. Thompson Avenue, Cambridge CB3 0HE (United Kingdom); Department of Chemistry and Department of Physics, University of St. Andrews, St. Andrews YX16 9ST (United Kingdom)

    2015-10-12

    Using a combination of computational simulations, atomic-scale resolution imaging and phenomenological modelling, we examine the underlying mechanism for nanodomain restructuring in lead zirconate titanate nanodisks driven by electron beams. The observed subhertz nanodomain dynamics are identified with relaxation oscillations where the charging/discharging cycle time is determined by saturation of charge traps and nanodomain wall creep. These results are unusual in that they indicate very slow athermal dynamics in nanoscale systems, and possible applications of gated versions are discussed.

  5. Design of memristive interface between electronic neurons

    Science.gov (United States)

    Gerasimova, S. A.; Mikhaylov, A. N.; Belov, A. I.; Korolev, D. S.; Guseinov, D. V.; Lebedeva, A. V.; Gorshkov, O. N.; Kazantsev, V. B.

    2018-05-01

    Nonlinear dynamics of two electronic oscillators coupled via a memristive device has been investigated. Such model mimics the interaction between synaptically coupled brain neurons with the memristive device imitating neuron axon. The synaptic connection is provided by the adaptive behavior of memristive device that changes its resistance under the action of spike-like activity. Mathematical model of such a memristive interface has been developed to describe and predict the experimentally observed regularities of forced synchronization of neuron-like oscillators.

  6. Flutter analysis of an airfoil with multiple nonlinearities and uncertainties

    Directory of Open Access Journals (Sweden)

    Haitao Liao

    2013-09-01

    Full Text Available An original method for calculating the limit cycle oscillations of nonlinear aero-elastic system is presented. The problem of determining the maximum vibration amplitude of limit cycle is transformed into a nonlinear optimization problem. The harmonic balance method and the Floquet theory are selected to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated and used to analyse the limit cycle oscillations of an airfoil with multiple nonlinearities and uncertainties. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

  7. Nonlinear magnetic electron tripolar vortices in streaming plasmas.

    Science.gov (United States)

    Vranjes, J; Marić, G; Shukla, P K

    2000-06-01

    Magnetic electron modes in nonuniform magnetized and unmagnetized streaming plasmas, with characteristic frequencies between the ion and electron plasma frequencies and at spatial scales of the order of the collisionless skin depth, are studied. Two coupled equations, for the perturbed (in the case of magnetized plasma) or self-generated (for the unmagnetized plasma case) magnetic field, and the temperature, are solved in the strongly nonlinear regime and stationary traveling solutions in the form of tripolar vortices are found.

  8. Prediction of pilot induced oscillations

    Directory of Open Access Journals (Sweden)

    Valentin PANĂ

    2011-03-01

    Full Text Available An important problem in the design of flight-control systems for aircraft under pilotedcontrol is the determination of handling qualities and pilot-induced oscillations (PIO tendencieswhen significant nonlinearities exist in the vehicle description. The paper presents a method to detectpossible pilot-induced oscillations of Category II (with rate and position limiting, a phenomenonusually due to a misadaptation between the pilot and the aircraft response during some tasks in whichtight closed loop control of the aircraft is required from the pilot. For the analysis of Pilot in the LoopOscillations an approach, based on robust stability analysis of a system subject to uncertainparameters, is proposed. In this analysis the nonlinear elements are substituted by linear uncertainparameters. This approach assumes that PIO are characterized by a limit cycle behavior.

  9. Phase-locked Josephson soliton oscillators

    DEFF Research Database (Denmark)

    Holst, T.; Hansen, Jørn Bindslev; Grønbech-Jensen, N.

    1991-01-01

    Detailed experimental characterization of the phase-locking at both DC and at microwave frequencies is presented for two closely spaced Josephson soliton (fluxon) oscillators. In the phase-locked state, the radiated microwave power exhibited an effective gain. With one common bias source......, a frequency tunability of the phase-locked oscillators up to 7% at 10 GHz was observed. The interacting soliton oscillators were modeled by two inductively coupled nonlinear transmission lines...

  10. The landscape of nonlinear structural dynamics: an introduction.

    Science.gov (United States)

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

    2015-09-28

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

  11. Ion-acoustic nonlinear periodic waves in electron-positron-ion plasma

    International Nuclear Information System (INIS)

    Chawla, J. K.; Mishra, M. K.

    2010-01-01

    Ion-acoustic nonlinear periodic waves, namely, ion-acoustic cnoidal waves have been studied in electron-positron-ion plasma. Using reductive perturbation method and appropriate boundary condition for nonlinear periodic waves, the Korteweg-de Vries (KdV) equation is derived for the system. The cnoidal wave solution of the KdV equation is discussed in detail. It is found that the frequency of the cnoidal wave is a function of its amplitude. It is also found that the positron concentration modifies the properties of the ion-acoustic cnoidal waves. The existence regions for ion-acoustic cnoidal wave in the parameters space (p,σ), where p and σ are the positron concentration and temperature ratio of electron to positron, are discussed in detail. In the limiting case these ion-acoustic cnoidal waves reduce to the ion-acoustic soliton solutions. The effect of other parameters on the characteristics of the nonlinear periodic waves is also discussed.

  12. A multi-harmonic generalized energy balance method for studying autonomous oscillations of nonlinear conservative systems

    Science.gov (United States)

    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.

  13. Relativistic nonlinear waves of cyclotron in electron and electron-ion plasmas

    International Nuclear Information System (INIS)

    Bruno, R.

    1981-12-01

    Dispersion relations for electron-cyclotron and ion-cyclotron waves are examined in two models of plasmas, the first propagating in fluent electronic plasmas (''streaming'') as well as in fluent electron-ionic plasmas, and the last in fluent electron-ionic plasmas. The identification of the propagation modes is realized with the aid of a special technique of polinomial expantion of the dispersion relation in the limit of large frequencies and short wavelenghts. The analisys so developed on these dispersion relations for fluent plasmas show that: (i) the wave amplitudes are frequency dependent; (ii) the ''resonances'' frequencies of the respective estationary plasmas must be re-examined with the relations between wave amplitudes and the propagation frequencies near these frequencies; (iii) the electric field amplitudes for the non-linear waves of electron-cyclotron and ion-cyclotron go to zero in the limits of the respective cyclotron frequencies in both fluent plasma models. (M.W.O.) [pt

  14. Oscillation mode transformation of edge magnetoplasmons in two-dimensional electron system on liquid-helium surface

    International Nuclear Information System (INIS)

    Yamanaka, Shuji; Yayama, Hideki; Arai, Toshikazau; Anju Sawada, Anju; Fukuda, Akira

    2013-01-01

    We measured the resonance spectra of edge magnetoplasmon (EMP) oscillations in a two-dimensional (2D) electron system located on a liquid-helium surface below 1.1 K. Systematic measurements of the resonance frequency and the damping rate as a function of the lateral confinement electric field strength shows clear evidence of the oscillation mode transformation. A pronounced change corresponding to the mode transformation was observed in the damping rate. When 2D electrons are confined in a strong lateral electric field, the damping is weak. As the lateral confinement electric field is reduced below a certain threshold value, an abrupt enhancement of the damping rate is observed. We hypothesize that the weak damping mode in the strong lateral confinement electric field is the compressive density oscillation of the electrons near the edge (conventional EMP) and the strong damping mode in the weak confinement field is the coupled mode of conventional EMP and the boundary displacement wave (BDW). The observation of the strong damping in the BDW-EMP coupled mode is a manifestation of the nearly incompressible feature of strongly interacting classical electrons, which agrees with earlier theoretical predictions.

  15. A Conspiracy of Oscillators

    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....

  16. Electron heating via self-excited plasma series resonance in geometrically symmetric multi-frequency capacitive plasmas

    International Nuclear Information System (INIS)

    Schüngel, E; Brandt, S; Schulze, J; Donkó, Z; Korolov, I; Derzsi, A

    2015-01-01

    The self-excitation of plasma series resonance (PSR) oscillations plays an important role in the electron heating dynamics in capacitively coupled radio-frequency (CCRF) plasmas. In a combined approach of PIC/MCC simulations and a theoretical model based on an equivalent circuit, we investigate the self-excitation of PSR oscillations and their effect on the electron heating in geometrically symmetric CCRF plasmas driven by multiple consecutive harmonics. The discharge symmetry is controlled via the electrical asymmetry effect (EAE), i.e. by varying the total number of harmonics and tuning the phase shifts between them. It is demonstrated that PSR oscillations will be self-excited under both symmetric and asymmetric conditions, if (i) the charge–voltage relation of the plasma sheaths deviates from a simple quadratic behavior and (ii) the inductance of the plasma bulk exhibits a temporal modulation. These two effects have been neglected up to now, but we show that they must be included in the model in order to properly describe the nonlinear series resonance circuit and reproduce the self-excitation of PSR oscillations, which are observed in the electron current density resulting from simulations of geometrically symmetric CCRF plasmas. Furthermore, the effect of PSR self-excitation on the discharge current and the plasma properties, such as the potential profile, is illustrated by applying Fourier analysis. High-frequency oscillations in the entire spectrum between the applied frequencies and the local electron plasma frequency are observed. As a consequence, the electron heating is strongly enhanced by the presence of PSR oscillations. A complex electron heating dynamics is found during the expansion phase of the sheath, which is fully collapsed, when the PSR is initially self-excited. The nonlinear electron resonance heating (NERH) associated with the PSR oscillations causes a spatial asymmetry in the electron heating. By discussing the resulting ionization

  17. Nonlinear analysis on power reactor dynamics

    International Nuclear Information System (INIS)

    Konno, H.; Hayashi, K.

    1997-01-01

    We have shown that the origin of intermittent oscillation observed in a BWR can be ascribed to the couplings among the spatial modes starting from a non-linear center manifold equation with a delay-time and a spatial diffusion. We can reduce the problem to the stochastic coupled van der Pol oscillators with non-linear coupling term. This non-linear coupling term plays an important role to break the symmetry of the system and the non-linear damping of the system. The phenomenological generalization of van der Pol oscillator coupled by the linear diffusion term is not appropriate for describing the nuclear power reactors. However, one must start from the coupled partial differential equations by taking into account the two energy group neutrons, the thermo-hydraulic equations including two-phase flow. In this case, the diffusion constant must be a complex number as is demonstrated in a previous paper. The results will be reported in the near future. (J.P.N.)

  18. A tapered multi-gap multi-aperture pseudospark-sourced electron gun based X-band slow wave oscillator

    Science.gov (United States)

    Kumar, N.; Lamba, R. P.; Hossain, A. M.; Pal, U. N.; Phelps, A. D. R.; Prakash, R.

    2017-11-01

    The experimental study of a tapered, multi-gap, multi-aperture pseudospark-sourced electron gun based X-band plasma assisted slow wave oscillator is presented. The designed electron gun is based on the pseudospark discharge concept and has been used to generate a high current density and high energy electron beam simultaneously. The distribution of apertures has been arranged such that the field penetration potency inside the backspace of the hollow-cathode is different while passing through the tapered gap region. This leads to non-concurrent ignition of the discharge through all the channels which is, in general, quite challenging in the case of multi-aperture plasma cathode electron gun geometries. Multiple and successive hollow cathode phases are reported from this electron gun geometry, which have been confirmed using simulations. This geometry also has led to the achievement of ˜71% fill factor inside the slow wave oscillator for an electron beam of energy of 20 keV and a beam current density in the range of 115-190 A/cm2 at a working argon gas pressure of 18 Pa. The oscillator has generated broadband microwave output in the frequency range of 10-11.7 GHz with a peak power of ˜10 kW for ˜50 ns.

  19. Electron non-linearities in Langmuir waves with application to beat-wave experiments

    International Nuclear Information System (INIS)

    Bell, A.R.; Gibbon, P.

    1988-01-01

    Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)

  20. Considerations on 'Harmonic balancing approach to nonlinear oscillations of a punctual charge in the electric field of charged ring'

    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.

  1. Oscillator, neutron modulator

    International Nuclear Information System (INIS)

    Agaisse, R.; Leguen, R.; Ombredane, D.

    1960-01-01

    The authors present a mechanical device and an electronic control circuit which have been designed to sinusoidally modulate the reactivity of the Proserpine atomic pile. The mechanical device comprises an oscillator and a mechanism assembly. The oscillator is made of cadmium blades which generate the reactivity oscillation. The mechanism assembly comprises a pulse generator for cycle splitting, a gearbox and an engine. The electronic device comprises or performs pulse detection, an on-off device, cycle pulse shaping, phase separation, a dephasing amplifier, electronic switches, counting scales, and control devices. All these elements are briefly presented

  2. Origin of fine oscillations in the photoluminescence spectrum of 2-dimensional electron gas formed in AlGaN/GaN high electron mobility transistor structures

    Energy Technology Data Exchange (ETDEWEB)

    Jana, Dipankar, E-mail: dip2602@gmail.com; Porwal, S.; Oak, S. M.; Sharma, T. K., E-mail: tarun@rrcat.gov.in [Semiconductor Physics and Devices Laboratory, Raja Ramanna Centre for Advanced Technology, Indore 452013, Madhya Pradesh (India); Jain, Anubha [Solid State Physics Laboratory, Lucknow Road, New Delhi 110054 (India)

    2015-10-28

    An unambiguous identification of the fine oscillations observed in the low temperature photoluminescence (PL) spectra of AlGaN/GaN based high electron mobility transistor (HEMT) structures is carried out. In literature, such oscillations have been erroneously identified as the sub-levels of 2-dimensional electron gas (2DEG) formed at AlGaN/GaN heterointerface. Here, the origin of these oscillations is probed by performing the angle dependent PL and reflectivity measurements under identical conditions. Contrary to the reports available in literature, we find that the fine oscillations are not related to 2DEG sub-levels. The optical characteristics of these oscillations are mainly governed by an interference phenomenon. In particular, peculiar temperature dependent redshift and excitation intensity dependent blueshift, which have been interpreted as the characteristics of 2DEG sub-levels in HEMT structures by other researchers, are understood by invoking the wavelength and temperature dependence of the refractive index of GaN within the framework of interference phenomenon. The results of other researchers are also consistently explained by considering the fine oscillatory features as the interference oscillations.

  3. Nonlinear relativistic plasma resonance: Renormalization group approach

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-02-15

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

  4. Oscillators and operational amplifiers

    OpenAIRE

    Lindberg, Erik

    2005-01-01

    A generalized approach to the design of oscillators using operational amplifiers as active elements is presented. A piecewise-linear model of the amplifier is used so that it make sense to investigate the eigenvalues of the Jacobian of the differential equations. The characteristic equation of the general circuit is derived. The dynamic nonlinear transfer characteristic of the amplifier is investigated. Examples of negative resistance oscillators are discussed.

  5. Self-focusing of electron bunches in a nonlinear plasma

    International Nuclear Information System (INIS)

    Krasovitskii, V.B.; Osmolovsky, S.I.

    1994-01-01

    The phenomena of self-focusing of previously bunched electron beam in hot nonlinear plasma with the frequency which less than the plasma one is studied. It is established that influence of the Miller's force nonlinearity of the plasma don't leads to self-focusing breaking. However in the case of a dense beam, the appearance strong resonant electric field is followed by the change of the sign of the plasma dielectric constant to positive at the beam axis. But the dielectric constant remain negative at the outer of the beam

  6. Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

    Science.gov (United States)

    Masood, W.; Zahoor, Sara; Gul-e-Ali, Ahmad, Ali

    2016-09-01

    Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existence regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.

  7. Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with non-Maxwellian electrons

    Energy Technology Data Exchange (ETDEWEB)

    Masood, W. [COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad (Pakistan); National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan); Zahoor, Sara [COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad (Pakistan); Gul-e-Ali [Theoretical Plasma Physics Group, Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Ahmad, Ali, E-mail: aliahmad79@hotmail.com [National Centre for Physics, Shahdara Valley Road, Islamabad (Pakistan)

    2016-09-15

    Nonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with non-Maxwellian electrons. The dissipation is incorporated in the system through ion-neutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled drift-ion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existence regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.

  8. Chaotic solar oscillations

    Energy Technology Data Exchange (ETDEWEB)

    Blacher, S; Perdang, J [Institut d' Astrophysique, B-4200 Cointe-Ougree (Belgium)

    1981-09-01

    A numerical experiment on Hamiltonian oscillations demonstrates the existence of chaotic motions which satisfy the property of phase coherence. It is observed that the low-frequency end of the power spectrum of such motions is remarkably similar in structure to the low-frequency SCLERA spectra. Since the smallness of the observed solar amplitudes is not a sufficient mathematical ground for inefficiency of non-linear effects the possibility of chaos among solar oscillations cannot be discarded a priori.

  9. Chaotic dynamics of electron beam with virtual cathode in the bounded system

    Energy Technology Data Exchange (ETDEWEB)

    Anfinogentov, V G [College of Applied Science, Saratov (Russian Federation)

    1997-12-31

    The electron beam with a virtual cathode in the bounded system with feedback was studied with the help of PIC simulation. Different types of nonlinear behavior were found. The typical structures were recognized and the effect of feedback on the structure formation was investigated. Relations between nonlinear oscillations and structure formation and interaction are discussed. (author). 5 figs., 7 refs.

  10. Chaotic dynamics of electron beam with virtual cathode in the bounded system

    International Nuclear Information System (INIS)

    Anfinogentov, V.G.

    1996-01-01

    The electron beam with a virtual cathode in the bounded system with feedback was studied with the help of PIC simulation. Different types of nonlinear behavior were found. The typical structures were recognized and the effect of feedback on the structure formation was investigated. Relations between nonlinear oscillations and structure formation and interaction are discussed. (author). 5 figs., 7 refs

  11. Asymmetric Collision of Concepts: Why Eigenstates Alone are Not Enough for Neutrino Flavor Oscillations

    OpenAIRE

    Williams, John Michael

    2000-01-01

    The symmetry of the problem of the apparent deficit in upward-going atmospheric muon neutrinos reveals two possible, nonexclusive kinds of solution: Nonlinearity in distance or nonlinearity in angle of observation. Nonlinearity in distance leads to the most popular theory for the atmospheric problem, neutrino flavor oscillations. If the observed deficit is caused by oscillations and not, say, flavor-changing or other weak-force scattering, neutrinos must be massive. But, if flavor oscillation...

  12. Saturation of drift instabilities by ExB advection of resonant electrons

    International Nuclear Information System (INIS)

    Dimits, A.M.

    1990-01-01

    Saturation of the collisionless and weakly collisional drift instabilities by nonlinear ExB advection of resonant electrons is considered. The nonlinear ExB advection of the resonant electrons around the O points and X points of the potential shuts off the linear phase shift between the electron density and the potential, and hence the linear growth, and produces residual oscillations at the ExB-trapping frequency. Two analytical solutions of a three-mode model of Lee et al. [Phys. Fluids 27, 2652 (1984)], which describes the saturation of drift waves by this mechanism, are found. The first is an exact solution in the form of a steadily propagating wave of constant amplitude, and is relevant when electron pitch-angle scattering is present. The second is an approximate time-dependent analytical solution, obtained using the method of O'Neil [Phys. Fluids 8, 2255 (1965)], and is relevant to the collisionless case. The predictions that follow from this solution for the saturation level and for the amplitude oscillation frequency are in excellent agreement with the direct numerical solutions of the three-mode system

  13. Memcapacitor model and its application in chaotic oscillator with memristor.

    Science.gov (United States)

    Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching

    2017-01-01

    Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

  14. Nonlinear spin fluctuations in the Fermi liquid of itinerant electron ferromagnets

    International Nuclear Information System (INIS)

    Solontsov, A.; Lacroix, C.

    2003-01-01

    A microscopic derivation of nonlinear equations of magnetic dynamics for itinerant ferromagnets is presented within the electron Fermi liquid model accounting for both long-range Coulomb and short-range interactions of quasiparticles, which founds the basis for the phenomenological description of nonlinear spin fluctuations (SF) using the Ginsburg-Landau formalism. Crystal lattice is shown to play a significant role screening the long-range Coulomb interaction and affecting magnetic dynamics. The spectrum of longitudinal SF with account of nonlinear mode-mode coupling is shown to result from an interplay of quasielastic SF and inelastic excitations near the magnon frequencies, both having mainly the nonlinear nature and arising due to their emission (absorption) by magnons

  15. Reactor oscillator - I - III, Part I; Reaktorski oscilator - I-III, I Deo

    Energy Technology Data Exchange (ETDEWEB)

    Lolic, B [Institute of Nuclear Sciences Boris Kidric, Laboratorija za fiziku reaktora, Vinca, Beograd (Serbia and Montenegro)

    1961-12-15

    Project 'Reactor oscillator' covers the following activities: designing reactor oscillators for reactors RA and RB with detailed engineering drawings; constructing and mounting of the oscillator; designing and constructing the appropriate electronic equipment for the oscillator; measurements at the RA and RB reactors needed for completing the oscillator construction.

  16. Nonlinear Cyclotron absorption of a hole doppleron in cadmium

    Energy Technology Data Exchange (ETDEWEB)

    Voloshin, I.F.; Bugal' ter, G.A.; Demikhovskii, V.Y.; Fisher, L.M.; Yudin, V.A.

    1977-10-01

    We investigated experimentally the nonlinear behavior of the impedance of a cadmium plate in the region of existence of the hole doppleron. It is shown theoretically that this phenomenon can be attributed to nonlinear cyclotron absorption of the wave in the metal. A theory of nonlinear cyclotron absorption of a hole doppleron in cadmium is constructed. The nonlinearity is due to the influence of the wave magnetic field H that alters the trajectories of the resonant electrons responsible for the cyclotron asorption. The Lorentz force connected with the field H modulates the particle velocity along the magnetic field at a characteristic frequency ..omega../sub 0/ proportional to the square root of the wave amplitude. The modulation of the longitudinal particle velocity leads to violation of the condition of their resonant interaction with the wave, as a result of which the absorption coefficient decreases. The nonlinearity is significant when the frequency ..omega../sub 0/ is large compared with the electron-collision frequency. A decrease of the cyclotron absorption changes radically the picture of the surface-impedance oscillations of the plate in the magnetic field. We studied in the experiment the influence of the temperature, of the angle of inclination of the magnetic field, and of the frequency on the nonlinear-effect threshold field that separates the regions of linear and nonlinear behavior of the sample impedance. The measurement results are in qualitative agreement with the conclusions of the theory.

  17. Nonlinear trapped electron mode and anomalous heat transport in tokamaks

    International Nuclear Information System (INIS)

    Kaw, P.K.

    1982-01-01

    We take the phenomenological point of view that the anomalous electron thermal conductivity produced by the non-linear trapped electron mode should also influence the stability properties of the mode itself. Using a model equation, we show that this effect makes the mode self-stabilizing. A simple expression for the anomalous thermal conductivity is derived, and its scaling properties are discussed. (orig.)

  18. Hyperchaotic circuit with damped harmonic oscillators

    DEFF Research Database (Denmark)

    Lindberg, Erik; Murali, K.; Tamasevicius, A.

    2001-01-01

    A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance, two ideal...... capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...... by means of numerical integration of the appropriate differential equations....

  19. Nonlinear effects on Turing patterns: Time oscillations and chaos

    KAUST Repository

    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

  20. Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

    Directory of Open Access Journals (Sweden)

    A. M. El-Naggar

    2015-11-01

    Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.

  1. On the Possibility of Using Nonlinear Elements for Landau Damping in High-Intensity Beams

    Energy Technology Data Exchange (ETDEWEB)

    Alexahin, Y. [Fermilab; Gianfelice-Wendt, E. [Fermilab; Lebedev, V. [Fermilab; Valishev, A. [Fermilab

    2016-09-30

    Direct space-charge force shifts incoherent tunes downwards from the coherent ones breaking the Landau mechanism of coherent oscillations damping at high beam intensity. To restore it nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a “nonlinear integrable optics” insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II (PIP II) parameters the required nonlinear tune shift can be created without destroying the dynamic aperture.

  2. 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.

  3. J-PARC Press Release: Electron neutrino oscillation detected at T2K

    CERN Multimedia

    T2K Press Office

    2011-01-01

    Tsukuba, Japan, June 15, 2011. The T2K experiment, whose primary purpose is to study neutrino interactions at a large distance from their source, has detected 6 electron neutrino candidate events based on the data collected before March 11, 2011. For the first time, it was possible to observe an indication that muon neutrinos are able to transform into electron neutrinos over a distance of 295 km through the quantum mechanical phenomena of neutrino flavor oscillations.   The Super-Kamiokande detector, in Japan. © 2011, High Energy Accelerator Research Organization, KEK. The T2K experiment is searching for the neutrino oscillation phenomena, where particular types of neutrinos transform into other types of neutrinos. These observations help determine neutrino masses, as well elucidating the uncharted nature of neutrinos, such as the relationship among three neutrino generations (types). T2K aims at the world’s best sensitivity by detecting neutrinos with the Super-Kamiokande d...

  4. Global plasma oscillations in electron internal transport barriers in TCV

    Energy Technology Data Exchange (ETDEWEB)

    Udintsev, V S; Sauter, O; Asp, E; Fable, E; Goodman, T P; Turri, G; Graves, J P; Zucca, C [Association Euratom-Confederation Suisse, EPFL/SB/CRPP, Station 13, CH-1015, Lausanne (Switzerland); Scarabosio, A [Max-Planck Institut fuer Plasmaphysik, IPP-EURATOM Association, Garching (Germany); Zhuang, G [Huazhong University of Science and Technology, Wuhan, Hubei (China)

    2008-12-15

    In the Tokamak a Configuration Variable (TCV) (Hofmann F et al1994 Plasma Phys. Control. Fusion 36 B277), global plasma oscillations have been discovered in fully non-inductively driven plasmas featuring electron internal transport barriers (ITB) with strong ECRH/ECCD. These oscillations are linked to the destabilization and stabilization of MHD modes near the foot of the ITB and can lead to large oscillations of the total plasma current and line-averaged density, among others. They are intrinsically related to the fact that ITBs have large pressure gradients in a region of low magnetic shear. Therefore, the ideal MHD limit is relatively low and infernal modes can be unstable. Depending on the proximity to the ideal limit, small crashes or resistive modes can appear which affect the time evolution of the discharge. Being near marginal stability, the modes can self-stabilize due to the modification of the pressure gradient and local q-profile. The plasma recovers good confinement, reverses shear and the ITB builds up, until a new MHD mode is destabilized. TCV results show that this cycling behaviour can be controlled by modifying the current density or the pressure profiles, either with Ohmic current density perturbation or by modifying the ECH/ECCD power. It is demonstrated that many observations such as q {>=} 2 sawteeth, beta collapses, minor disruptions and oscillation regimes in ITBs can be assigned to the same physics origin: the proximity to the infernal mode stability limit.

  5. Global plasma oscillations in electron internal transport barriers in TCV

    Science.gov (United States)

    Udintsev, V. S.; Sauter, O.; Asp, E.; Fable, E.; Goodman, T. P.; Turri, G.; Graves, J. P.; Scarabosio, A.; Zhuang, G.; Zucca, C.; TCV Team

    2008-12-01

    In the Tokamak à Configuration Variable (TCV) (Hofmann F et al1994 Plasma Phys. Control. Fusion 36 B277), global plasma oscillations have been discovered in fully non-inductively driven plasmas featuring electron internal transport barriers (ITB) with strong ECRH/ECCD. These oscillations are linked to the destabilization and stabilization of MHD modes near the foot of the ITB and can lead to large oscillations of the total plasma current and line-averaged density, among others. They are intrinsically related to the fact that ITBs have large pressure gradients in a region of low magnetic shear. Therefore, the ideal MHD limit is relatively low and infernal modes can be unstable. Depending on the proximity to the ideal limit, small crashes or resistive modes can appear which affect the time evolution of the discharge. Being near marginal stability, the modes can self-stabilize due to the modification of the pressure gradient and local q-profile. The plasma recovers good confinement, reverses shear and the ITB builds up, until a new MHD mode is destabilized. TCV results show that this cycling behaviour can be controlled by modifying the current density or the pressure profiles, either with Ohmic current density perturbation or by modifying the ECH/ECCD power. It is demonstrated that many observations such as q >= 2 sawteeth, beta collapses, minor disruptions and oscillation regimes in ITBs can be assigned to the same physics origin: the proximity to the infernal mode stability limit.

  6. Nonlinear dynamic effects in a two-wave CO2 laser

    International Nuclear Information System (INIS)

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

    1999-01-01

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

  7. Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas

    International Nuclear Information System (INIS)

    Masood, W.; Rizvi, H.

    2011-01-01

    Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the small amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.

  8. PROTECTION OF HOUSEHOLD APPLIANCES INDUCTION MOTORS AGAINST OVERCURRENT TAKING INTO ACCOUNT NONLINEAR DISTORTION OF PHASE CURRENT

    Directory of Open Access Journals (Sweden)

    A.G. Sereda

    2015-06-01

    Full Text Available Purpose. Theoretical justification and engineering of induction motors heat protection method from overload currents taking into account nonlinear distortion of the phase current and implementation as a microprocessor device functioning algorithm. Methodology. To solve the problem used the theory of the representing complex harmonic oscillations analog signals expansion into the oscillation spectrum forming elementary harmonic components in order to compare their properties by applying the theory of discrete signals and systems, as well as methods of spectral analysis and discrete signals filtering. The harmonic analysis versatility is that any periodic signal may be synthesized from harmonic oscillation of certain amplitude, frequency and initial phase. A mathematical model for determining the phase current harmonic content of power supply networks with isolated neutral and non-linear loads types and, as a consequence, the distortion of sinusoidal phase current change is developed by multiplying the analog current in time dependency on the grate delta-function with different sampling intervals, in which the use of simple and widely used in relay protection units, in particular electronic overcurrent relays, mathematical operations of integration squares instantaneous current allows the most in harmony with the mathematical tools to build other network protection types. Findings. The necessity to increase the sensitivity of the induction motors heat protection from overload currents taking into account nonlinear distortion of the phase currents is proved. By nonlinear distortion harmonic analysis of the phase currents the motor protection reliability increasing provided by taking into account the higher harmonic components of the phase currents, which causes to additional losses and heating of the stator winding. It uses the simplest and widely used in protective relaying mathematical apparatus determining of most significant higher harmonics

  9. Modeling of Nonlinear Dynamics and Synchronized Oscillations of Microbial Populations, Carbon and Oxygen Concentrations, Induced by Root Exudation in the Rhizosphere

    Science.gov (United States)

    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.

  10. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

    Science.gov (United States)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

    2017-12-01

    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

  11. Uncertainty Quantification and Bifurcation Analysis of an Airfoil with Multiple Nonlinearities

    Directory of Open Access Journals (Sweden)

    Haitao Liao

    2013-01-01

    Full Text Available In order to calculate the limit cycle oscillations and bifurcations of nonlinear aeroelastic system, the problem of finding periodic solutions with maximum vibration amplitude is transformed into a nonlinear optimization problem. An algebraic system of equations obtained by the harmonic balance method and the stability condition derived from the Floquet theory are used to construct the general nonlinear equality and inequality constraints. The resulting constrained maximization problem is then solved by using the MultiStart algorithm. Finally, the proposed approach is validated, and the effects of structural parameter uncertainty on the limit cycle oscillations and bifurcations of an airfoil with multiple nonlinearities are studied. Numerical examples show that the coexistence of multiple nonlinearities may lead to low amplitude limit cycle oscillation.

  12. Structure, Electronic and Nonlinear Optical Properties of Furyloxazoles and Thienyloxazoles

    International Nuclear Information System (INIS)

    Dagli, Ozlem; Gok, Rabia; Bahat, Mehmet; Ozbay, Akif

    2016-01-01

    Geometry optimization, electronic and nonlinear optical properties of isomers of furyloxazole and thienyloxazole molecules are carried out at the B3LYP/6-311++G(2d,p) level. The conformational analysis of 12 compounds have been studied as a function of torsional angle between rings. Electronic and NLO properties such as dipole moment, energy gap, polarizability and first hyperpolarizability were also calculated. (paper)

  13. Driven, autoresonant three-oscillator interactions

    International Nuclear Information System (INIS)

    Yaakobi, O.; Friedland, L.; Henis, Z.

    2007-01-01

    An efficient control scheme of resonant three-oscillator interactions using an external chirped frequency drive is suggested. The approach is based on formation of a double phase-locked (autoresonant) state in the system, as the driving oscillation passes linear resonance with one of the interacting oscillators. When doubly phase locked, the amplitudes of the oscillators increase with time in proportion to the driving frequency deviation from the linear resonance. The stability of this phase-locked state and the effects of dissipation and of the initial three-oscillator frequency mismatch on the autoresonance are analyzed. The associated autoresonance threshold phenomenon in the driving amplitude is also discussed. In contrast to other nonlinear systems, driven, autoresonant three-oscillator excitations are independent of the sign of the driving frequency chirp rate

  14. On some practical consideration of the electron beam breakup transit time oscillator

    International Nuclear Information System (INIS)

    Kwan, T.J.T.

    1992-01-01

    The electron beam breakup transit time oscillator (BTO) makes use of the interaction between an electron beam and the azimuthally azimuthally asymmetric transverse magnetic mode (TM 110 ) of a cavity to facilitate the exchange of energy between them. Linear theory has shown a large growth rate in the regime where space-charge effects can be ignored. In this study, we have investigated the non-ideal elements in the BTO and evaluated their effects accordingly. The practical issues under consideration are electron beam quality, energy, and space-charge potential. Our calculations indicate only a modest unfavorable scalings with respect to these parameters

  15. New Approach for the Analysis of Damped Vibrations of Fractional Oscillators

    Directory of Open Access Journals (Sweden)

    Yuriy A. Rossikhin

    2009-01-01

    Full Text Available The dynamic behavior of linear and nonlinear mechanical oscillators with constitutive equations involving fractional derivatives defined as a fractional power of the operator of conventional time-derivative is considered. Such a definition of the fractional derivative enables one to analyse approximately vibratory regimes of the oscillator without considering the drift of its position of equilibrium. The assumption of small fractional derivative terms allows one to use the method of multiple time scales whereby a comparative analysis of the solutions obtained for different orders of low-level fractional derivatives and nonlinear elastic terms is possible to be carried out. The interrelationship of the fractional parameter (order of the fractional operator and nonlinearity manifests itself in full measure when orders of the small fractional derivative term and of the cubic nonlinearity entering in the oscillator's constitutive equation coincide.

  16. Asymptotic representation of relaxation oscillations in lasers

    CERN Document Server

    Grigorieva, Elena V

    2017-01-01

    In this book we analyze relaxation oscillations in models of lasers with nonlinear elements controlling light dynamics. The models are based on rate equations taking into account periodic modulation of parameters, optoelectronic delayed feedback, mutual coupling between lasers, intermodal interaction and other factors. With the aim to study relaxation oscillations we present the special asymptotic method of integration for ordinary differential equations and differential-difference equations. As a result, they are reduced to discrete maps. Analyzing the maps we describe analytically such nonlinear phenomena in lasers as multistability of large-amplitude relaxation cycles, bifurcations of cycles, controlled switching of regimes, phase synchronization in an ensemble of coupled systems and others. The book can be fruitful for students and technicians in nonlinear laser dynamics and in differential equations.

  17. Nonlinear behaviors of a bounded electron beam-plasma system

    International Nuclear Information System (INIS)

    Iizuka, Satoru; Saeki, Koichi; Sato, Noriyoshi; Hatta, Yoshisuke

    1985-01-01

    Nonlinear developments of a bounded electron beam-plasma system including stationary electrons are investigated experimentally. A stable double layer is formed as a result of ion trapping in a growing negative potential dip induced by the Pierce instability above the current regime of the Buneman instability. In the in-between regime of the Buneman and Pierce instabilities, energetic ions are observed. This effective ion heating is caused by ion detrapping due to double-layer disruption, being consistent with computer simulation. (author)

  18. Electrodynamic soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in nonlinear acoustic landmine detection

    Science.gov (United States)

    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

  19. Signatures of nonlinearity in single cell noise-induced oscillations

    NARCIS (Netherlands)

    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

  20. Exact folded-band chaotic oscillator.

    Science.gov (United States)

    Corron, Ned J; Blakely, Jonathan N

    2012-06-01

    An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

  1. Engineering high-order nonlinear dissipation for quantum superconducting circuits

    Science.gov (United States)

    Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

    Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

  2. 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.

  3. Relativistic electron beam acceleration by cascading nonlinear Landau damping of electromagnetic waves in a plasma

    International Nuclear Information System (INIS)

    Sugaya, R.; Ue, A.; Maehara, T.; Sugawa, M.

    1996-01-01

    Acceleration and heating of a relativistic electron beam by cascading nonlinear Landau damping involving three or four intense electromagnetic waves in a plasma are studied theoretically based on kinetic wave equations and transport equations derived from relativistic Vlasov endash Maxwell equations. Three or four electromagnetic waves excite successively two or three nonresonant beat-wave-driven relativistic electron plasma waves with a phase velocity near the speed of light [v p =c(1-γ -2 p ) 1/2 , γ p =ω/ω pe ]. Three beat waves interact nonlinearly with the electron beam and accelerate it to a highly relativistic energy γ p m e c 2 more effectively than by the usual nonlinear Landau damping of two electromagnetic waves. It is proved that the electron beam can be accelerated to more highly relativistic energy in the plasma whose electron density decreases temporally with an appropriate rate because of the temporal increase of γ p . copyright 1996 American Institute of Physics

  4. Neutrino oscillation study in the muon neutrino → electron neutrino channel at the Brookhaven accelerator

    International Nuclear Information System (INIS)

    Astier, P.

    1987-09-01

    The E816 experiment described in this thesis is devoted to a neutrino oscillation search at the Brookhaven AGS. The method used here is to look with a fine grained calorimeter for the appearence of electron neutrino in a muon neutrino beam. After recalling the theoretical treatment of the neutrino mass problem, the experimental phenomenology of massive neutrinos and more specifically neutrino oscillations is reviewed. The experiment itself is then extensively described, both on the technical side (detector, beam, simulation) and on the analysis side. In particular the statistical separation of the electromagnetic showers from electrons - our signal - and from photons - our background - treated in detail. The present analysis is based on 2/3 of the final statistics and it leads to the - preliminary - observation of an electron excess in the neutrino interactions yielding 19 ± 15.6 (stat) ± 7 (syst) [fr

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

    International Nuclear Information System (INIS)

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

    2011-01-01

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

  6. Nonlinear low frequency electrostatic structures in a magnetized two-component auroral plasma

    Energy Technology Data Exchange (ETDEWEB)

    Rufai, O. R., E-mail: rajirufai@gmail.com [University of the Western Cape, Bellville 7535, Cape-Town (South Africa); Scientific Computing, Memorial University of Newfoundland, St John' s, Newfoundland and Labrador A1C 5S7 (Canada); Bharuthram, R., E-mail: rbharuthram@uwc.ac.za [University of the Western Cape, Bellville 7535, Cape-Town (South Africa); Singh, S. V., E-mail: satyavir@iigs.iigm.res.in; Lakhina, G. S., E-mail: lakhina@iigs.iigm.res.in [University of the Western Cape, Bellville 7535, Cape-Town (South Africa); Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai 410218 (India)

    2016-03-15

    Finite amplitude nonlinear ion-acoustic solitons, double layers, and supersolitons in a magnetized two-component plasma composed of adiabatic warm ions fluid and energetic nonthermal electrons are studied by employing the Sagdeev pseudopotential technique and assuming the charge neutrality condition at equilibrium. The model generates supersoliton structures at supersonic Mach numbers regime in addition to solitons and double layers, whereas in the unmagnetized two-component plasma case only, soliton and double layer solutions can be obtained. Further investigation revealed that wave obliqueness plays a critical role for the evolution of supersoliton structures in magnetized two-component plasmas. In addition, the effect of ion temperature and nonthermal energetic electron tends to decrease the speed of oscillation of the nonlinear electrostatic structures. The present theoretical results are compared with Viking satellite observations.

  7. Location identification of closed crack based on Duffing oscillator transient transition

    Science.gov (United States)

    Liu, Xiaofeng; Bo, Lin; Liu, Yaolu; Zhao, Youxuan; Zhang, Jun; Deng, Mingxi; Hu, Ning

    2018-02-01

    The existence of a closed micro-crack in plates can be detected by using the nonlinear harmonic characteristics of the Lamb wave. However, its location identification is difficult. By considering the transient nonlinear Lamb under the noise interference, we proposed a location identification method for the closed crack based on the quantitative measurement of Duffing oscillator transient transfer in the phase space. The sliding short-time window was used to create a window truncation of to-be-detected signal. And then, the periodic extension processing for transient nonlinear Lamb wave was performed to ensure that the Duffing oscillator has adequate response time to reach a steady state. The transient autocorrelation method was used to reduce the occurrence of missed harmonic detection due to the random variable phase of nonlinear Lamb wave. Moreover, to overcome the deficiency in the quantitative analysis of Duffing system state by phase trajectory diagram and eliminate the misjudgment caused by harmonic frequency component contained in broadband noise, logic operation method of oscillator state transition function based on circular zone partition was adopted to establish the mapping relation between the oscillator transition state and the nonlinear harmonic time domain information. Final state transition discriminant function of Duffing oscillator was used as basis for identifying the reflected and transmitted harmonics from the crack. Chirplet time-frequency analysis was conducted to identify the mode of generated harmonics and determine the propagation speed. Through these steps, accurate position identification of the closed crack was achieved.

  8. Effects of electron beam parameters and velocity spread on radio frequency output of a photonic band gap cavity gyrotron oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Ashutosh, E-mail: asingh.rs.ece@iitbhu.ac.in [Faculty of Physical Sciences, Institute of Natural Sciences and Humanities, Shri Ramswaroop Memorial University, Lucknow-Deva Road, Uttar Pradesh 225003 (India); Center of Research in Microwave Tubes, Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005 (India); Jain, P. K. [Center of Research in Microwave Tubes, Department of Electronics Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005 (India)

    2015-09-15

    In this paper, the effects of electron beam parameters and velocity spread on the RF behavior of a metallic photonic band gap (PBG) cavity gyrotron operating at 35 GHz with TE{sub 041}–like mode have been theoretically demonstrated. PBG cavity is used here to achieve a single mode operation of the overmoded cavity. The nonlinear time-dependent multimode analysis has been used to observe the beam-wave interaction behavior of the PBG cavity gyrotron, and a commercially available PIC code “CST Particle Studio” has been reconfigured to obtain 3D simulation results in order to validate the analytical values. The output power for this typical PBG gyrotron has been obtained ∼108 kW with ∼15.5% efficiency in a well confined TE{sub 041}–like mode, while all other competing modes have significantly low values of power output. The output power and efficiency of a gyrotron depend highly on the electron beam parameters and velocity spread. The influence of several electron beam parameters, e.g., beam voltage, beam current, beam velocity pitch factor, and DC magnetic field, on the PBG gyrotron operations has been investigated. This study would be helpful in optimising the electron beam parameters and estimating accurate RF output power of the high frequency PBG cavity based gyrotron oscillators.

  9. Theory of nonlinear harmonic generation in free-electron lasers with helical wigglers

    International Nuclear Information System (INIS)

    Geloni, G.; Saldin, E.; Schneidmiller, E.; Yurkov, M.

    2007-05-01

    CoherentHarmonicGeneration (CHG), and in particularNonlinearHarmonicGeneration (NHG), is of importance for both short wavelength Free-Electron Lasers (FELs), in relation with the achievement of shorter wavelengths with a fixed electron-beam energy, and high-average power FEL resonators, in relation with destructive effects of higher harmonics radiation on mirrors. In this paper we present a treatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study is based on an exact analytical solution of Maxwell's equations, derived with the help of a Green's function method. In particular, we demonstrate that nonlinear harmonic generation (NHG) fromhelicalwigglers vanishes on axis. Our conclusion is in open contrast with results in literature, that include a kinematical mistake in the description of the electron motion. (orig.)

  10. Low-pressure glow discharges with oscillating electrons in different electrode systems

    International Nuclear Information System (INIS)

    Bersenev, V.V.; Gavriolv, N.V.; Nikulin, S.P.

    1995-01-01

    One of the main applications of low - pressure glow discharges is the development on their basis of charged - particle beam sources. The use of glow discharges with oscillating electrons, which can operate stably in the voltage and pressure range to the left of the left branch of Pashen's curve, shows promise, because the decrease in critical pressure p 0 , below which the discharge operation becomes impossible, in the discharge system of a source promotes an increase in the electrical strength of its accelerating system. This, in its turn, makes possible the expansion of the operation range of accelerating voltages. This experimental investigation of glow discharges in such well - known systems with oscillating electrons, as Hollow Cathode (HC), Penning's System (PS) and Inverse Magnetron (IM), is aimed at revealing the system operating at the lowest pressure. Besides, both common features and peculiarities of discharge operation in these systems are discussed. Though there is an extensive amount of published information covering all the specified discharges, the carrying out of such investigation is justified, since a comparative analysis of results obtained by different authors is hampered by various conditions of their experiments

  11. The Oscillator Principle of Nature

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2012-01-01

    Oscillators are found on all levels in Nature. The general oscillator concept is defined and investigated. Oscillators may synchronize into fractal patterns. Apparently oscillators are the basic principle in Nature. The concepts of zero and infinite are discussed. Electronic manmade oscillators...

  12. Analysis of the power flow in nonlinear oscillators driven by random excitation using the first Wiener kernel

    Science.gov (United States)

    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.

  13. Chimera states in two-dimensional networks of locally coupled oscillators

    Science.gov (United States)

    Kundu, Srilena; Majhi, Soumen; Bera, Bidesh K.; Ghosh, Dibakar; Lakshmanan, M.

    2018-02-01

    Chimera state is defined as a mixed type of collective state in which synchronized and desynchronized subpopulations of a network of coupled oscillators coexist and the appearance of such anomalous behavior has strong connection to diverse neuronal developments. Most of the previous studies on chimera states are not extensively done in two-dimensional ensembles of coupled oscillators by taking neuronal systems with nonlinear coupling function into account while such ensembles of oscillators are more realistic from a neurobiological point of view. In this paper, we report the emergence and existence of chimera states by considering locally coupled two-dimensional networks of identical oscillators where each node is interacting through nonlinear coupling function. This is in contrast with the existence of chimera states in two-dimensional nonlocally coupled oscillators with rectangular kernel in the coupling function. We find that the presence of nonlinearity in the coupling function plays a key role to produce chimera states in two-dimensional locally coupled oscillators. We analytically verify explicitly in the case of a network of coupled Stuart-Landau oscillators in two dimensions that the obtained results using Ott-Antonsen approach and our analytical finding very well matches with the numerical results. Next, we consider another type of important nonlinear coupling function which exists in neuronal systems, namely chemical synaptic function, through which the nearest-neighbor (locally coupled) neurons interact with each other. It is shown that such synaptic interacting function promotes the emergence of chimera states in two-dimensional lattices of locally coupled neuronal oscillators. In numerical simulations, we consider two paradigmatic neuronal oscillators, namely Hindmarsh-Rose neuron model and Rulkov map for each node which exhibit bursting dynamics. By associating various spatiotemporal behaviors and snapshots at particular times, we study the chimera

  14. Observing Muon Neutrino to Electron Neutrino Oscillations in the NOνA Experiment

    Energy Technology Data Exchange (ETDEWEB)

    Xin, Tian [Iowa State U.

    2016-01-01

    Neutrino oscillations offers an insight on new physics beyond the Standard Model. The three mixing angles (θ12, θ13 and θ23) and the two mass splittings (Δm2 and Αm2 ) have been measured by different neutrino oscillation experiments. Some other parameters including the mass ordering of different neutrino mass eigenstates and the CP violation phase are still unknown. NOνA is a long-baseline accelerator neutrino experiment, using neutrinos from the NuMI beam at Fermilab. The experiment is equipped with two functionally identical detectors about 810 kilometers apart and 14 mrad off the beam axis. In this configuration, the muon neutrinos from the NuMI beam reach the disappearance maximum in the far detector and a small fraction of that oscillates into electron neutrinos. The sensitivity to the mass ordering and CP viola- tion phase determination is greately enhanced. This thesis presents the νeappearance analysis using the neutrino data collected with the NOνA experiment between February 2014 and May 2015, which corresponds to 3.45 ×1020 protons-on-target (POT). The νe appearance analysis is performed by comparing the observed νe CC-like events to the estimated background at the far detector. The total background is predicted to be 0.95 events with 0.89 originated from beam events and 0.06 from cosmic ray events. The beam background is obtained by extrapolating near detector data through different oscillation channels, while the cosmic ray background is calculated based on out-of-time NuMI trigger data. A total of 6 electron neutrino candidates are observed in the end at the far detector which represents 3.3 σ excess over the predicted background. The NOνA result disfavors inverted mass hierarchy for δcp ϵ [0, 0.6π] at 90% C.L.

  15. Probing collective oscillation of d -orbital electrons at the nanoscale

    Energy Technology Data Exchange (ETDEWEB)

    Dhall, Rohan [Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA; Vigil-Fowler, Derek [National Renewable Energy Laboratory, Golden, Colorado 80401, USA; Houston Dycus, J. [Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA; Kirste, Ronny [Adroit Materials, Inc., Cary, North Carolina 27518, USA; Mita, Seiji [Adroit Materials, Inc., Cary, North Carolina 27518, USA; Sitar, Zlatko [Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA; Collazo, Ramon [Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695, USA; LeBeau, James M. [Adroit Materials, Inc., Cary, North Carolina 27518, USA

    2018-02-05

    Here, we demonstrate that high energy electrons can be used to explore the collective oscillation of s, p, and d orbital electrons at the nanometer length scale. Using epitaxial AlGaN/AlN quantum wells as a test system, we observe the emergence of additional features in the loss spectrum with the increasing Ga content. A comparison of the observed spectra with ab-initio theory reveals that the origin of these spectral features lies in excitations of 3d-electrons contributed by Ga. We find that these modes differ in energy from the valence electron plasmons in Al1-xGaxN due to the different polarizabilities of the d electrons. Finally, we study the dependence of observed spectral features on the Ga content, lending insights into the origin of these spectral features, and their coupling with electron-hole excitations.

  16. Nonlinear structure formation in ion-temperature-gradient driven drift waves in pair-ion plasma with nonthermal electron distribution

    Science.gov (United States)

    Razzaq, Javaria; Haque, Q.; Khan, Majid; Bhatti, Adnan Mehmood; Kamran, M.; Mirza, Arshad M.

    2018-02-01

    Nonlinear structure formation in ion-temperature-gradient (ITG) driven waves is investigated in pair-ion plasma comprising ions and nonthermal electrons (kappa, Cairns). By using the transport equations of the Braginskii model, a new set of nonlinear equations are derived. A linear dispersion relation is obtained and discussed analytically as well as numerically. It is shown that the nonthermal population of electrons affects both the linear and nonlinear characteristics of the ITG mode in pair-ion plasma. This work will be useful in tokamaks and stellarators where non-Maxwellian population of electrons may exist due to resonant frequency heating, electron cyclotron heating, runaway electrons, etc.

  17. Effect of external magnetic field on critical current for the onset of virtual cathode oscillations in relativistic electron beams

    International Nuclear Information System (INIS)

    Hramov, Alexander; Koronovskii, Alexey; Morozov, Mikhail; Mushtakov, Alexander

    2008-01-01

    In this Letter we research the space charge limiting current value at which the oscillating virtual cathode is formed in the relativistic electron beam as a function of the external magnetic field guiding the beam electrons. It is shown that the space charge limiting (critical) current decreases with growth of the external magnetic field, and that there is an optimal induction value of the magnetic field at which the critical current for the onset of virtual cathode oscillations in the electron beam is minimum. For the strong external magnetic field the space charge limiting current corresponds to the analytical relation derived under the assumption that the motion of the electron beam is one-dimensional [D.J. Sullivan, J.E. Walsh, E. Coutsias, in: V.L. Granatstein, I. Alexeff (Eds.), Virtual Cathode Oscillator (Vircator) Theory, in: High Power Microwave Sources, vol. 13, Artech House Microwave Library, 1987, Chapter 13]. Such behavior is explained by the characteristic features of the dynamics of electron space charge in the longitudinal and radial directions in the drift space at the different external magnetic fields

  18. Nonlinear optical diagnostic of semimagnetic semiconductors Pb1-xYb xX (X = S, Se, Te)

    International Nuclear Information System (INIS)

    Nouneh, K.; Kityk, I.V.; Viennois, R.; Benet, S.; Charar, S.; Plucinski, K.J.

    2007-01-01

    Nonlinear optical measurements were performed to elucidate the influence of magnetic ions on the behavior of charge carriers in magnetic semiconductors-Pb 1-x Yb x X (X = S, Se, Te at x = 1-3%). It was shown that nonlinear optical methods could be used as sensitive tools for investigations of electron-phonon anharmonicity near low-temperature semiconductor-insulator phase transitions. There exists a difference between surface and bulk-like contributions to the nonlinear optical effects. It was shown that only low-temperature Two Photon Absorption (TPA) oscillator may be related to the number of the electron-phonon anharmonic modes responsible for the observed phase transformation. The explanation of the anomalous temperature dependences is given in accordance with dipole momentum's behaviors determined by low-temperature spin-spin interactions and by electron-phonon anharmonic interactions. We have discovered that low-temperature dependence of specific heat of Pb 1-x R x Te (R = Yb, Pr with x = 3% and 1.6%, respectively) exhibits a non-magnetic order caused by large electron-phonon contributions and structural disorder effects

  19. Nonlinear electrostatic emittance compensation in kA, fs electron bunches

    International Nuclear Information System (INIS)

    Geer, S.B. van der; Loos, M.J. de; Botman, J.I.M.; Luiten, O.J.; Wiel, M.J. van der

    2002-01-01

    Nonlinear space-charge effects play an important role in emittance growth in the production of kA electron bunches with a bunch length much smaller than the bunch diameter. We propose a scheme employing the radial third-order component of an electrostatic acceleration field, to fully compensate the nonlinear space-charge effects. This results in minimal transverse root-mean-square emittance. The principle is demonstrated using our design simulations of a device for the production of high-quality, high-current, subpicosecond electron bunches using electrostatic acceleration in a 1 GV/m field. Simulations using the GPT code produce a bunch of 100 pC and 73 fs full width at half maximum pulse width, resulting in a peak current of about 1.2 kA at an energy of 2 MeV. The compensation scheme reduces the root-mean-square emittance by 34% to 0.4π mm mrad

  20. OSCILLATION OF NONLINEAR DELAY DIFFERENCE EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    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.

  1. Autonomous third-order duffing-holmes type chaotic oscillator

    DEFF Research Database (Denmark)

    Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G

    2009-01-01

    feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...

  2. Electronic motion in the pre-oscillation phase of a smooth bore magnetron

    International Nuclear Information System (INIS)

    Garelis, E.; Hickman, R.B.

    1979-01-01

    The calculation of the electronic motion in the pre-oscillation phase of a smooth bore magnetron is the problem of calculating the electronic motion in the region between two concentric cylinders with an applied radial electric field and a constant axial B/sub z/ magnetic field. The inner cylinder represents the electron emitting cathode and the outer cylinder represents the anode. The emission is assumed to be space charge limited. This results in an electronic cloud surrounding the cathode. The radial velocity of the electrons is limited by the space charge and in addition the axial magnetic field tends to curve the path of the electrons so that they return to the cathode. Consequently, the electronic orbit extends to some distance r 0 from the cathode and for values of the radius r > r 0 exists a charge free region. The model assumes relativistic electronic motion with self-consistent magnetic fields. The magnetic flux is assumed to be conserved; i.e., conducting cylindrical walls

  3. Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators

    KAUST Repository

    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

  4. NONLINEAR DYNAMICS OF A ROTOR WITH CANTILEVERED DISK RESTING ON ANGULAR CONTACT BALL BEARINGS

    Directory of Open Access Journals (Sweden)

    S. Filipkovskyi

    2016-06-01

    Full Text Available The mathematical model of nonlinear oscillations of the rotor resting on angular contact ball bearings is developed. The disc is fixed on the console end of the shaft. The deflection of the shaft, and the elastic deformation of the bearings have the same order. Analysis of free oscillations is carried out, using nonlinear normal modes. The modes and backbone curves of rotor nonlinear oscillations are calculated. The system has soft characteristics.

  5. Quantum-mechanical analysis of low-gain free-electron laser oscillators

    Science.gov (United States)

    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.

  6. Optimization of power output and study of electron beam energy spread in a Free Electron Laser oscillator

    CERN Document Server

    Abramovich, A; Efimov, S; Gover, A; Pinhasi, Y; Yahalom, A

    2001-01-01

    Design of a multi-stage depressed collector for efficient operation of a Free Electron Laser (FEL) oscillator requires knowledge of the electron beam energy distribution. This knowledge is necessary to determine the voltages of the depressed collector electrodes that optimize the collection efficiency and overall energy conversion efficiency of the FEL. The energy spread in the electron beam is due to interaction in the wiggler region, as electrons enter the interaction region at different phases relative to the EM wave. This interaction can be simulated well by a three-dimensional simulation code such as FEL3D. The main adjustable parameters that determine the electron beam energy spread after interaction are the e-beam current, the initial beam energy, and the quality factor of the resonator out-coupling coefficient. Using FEL3D, we study the influence of these parameters on the available radiation power and on the electron beam energy distribution at the undulator exit. Simulations performed for I=1.5 A, E...

  7. Oscillations in the interactions among multiple solitons in an optical fibre

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Feng, Yu-Jie; Su, Chuan-Qi [Beijing University of Aeronautics and Astronautics (China). Ministry of Education Key Laboratory of Fluid Mechanics; Beijing University of Aeronautics and Astronautics (China). National Laboratory for Computational Fluid Dynamics

    2016-07-01

    In this article, under the investigation on the interactions among multiple solitons for an eighth-order nonlinear Schroedinger equation in an optical fibre, oscillations in the interaction zones are observed theoretically. With different coefficients of the operators in this equation, we find that (1) the oscillations in the solitonic interaction zones have different forms with different spectral parameters of this equation; (2) the oscillations in the interactions among the multiple solitons are affected by the choice of spectral parameters, the dispersive effects and nonlinearity of the eighth-order operator; (3) the second-, fifth-, sixth-, and seventh-order operators restrain oscillations in the solitonic interaction zones and the higher-order operators have stronger attenuated effects than the lower ones, while the third- and fourth-order operators stimulate and extend the scope of oscillations.

  8. Bursts of electron waves modulated by oblique ion waves

    International Nuclear Information System (INIS)

    Boswell, R.W.

    1984-01-01

    Experimental evidence is presented which shows small packets of electron plasma waves modulated by large amplitude obliquely propagating non-linear ion plasma waves. Very often the whole system is modulated by an oscillation near the ion gyro frequency or its harmonics. The ion waves seem to be similar to those measured in the current carrying auroral plasma. These results suggest that the generation of ion and electron waves in the auroral plasma may be correlated

  9. Nonlinear dynamic of interaction of the relativistic electron beam with plasma

    International Nuclear Information System (INIS)

    Dorofeenko, V.G.; Krasovitskii, V.B.; Osmolovsky, S.I.

    1994-01-01

    Quasi-transverse instability of thin relativistic electron beam in a dense plasma is studied numerically and analytically in a broad range of the frequency of the beam modulation and external longitudinal magnetic field. It is shown that the nonlinear stage of solution depends on the increment of the instability. It is permitted to classify possible nonlinear solutions and also to determine optimal regimes of the modulation for transport of beam along magnetic field in a plasma without substantial radial divergence. Numerical calculations show, that injection of the bunches with parameters, corresponding nonlinear regime of the beam's instability, in neutrally-charged plasma permits to output on the stationary regime without loss of particles

  10. Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons

    Science.gov (United States)

    El-Hanbaly, A. M.; El-Shewy, E. K.; Kassem, A. I.; Darweesh, H. F.

    2016-01-01

    The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained. The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

  11. Effect of nonlinear wave-particle interaction on electron-cyclotron absorption

    Energy Technology Data Exchange (ETDEWEB)

    Tsironis, C; Vlahos, L [Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece)

    2006-09-15

    We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER.

  12. Effect of nonlinear wave-particle interaction on electron-cyclotron absorption

    International Nuclear Information System (INIS)

    Tsironis, C; Vlahos, L

    2006-01-01

    We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER

  13. The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

    International Nuclear Information System (INIS)

    Kong, Ling-Bao; Wang, Hong-Yu; Hou, Zhi-Ling; Jin, Hai-Bo; Du, Chao-Hai

    2013-01-01

    The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained

  14. The nonlinear theory of slow-wave electron cyclotron masers with inclusion of the beam velocity spread

    Energy Technology Data Exchange (ETDEWEB)

    Kong, Ling-Bao, E-mail: konglingbao@gmail.com [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Wang, Hong-Yu [School of Physics, Anshan Normal University, Anshan 114005 (China); Hou, Zhi-Ling, E-mail: houzl@mail.buct.edu.cn [School of Science, Beijing University of Chemical Technology, Beijing 100029 (China); Beijing Key Laboratory of Environmentally Harmful Chemicals Assessment, Beijing University of Chemical Technology, Beijing 100029 (China); Jin, Hai-Bo [School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081 (China); Du, Chao-Hai [Institute of Electronics, Chinese Academy of Sciences, Beijing 100190 (China)

    2013-12-15

    The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency. -- Highlights: •The theory of slow-wave electron cyclotron masers is considered. •The calculation of efficiency under the resonance condition is presented. •The efficiency under Gaussian velocity spreads has been obtained.

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

    Directory of Open Access Journals (Sweden)

    S.H. Chen

    1996-01-01

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

  16. Analog electronic model of the lobster pyloric central pattern generator

    Energy Technology Data Exchange (ETDEWEB)

    Volkovskii, A [Institute for Nonlinear Science, University of California San Diego, CA (United States); Brugioni, S [Institute for Nonlinear Science, University of California San Diego, CA (United States); Istituto Nazionale di Ottica Applicata Largo E. Fermi 6 50125 Florence (Italy); Levi, R [Institute for Nonlinear Science, University of California San Diego, CA (United States); Rabinovich, M [Institute for Nonlinear Science, University of California San Diego, CA (United States); Selverston, A [Institute for Nonlinear Science, University of California San Diego, CA (United States); Abarbane, H D I [Institute for Nonlinear Science, University of California San Diego, CA (United States)

    2005-01-01

    An electronic circuit intended to simulate the nonlinear dynamics of a simplified 3-cell model of the pyloric central pattern generator in California spiny lobster stomato gastric ganglion is presented. The model employs the synaptic phase locked loop (SPLL) concept where the frequency of oscillations of a postsynaptic cell is mainly controlled by the synaptic current which depends on the phase shift between the oscillations. The theoretical study showed that the system has a stable steady state with correct phase shifts between the oscillations and that this regime is stable when the frequency of the pacemaker cell is varied over a wide range. The main bifurcations in the system were studied analytically, in computer simulations, and in experiments with the electronic circuit. The experimental measurements are in good agreement with the expectations of the theoretical model.

  17. Effect of beam oscillation on borated stainless steel electron beam welds

    Energy Technology Data Exchange (ETDEWEB)

    RajaKumar, Guttikonda [Tagore Engineering College, Chennai (India). Dept. of Mechanical Engineering; Ram, G.D. Janaki [Indian Institute of Technology (IIT), Chennai (India). Dept. of Metallurgical and Materials Engineering; Rao, S.R. Koteswara [SSN College of Engineering, Chennai (India). Mechanical Engineering

    2015-07-01

    Borated stainless steels are used in nuclear power plants to control neutron criticality in reactors as control rods, shielding material, spent fuel storage racks and transportation casks. In this study, bead on plate welds were made using gas tungsten arc welding (GTAW) and electron beam welding (EBW) processes. Electron beam welds made using beam oscillation technique exhibited higher tensile strength values compared to that of GTA welds. Electron beam welds were found to show fine dendritic microstructure while GTA welds exhibited larger dendrites. While both processes produced defect free welds, GTA welds are marked by partially melted zone (PMZ) where the hardness is low. EBW obviate the PMZ failure due to low heat input and in case of high heat input GTA welding process failure occurs in the PMZ.

  18. Effect of beam oscillation on borated stainless steel electron beam welds

    International Nuclear Information System (INIS)

    RajaKumar, Guttikonda; Ram, G.D. Janaki; Rao, S.R. Koteswara

    2015-01-01

    Borated stainless steels are used in nuclear power plants to control neutron criticality in reactors as control rods, shielding material, spent fuel storage racks and transportation casks. In this study, bead on plate welds were made using gas tungsten arc welding (GTAW) and electron beam welding (EBW) processes. Electron beam welds made using beam oscillation technique exhibited higher tensile strength values compared to that of GTA welds. Electron beam welds were found to show fine dendritic microstructure while GTA welds exhibited larger dendrites. While both processes produced defect free welds, GTA welds are marked by partially melted zone (PMZ) where the hardness is low. EBW obviate the PMZ failure due to low heat input and in case of high heat input GTA welding process failure occurs in the PMZ.

  19. Nonlinear chaos control in a permanent magnet reluctance machine

    International Nuclear Information System (INIS)

    Harb, Ahmad M.

    2004-01-01

    The dynamics of a permanent magnet synchronous machine (PMSM) is analyzed. The study shows that under certain conditions the PMSM is experiencing chaotic behavior. To control these unwanted chaotic oscillations, a nonlinear controller based on the backstepping nonlinear control theory is designed. The objective of the designed control is to stabilize the output chaotic trajectory by forcing it to the nearest constant solution in the basin of attraction. The result is compared with a nonlinear sliding mode controller. The designed controller that based on backstepping nonlinear control was able to eliminate the chaotic oscillations. Also the study shows that the designed controller is mush better than the sliding mode control

  20. Transient and chaotic low-energy transfers in a system with bistable nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

    Romeo, F., E-mail: francesco.romeo@uniroma1.it [Department of Structural and Geotechnical Engineering, SAPIENZA University of Rome, Rome (Italy); Manevitch, L. I. [Institute of Chemical Physics, RAS, Moscow (Russian Federation); Bergman, L. A.; Vakakis, A. [College of Engineering, University of Illinois at Urbana–Champaign, Champaign, Illinois 61820 (United States)

    2015-05-15

    The low-energy dynamics of a two-dof system composed of a grounded linear oscillator coupled to a lightweight mass by means of a spring with both cubic nonlinear and negative linear components is investigated. The mechanisms leading to intense energy exchanges between the linear oscillator, excited by a low-energy impulse, and the nonlinear attachment are addressed. For lightly damped systems, it is shown that two main mechanisms arise: Aperiodic alternating in-well and cross-well oscillations of the nonlinear attachment, and secondary nonlinear beats occurring once the dynamics evolves solely in-well. The description of the former dissipative phenomenon is provided in a two-dimensional projection of the phase space, where transitions between in-well and cross-well oscillations are associated with sequences of crossings across a pseudo-separatrix. Whereas the second mechanism is described in terms of secondary limiting phase trajectories of the nonlinear attachment under certain resonance conditions. The analytical treatment of the two aformentioned low-energy transfer mechanisms relies on the reduction of the nonlinear dynamics and consequent analysis of the reduced dynamics by asymptotic techniques. Direct numerical simulations fully validate our analytical predictions.

  1. Nonlinear extraordinary wave in dense plasma

    Energy Technology Data Exchange (ETDEWEB)

    Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)

    2013-10-15

    Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.

  2. NR-code: Nonlinear reconstruction code

    Science.gov (United States)

    Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming

    2018-04-01

    NR-code applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial Lagrangian positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.

  3. Modulation linearization of a frequency-modulated voltage controlled oscillator, part 3

    Science.gov (United States)

    Honnell, M. A.

    1975-01-01

    An analysis is presented for the voltage versus frequency characteristics of a varactor modulated VHF voltage controlled oscillator in which the frequency deviation is linearized by using the nonlinear characteristics of a field effect transistor as a signal amplifier. The equations developed are used to calculate the oscillator output frequency in terms of pertinent circuit parameters. It is shown that the nonlinearity exponent of the FET has a pronounced influence on frequency deviation linearity, whereas the junction exponent of the varactor controls total frequency deviation for a given input signal. A design example for a 250 MHz frequency modulated oscillator is presented.

  4. Superconducting nanowires as nonlinear inductive elements for qubits

    Science.gov (United States)

    Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey

    2011-03-01

    We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a ``crater'' at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. NSF DMR-1005645, DOE DO-FG02-07ER46453.

  5. Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

    Science.gov (United States)

    Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

    2018-04-01

    Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

  6. Nonlinear ionization of many-electron systems over a broad photon-energy range

    International Nuclear Information System (INIS)

    Karamatskou, Antonia

    2015-11-01

    Rapid developments in laser technology and, in particular, the advances in the realm of free-electron lasers have initiated tremendous progress in both theoretical and experimental atomic, molecular and optical physics. Owing to high intensities in combination with short pulse durations we can enter the utterly nonlinear regime of light-matter interaction and study the dynamics and features of matter under extreme conditions. The capabilities of X-ray free-electron laser sources have promoted the importance of nonlinear optics also in the X-ray regime. I show in my thesis how we can exploit the nonlinear response regime to reveal hidden information about resonance structures that are not resolved in the weak-field regime. This prospect points to many applications for future investigations of various complex systems with free-electron lasers. In the present thesis the interaction of atomic closed-shell systems with ultrashort and strong laser pulses is investigated. Over a broad photon-energy range the characteristics of the atomic shell are studied with a particular focus on the nonlinear response regime and on electron correlation effects. Several computational extensions of the XCID package for multi-electron dynamics are presented and their applications in various studies are demonstrated; a completely new capability of the numerical method is realized by implementing the calculation of photoelectron spectra and by calculating eigenstates of the many-electron Hamiltonian. The field of study within the present work encompasses (1) the strong-field regime, where the question of the adiabatic character in tunneling ionization is discussed and analyzed, especially for the case of few-cycle pulses; (2) the XUV regime, in which we show for the first time that the collectivity in resonant excitation reveals new information; and (3) the (hard) x-ray regime, which is highly relevant for x-ray free-electron laser experiments, and where we show how important two

  7. Nonlinear effects and conversion efficiency of free electron laser in compton regime

    International Nuclear Information System (INIS)

    Taguchi, Toshihiro; Mima, Kunioki; Mochizuki, Takayasu

    1980-01-01

    Nonlinear evolutions of free electron laser are analyzed by using quasi-linear theory. By the analysis, the energy conversion rates and the spectral width of the emitted radiations are calculated self-consistently. Moreover, it is found that the energy conversion rate is remarkably improved, when a RF field is applied to reaccelerate electron beam. (author)

  8. Transition from weak to strong measurements by nonlinear quantum feedback control

    International Nuclear Information System (INIS)

    Zhang Jing; Liu Yuxi; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

    2010-01-01

    We find that feedback control may induce 'pseudo'-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

  9. Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

    Science.gov (United States)

    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.

  10. Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

    Science.gov (United States)

    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.

  11. A theoretical study of structural, opto-electronic and nonlinear properties of arylboroxine derivatives

    Science.gov (United States)

    Islam, Nasarul; Pandith, Altaf Hussain

    2018-01-01

    Density functional theory at CAM-B3LYP/6-311G++ (2d, 2p) level was employed to study the Triphenylboroxine derivatives ( TB) containing electron donating and electron substituents, for their charge transfer and nonlinear optical properties. The results reveal that electron donating groups facilitate the rapid electron injection as compared to unsubstituted TB. It was observed that upon substitution with electron donating groups, the TB derivatives show an increased double bond character in the B3-C18 bond indicating an increase in the degree of conjugation. The Frontier molecular orbital studies indicate that highest occupied molecular orbitals of the neutral molecules delocalize primarily over the three phenyl rings and bridging oxygen atoms, whereas the lowest unoccupied molecular orbitals localize largely on the two phenyl rings and the boron atoms. Further, the TD-DFT studies indicate that the maximum absorption band results from the electron transitions from the initial states that are contributed by the HOMO and HOMO-1 to the final states that are mainly contributed by the LUMOs. In addition, we have observed that the introduction of electron donating group to the TB-7 leads to more active nonlinear performance.

  12. Dipole term and first derivative at K=0 of the generalized oscillator strength of He by keV electron impact

    International Nuclear Information System (INIS)

    Backx, C.; Tol, R.R.; Wight, G.R.; Wiel, M.J. van der

    1975-01-01

    An approximate method is described for obtaining the derivative to K 2 of the generalized oscillator strength for keV electron scattering at zero momentum transfer, over a large range of energy losses. The measured data enable the reduction of the systematical uncertainty in the derivation of optical oscillator strengths to below 1%. Results are presented for He over the spectral range of 19 to 65 eV. The data for the derivation are in satisfactory agreement with earlier electron scattering results at lower impact energy and extend over a sufficient range to allow the application of a sum rule for this term of the generalized oscillator strength. (Auth.)

  13. Quantum electronics and Moscow State University's Khokhlov-Akhmanov school of coherent and nonlinear optics

    International Nuclear Information System (INIS)

    Makarov, V.A.

    2004-01-01

    The aim of the report is to describe the history of the Moscow University Coherent and Nonlinear Optics School headed by R.V. Khokhlov and S.A. Akhmanov being a part of the history of the Russian efforts to investigate into quantum electronics. The reports describes briefly the most significant results of the mentioned School activity, in particular, thermonuclear reactions initiated by laser pulses in plasma; the procedure to accelerate electrons up to 1 GeV using the present-day lasers; the nonlinear-optical analogues of the Faraday and the Kerr effects [ru

  14. Practical design of a nonlinear tuned vibration absorber

    DEFF Research Database (Denmark)

    Grappasonni, C.; Habib, G.; Detroux, T.

    2014-01-01

    The aim of the paper is to develop a new nonlinear tuned vibration absorber (NLTVA) capable of mitigating the vibrations of nonlinear systems which are known to exhibit frequency-energy-dependent oscillations. A nonlinear generalization of Den Hartog's equal-peak method is proposed to ensure equa...

  15. The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

    Science.gov (United States)

    Verreault, René

    2017-08-01

    In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.

  16. A new analytical approximation to the Duffing-harmonic oscillator

    International Nuclear Information System (INIS)

    Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.

    2009-01-01

    In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.

  17. Some aspects of floor spectra of 1DOF nonlinear primary structures

    International Nuclear Information System (INIS)

    Politopoulos, I.; Feau, C.

    2007-01-01

    In this paper the influence of the nonlinear behaviour of the primary structure on floor spectra is investigated by means of simple models. The general trends of floor spectra for different types of nonlinear behaviour of one degree of freedom (1DOF) primary structure are shown and we point out their common futures and their differences. A special attention is given to the cases of elastoplastic and nonlinear elastic behaviours and methods to determine an equivalent linear oscillator are proposed. The properties (frequency and damping) of this equivalent linear oscillator are quite different from the properties of equivalent linear oscillators commonly considered in practice. In particular, in the case of elastoplastic behaviour, there is no frequency shift and damping is smaller than assumed by other methods commonly used. In the case of nonlinear elastic behaviour, the concept of an equivalent frequency which is a random variable is used. Finally, a design floor spectrum of primary structures, exhibiting energy dissipating nonlinear behaviour is proposed. (authors)

  18. Studies of hydromagnetic waves and oscillations in plasmas

    International Nuclear Information System (INIS)

    Sawley, M.L.

    1980-10-01

    Small amplitude magnetoacoustic oscillations in a partially ionized, non-uniform, current carrying plasma column of finite beta are considered. The linearized magnetohydrodynamic equations are used to develop a theory describing both free and forced magnetoacoustic oscillations. The results of numerical calculations are given for the specific case of diffuse pinch equilibrium configurations. In an experimental study the amplitude of the oscillating axial magnetic flux is determined for several frequencies in the vicinity of the first magnetoacoustic resonance. Accurate determination of the plasma density profile is shown to be possible. Finite-amplitude effects on the propagation of axisymmetric hydromagnetic waves are examined. A nonlinear theory is developed which describes the second-order perturbation that accompanies the primary wave. The influence of Hall currents and the presence of neutral atoms on the second-order fields is treated. In an investigation on the propagation of torsional waves the observed second-order fields are shown to exhibit good quantitative agreement with theoretical calculations for moderate primary wave amplitudes. The re-ionization of the plasma by a torsional wave is investigated. A theoretical description is given of the nonlinear excitation of magnetoacoustic oscillations by means of an oscillating axial current

  19. Deterministic nonlinear phase gates induced by a single qubit

    Science.gov (United States)

    Park, Kimin; Marek, Petr; Filip, Radim

    2018-05-01

    We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.

  20. Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

    Science.gov (United States)

    Bonilla, L L; Carretero, M; Segura, A

    2017-12-01

    When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

  1. Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

    Science.gov (United States)

    Bonilla, L. L.; Carretero, M.; Segura, A.

    2017-12-01

    When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

  2. Nonlinear Dynamic Models in Advanced Life Support

    Science.gov (United States)

    Jones, Harry

    2002-01-01

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

  3. Non-linear Relationship between BOLD Activation and Amplitude of Beta Oscillations in the Supplementary Motor Area during Rhythmic Finger Tapping and Internal Timing

    Science.gov (United States)

    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

  4. Non-linear Relationship between BOLD Activation and Amplitude of Beta Oscillations in the Supplementary Motor Area during Rhythmic Finger Tapping and Internal Timing.

    Science.gov (United States)

    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.

  5. Nonlinear Entanglement and its Application to Generating Cat States

    Science.gov (United 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.

  6. Propagation of nonlinear ion acoustic wave with generation of long-wavelength waves

    International Nuclear Information System (INIS)

    Ohsawa, Yukiharu; Kamimura, Tetsuo

    1978-01-01

    The nonlinear propagation of the wave packet of an ion acoustic wave with wavenumber k 0 asymptotically equals k sub(De) (the electron Debye wavenumber) is investigated by computer simulations. From the wave packet of the ion acoustic wave, waves with long wavelengths are observed to be produced within a few periods for the amplitude oscillation of the original wave packet. These waves are generated in the region where the original wave packet exists. Their characteristic wavelength is of the order of the length of the wave packet, and their propagation velocity is almost equal to the ion acoustic speed. The long-wavelength waves thus produced strongly affect the nonlinear evolution of the original wave packet. (auth.)

  7. Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

    International Nuclear Information System (INIS)

    Gao Jie

    2009-01-01

    In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations. (author)

  8. Transition to chaos in the damped and forced non-lnear oscillator

    International Nuclear Information System (INIS)

    Montenegro Joo, J.; Universidad Nacional Mayor de San Marcos, Lima

    2009-01-01

    A Virtual Lab to study the Transition to Chaos in second order non-linear differential equations has been developed and successfully applied to the search for chaotic behavior in the damped and forced non-linear oscillator. This simulation and visualization software evaluates the equation under investigation at up to one million time-steps, generating in real-time and on the screen, plots like amplitude of oscillation, phase diagram, amplitude oscillation peaks and an animation of an oscillator governed by the problem equation. In this way the investigator not only gets important behavior graphs but he or she also gets a physical visualization of the system under investigation. Visualizing an animation of the system under study is an enormous help because it is not always easy to interpret behavior graphs. (author).

  9. Ballistic magnetotransport in a suspended two-dimensional electron gas with periodic antidot lattices

    Energy Technology Data Exchange (ETDEWEB)

    Zhdanov, E. Yu., E-mail: zhdanov@isp.nsc.ru; Pogosov, A. G.; Budantsev, M. V.; Pokhabov, D. A.; Bakarov, A. K. [Siberian Branch of the Russian Academy of Sciences, Rzhanov Institute of Semiconductor Physics (Russian Federation)

    2017-01-15

    The magnetoresistance of suspended semiconductor nanostructures with a two-dimensional electron gas structured by periodic square antidot lattices is studied. It is shown that the ballistic regime of electron transport is retained after detaching the sample from the substrate. Direct comparative analysis of commensurability oscillations of magnetoresistance and their temperature dependences in samples before and after suspension is performed. It is found that the temperature dependences are almost identical for non-suspended and suspended samples, whereas significant differences are observed in the nonlinear regime, caused by direct current passage. Commensurability oscillations in the suspended samples are more stable with respect to exposure to direct current, which can be presumably explained by electron–electron interaction enhancement after detaching nanostructures from the high-permittivity substrate.

  10. Digital power and performance analysis of inkjet printed ring oscillators based on electrolyte-gated oxide electronics

    Science.gov (United States)

    Cadilha Marques, Gabriel; Garlapati, Suresh Kumar; Dehm, Simone; Dasgupta, Subho; Hahn, Horst; Tahoori, Mehdi; Aghassi-Hagmann, Jasmin

    2017-09-01

    Printed electronic components offer certain technological advantages over their silicon based counterparts, like mechanical flexibility, low process temperatures, maskless and additive manufacturing possibilities. However, to be compatible to the fields of smart sensors, Internet of Things, and wearables, it is essential that devices operate at small supply voltages. In printed electronics, mostly silicon dioxide or organic dielectrics with low dielectric constants have been used as gate isolators, which in turn have resulted in high power transistors operable only at tens of volts. Here, we present inkjet printed circuits which are able to operate at supply voltages as low as ≤2 V. Our transistor technology is based on lithographically patterned drive electrodes, the dimensions of which are carefully kept well within the printing resolutions; the oxide semiconductor, the electrolytic insulator and the top-gate electrodes have been inkjet printed. Our inverters show a gain of ˜4 and 2.3 ms propagation delay time at 1 V supply voltage. Subsequently built 3-stage ring oscillators start to oscillate at a supply voltage of only 0.6 V with a frequency of ˜255 Hz and can reach frequencies up to ˜350 Hz at 2 V supply voltage. Furthermore, we have introduced a systematic methodology for characterizing ring oscillators in the printed electronics domain, which has been largely missing. Benefiting from this procedure, we are now able to predict the switching capacitance and driver capability at each stage, as well as the power consumption of our inkjet printed ring oscillators. These achievements will be essential for analyzing the performance and power characteristics of future inkjet printed digital circuits.

  11. Reactor oscillator - I - III, Part I

    International Nuclear Information System (INIS)

    Lolic, B.

    1961-12-01

    Project 'Reactor oscillator' covers the following activities: designing reactor oscillators for reactors RA and RB with detailed engineering drawings; constructing and mounting of the oscillator; designing and constructing the appropriate electronic equipment for the oscillator; measurements at the RA and RB reactors needed for completing the oscillator construction

  12. Non-linear time series analysis on flow instability of natural circulation under rolling motion condition

    International Nuclear Information System (INIS)

    Zhang, Wenchao; Tan, Sichao; Gao, Puzhen; Wang, Zhanwei; Zhang, Liansheng; Zhang, Hong

    2014-01-01

    Highlights: • Natural circulation flow instabilities in rolling motion are studied. • The method of non-linear time series analysis is used. • Non-linear evolution characteristic of flow instability is analyzed. • Irregular complex flow oscillations are chaotic oscillations. • The effect of rolling parameter on the threshold of chaotic oscillation is studied. - Abstract: Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions were studied by the method of non-linear time series analysis. Experimental flow time series of different dimensionless power and rolling parameters were analyzed based on phase space reconstruction theory. Attractors which were reconstructed in phase space and the geometric invariants, including correlation dimension, Kolmogorov entropy and largest Lyapunov exponent, were determined. Non-linear characteristics of natural circulation flow instabilities under rolling motion conditions was studied based on the results of the geometric invariant analysis. The results indicated that the values of the geometric invariants first increase and then decrease as dimensionless power increases which indicated the non-linear characteristics of the system first enhance and then weaken. The irregular complex flow oscillation is typical chaotic oscillation because the value of geometric invariants is at maximum. The threshold of chaotic oscillation becomes larger as the rolling frequency or rolling amplitude becomes big. The main influencing factors that influence the non-linear characteristics of the natural circulation system under rolling motion are thermal driving force, flow resistance and the additional forces caused by rolling motion. The non-linear characteristics of the natural circulation system under rolling motion changes caused by the change of the feedback and coupling degree among these influencing factors when the dimensionless power or rolling parameters changes

  13. Experimental studies of nonlinear beam dynamics

    International Nuclear Information System (INIS)

    Caussyn, D.D.; Ball, M.; Brabson, B.; Collins, J.; Curtis, S.A.; Derenchuck, V.; DuPlantis, D.; East, G.; Ellison, M.; Ellison, T.; Friesel, D.; Hamilton, B.; Jones, W.P.; Lamble, W.; Lee, S.Y.; Li, D.; Minty, M.G.; Sloan, T.; Xu, G.; Chao, A.W.; Ng, K.Y.; Tepikian, S.

    1992-01-01

    The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the Indiana University Cyclotron Facility cooler ring. Motion in one dimension was measured for betatron tunes near the third, fourth, fifth, and seventh integer resonances. This motion is described by coupling between the transverse modes of motion and nonlinear field errors. The Hamiltonian for nonlinear particle motion near the third- and fourth-integer-resonance conditions has been deduced

  14. Observation of Quasichanneling Oscillations

    International Nuclear Information System (INIS)

    Wistisen, T. N.; Mikkelsen, R. E.; Uggerhoj, University I.; Wienands, University; Markiewicz, T. W.

    2017-01-01

    Here, we report on the first experimental observations of quasichanneling oscillations, recently seen in simulations and described theoretically. Although above-barrier particles penetrating a single crystal are generally seen as behaving almost as in an amorphous substance, distinct oscillation peaks nevertheless appear for particles in that category. The quasichanneling oscillations were observed at SLAC National Accelerator Laboratory by aiming 20.35 GeV positrons and electrons at a thin silicon crystal bent to a radius of R = 0.15 m, exploiting the quasimosaic effect. For electrons, two relatively faint quasichanneling peaks were observed, while for positrons, seven quasichanneling peaks were clearly identified.

  15. Reconstructing baryon oscillations: A Lagrangian theory perspective

    International Nuclear Information System (INIS)

    Padmanabhan, Nikhil; White, Martin; Cohn, J. D.

    2009-01-01

    Recently Eisenstein and collaborators introduced a method to 'reconstruct' the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

  16. Nonlinear fiber optics formerly quantum electronics

    CERN Document Server

    Agrawal, Govind

    1995-01-01

    The field of nonlinear fiber optics has grown substantially since the First Edition of Nonlinear Fiber Optics, published in 1989. Like the First Edition, this Second Edition is a comprehensive, tutorial, and up-to-date account of nonlinear optical phenomena in fiber optics. It synthesizes widely scattered research material and presents it in an accessible manner for students and researchers already engaged in or wishing to enter the field of nonlinear fiber optics. Particular attention is paid to the importance of nonlinear effects in the design of optical fiber communication systems. This is

  17. Analytical approximations for the amplitude and period of a relaxation oscillator

    Directory of Open Access Journals (Sweden)

    Golkhou Vahid

    2009-01-01

    Full Text Available Abstract Background Analysis and design of complex systems benefit from mathematically tractable models, which are often derived by approximating a nonlinear system with an effective equivalent linear system. Biological oscillators with coupled positive and negative feedback loops, termed hysteresis or relaxation oscillators, are an important class of nonlinear systems and have been the subject of comprehensive computational studies. Analytical approximations have identified criteria for sustained oscillations, but have not linked the observed period and phase to compact formulas involving underlying molecular parameters. Results We present, to our knowledge, the first analytical expressions for the period and amplitude of a classic model for the animal circadian clock oscillator. These compact expressions are in good agreement with numerical solutions of corresponding continuous ODEs and for stochastic simulations executed at literature parameter values. The formulas are shown to be useful by permitting quick comparisons relative to a negative-feedback represillator oscillator for noise (10× less sensitive to protein decay rates, efficiency (2× more efficient, and dynamic range (30 to 60 decibel increase. The dynamic range is enhanced at its lower end by a new concentration scale defined by the crossing point of the activator and repressor, rather than from a steady-state expression level. Conclusion Analytical expressions for oscillator dynamics provide a physical understanding for the observations from numerical simulations and suggest additional properties not readily apparent or as yet unexplored. The methods described here may be applied to other nonlinear oscillator designs and biological circuits.

  18. Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

    KAUST Repository

    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.

  19. Analysis of bus width and delay on a fully digital signum nonlinearity chaotic oscillator

    KAUST Repository

    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.

  20. Complete solution of the modified Cherry oscillator problem

    International Nuclear Information System (INIS)

    Pfirsch, D.

    1990-04-01

    In 1925, T.M. Cherry presented a simple example demonstrating that linear stability analysis will in general not be sufficient for finding out whether a system is stable or not with respect to small-amplitude perturbations. The example consisted of two nonlinearly coupled oscillators, one possessing positive energy, the other negative energy, with frequencies ω 1 =2ω 2 allowing third-order resonance. In a previous paper, the present author reformulated Cherry's example and then generalized it to three coupled oscillators corresponding to three-wave interaction in a continuum theory like that of Maxwell-Vlasov. Cherry was able to present a two-parameter solution set for his example which would, however, allow a four-parameter solution set, and a three-parameter solution set for the resonant three-oscillator case was obtained which, however, would allow a six-parameter solution set. Nonlinear instability could therefore be proven only for a very small part of the phase space of the oscillators. This paper now gives the complete solution for the three-oscillator case and shows that, except for a singular case, all initial conditions, especially those with arbitrarily small amplitudes, lead to explosive behaviour. This is true of the resonant case. The non-resonant oscillators can sometimes also become explosively unstable, but only if the initial amplitudes are not infinitesimally small. (orig.)

  1. Prediction of partial synchronization in delay-coupled nonlinear oscillators, with application to Hindmarsh–Rose neurons

    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)

  2. Dissipative quantum trajectories in complex space: Damped harmonic oscillator

    Energy Technology Data Exchange (ETDEWEB)

    Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

    2016-10-15

    Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

  3. Dissipative quantum trajectories in complex space: Damped harmonic oscillator

    International Nuclear Information System (INIS)

    Chou, Chia-Chun

    2016-01-01

    Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.

  4. Nonlinear THz spectroscopy on n-type GaAs

    Energy Technology Data Exchange (ETDEWEB)

    Gaal, Peter

    2008-06-23

    In this thesis, the ultrafast dynamics of conduction band electrons in semiconductors are investigated by nonlinear terahertz (THz) spectroscopy. In particular, n-doped gallium arsenide samples with doping concentrations in the range of 10{sup 16} cm{sup -3} to 10{sup 17} cm{sup -3} are studied. A novel source for the generation of intense THz radiation is developed which yields single-cycle THz transients with field amplitudes of more then 400 kV/cm. The THz source uses ultrashort optical laser pulses provided by a Ti:sapphire oscillator. In addition, a two-color THz-pump mid-infrared-probe setup is implemented, which allows for two-dimensional time-resolved experiments in the far-infrared wavelength range. Field ionization of neutral shallow donors in gallium arsenide with intense, ultrashort THz pulses and subsequent coherent radiative recombination of electrons to impurity ground states is observed at room temperature. The superradiant decay of the nonlinear polarization results in the emission of a coherent signal with picosecond lifetimes. Such nonlinear signals, which exhibit a lifetime ten times longer than in the linear regime are observed for the first time. At low temperatures and THz field strengths below 5 kV/cm, Rabi flopping on shallow donor transitions is demonstrated. For the first time, the polar electron-LO phonon interaction is directly measured in the quantum kinetic transport regime. Quasi-instantaneous acceleration of conduction band electrons in the polar gallium arsenide lattice by the electric field of intense THz pulses and subsequent probing of the mid-infrared transmission reveals a modulation of the transmission along the THz-mid-infrared delay coordinate with the frequency of the LO phonon. These modulations directly display the relative phase between the electron motion and its surrounding virtual phonon cloud. Quantum kinetic model calculations fully account for the observed phenomena. (orig.)

  5. Coupled opto electronic oscillator with a passively mode locked extended cavity diode laser

    International Nuclear Information System (INIS)

    Lee, Jeongmin; Jang, Gwang Hoon; Yoon, Duseong; Song, Minsoo; Yoon, Tai Hyun

    2008-01-01

    An opto electronic oscillator(OEO)has very unique properties compared to the conventional quartz based microwave oscillators in that its oscillation frequency is determined by the beat note frequency of a phase coherent optical frequency comb generated as a side bands to an optical single mode carrier by using an electro optic modulator (EOM)or a direct current modulation of a semiconductor laser. Recently, a different type of OEO called a COEO has been demonstrated, where the optical carrier in the OEO system has been replaced by a mode locked laser so that an EOM or a direct current modulation are no longer necessary, but has potentially a much lower phase noise thanks to the high Q value of the optical frequency comb due to the mode locking mechanism. In this paper, we propose and demonstrate a COEO based on a passively mode locked ECDL at 852nm in which the fourth harmonic of the repetition frequency of the ECDL matched exactly the ground state hyperfine splitting frequency of the Cs atoms

  6. Coupled opto electronic oscillator with a passively mode locked extended cavity diode laser

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jeongmin; Jang, Gwang Hoon; Yoon, Duseong; Song, Minsoo; Yoon, Tai Hyun [Korea Univ., Seoul (Korea, Republic of)

    2008-11-15

    An opto electronic oscillator(OEO)has very unique properties compared to the conventional quartz based microwave oscillators in that its oscillation frequency is determined by the beat note frequency of a phase coherent optical frequency comb generated as a side bands to an optical single mode carrier by using an electro optic modulator (EOM)or a direct current modulation of a semiconductor laser. Recently, a different type of OEO called a COEO has been demonstrated, where the optical carrier in the OEO system has been replaced by a mode locked laser so that an EOM or a direct current modulation are no longer necessary, but has potentially a much lower phase noise thanks to the high Q value of the optical frequency comb due to the mode locking mechanism. In this paper, we propose and demonstrate a COEO based on a passively mode locked ECDL at 852nm in which the fourth harmonic of the repetition frequency of the ECDL matched exactly the ground state hyperfine splitting frequency of the Cs atoms.

  7. Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators

    DEFF Research Database (Denmark)

    Momeni, M.; Jamshidi, j.; Barari, Amin

    2011-01-01

    In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....

  8. Optimization of power output and study of electron beam energy spread in a Free Electron Laser oscillator

    International Nuclear Information System (INIS)

    Abramovich, A.; Pinhasi, Y.; Yahalom, A.; Bar-Lev, D.; Efimov, S.; Gover, A.

    2001-01-01

    Design of a multi-stage depressed collector for efficient operation of a Free Electron Laser (FEL) oscillator requires knowledge of the electron beam energy distribution. This knowledge is necessary to determine the voltages of the depressed collector electrodes that optimize the collection efficiency and overall energy conversion efficiency of the FEL. The energy spread in the electron beam is due to interaction in the wiggler region, as electrons enter the interaction region at different phases relative to the EM wave. This interaction can be simulated well by a three-dimensional simulation code such as FEL3D. The main adjustable parameters that determine the electron beam energy spread after interaction are the e-beam current, the initial beam energy, and the quality factor of the resonator out-coupling coefficient. Using FEL3D, we study the influence of these parameters on the available radiation power and on the electron beam energy distribution at the undulator exit. Simulations performed for I=1.5 A, E=1.4 MeV, L=20% (Internal loss factor) showed that the highest radiated output power and smallest energy spread are attained for an output coupler transmission coefficient T m congruent with 30%

  9. Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

    KAUST Repository

    Abdelkefi, Abdessattar

    2013-06-18

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

  10. CLIMATE CHANGE: LONG-TERM TRENDS AND SHORT-TERM OSCILLATIONS

    Institute of Scientific and Technical Information of China (English)

    GAO Xin-quan; ZHANG Xin; QIAN Wei-hong

    2006-01-01

    Identifying the Northern Hemisphere (NH) temperature reconstruction and instrumental data for the past 1000 years shows that climate change in the last millennium includes long-term trends and various oscillations. Two long-term trends and the quasi-70-year oscillation were detected in the global temperature series for the last 140 years and the NH millennium series. One important feature was emphasized that temperature decreases slowly but it increases rapidly based on the analysis of different series. Benefits can be obtained of climate change from understanding various long-term trends and oscillations. Millennial temperature proxies from the natural climate system and time series of nonlinear model system are used in understanding the natural climate change and recognizing potential benefits by using the method of wavelet transform analysis. The results from numerical modeling show that major oscillations contained in numerical solutions on the interdecadal timescale are consistent with that of natural proxies. It seems that these oscillations in the climate change are not directly linked with the solar radiation as an external forcing. This investigation may conclude that the climate variability at the interdecadal timescale strongly depends on the internal nonlinear effects in the climate system.

  11. 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 ...

  12. Integrability and symmetries for the Helmholtz oscillator with friction

    International Nuclear Information System (INIS)

    Almendral, Juan A; Sanjuan, Miguel A F

    2003-01-01

    This paper deals with the Helmholtz oscillator, which is a simple nonlinear oscillator whose equation presents a quadratic nonlinearity and the possibility of escape. When a periodic external force is introduced, the width of the stochastic layer, which is a region around the separatrix where orbits may exhibit transient chaos, is calculated. In the absence of friction and external force, it is well known that analytical solutions exist since it is completely integrable. When only friction is included, there is no analytical solution for all parameter values. However, by means of the Lie theory for differential equations we find a relation between parameters for which the oscillator is integrable. This is related to the fact that the system possesses a symmetry group and the corresponding symmetries are computed. Finally, the analytical explicit solutions are shown and related to the basins of attraction

  13. First integral method for an oscillator system

    Directory of Open Access Journals (Sweden)

    Xiaoqian Gong

    2013-04-01

    Full Text Available In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to explore a quasi-polynomial first integral to an equivalent autonomous system. Then, through solving an algebraic system we derive the first integral of the Duffing-van der Pol-type oscillator system under certain parametric condition.

  14. Modified Legendre Wavelets Technique for Fractional Oscillation Equations

    OpenAIRE

    Mohyud-Din, Syed; Iqbal, Muhammad; Hassan, Saleh

    2015-01-01

    Physical Phenomena’s located around us are primarily nonlinear in nature and their solutions are of highest significance for scientists and engineers. In order to have a better representation of these physical models, fractional calculus is used. Fractional order oscillation equations are included among these nonlinear phenomena’s. To tackle with the nonlinearity arising, in these phenomena’s we recommend a new method. In the proposed method, Picard’s iteration is used to convert the nonlinea...

  15. Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion

    International Nuclear Information System (INIS)

    Basko, D.M.

    2011-01-01

    Research highlights: → In a one-dimensional disordered chain of oscillators all normal modes are localized. → Nonlinearity leads to chaotic dynamics. → Chaos is concentrated on rare chaotic spots. → Chaotic spots drive energy exchange between oscillators. → Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.

  16. Energy flow theory of nonlinear dynamical systems with applications

    CERN Document Server

    Xing, Jing Tang

    2015-01-01

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

  17. Bifurcation analysis and spatio-temporal patterns of nonlinear oscillations in a delayed neural network with unidirectional coupling

    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

  18. Anisotropic Friedel oscillations in a two-dimensional electron gas with a Rashba-Dresselhaus spin-orbit interaction

    Science.gov (United States)

    Kozlov, I. V.; Kolesnichenko, Yu. A.

    2017-07-01

    We present a theoretical study of the spatial distribution of the local density of states (LDOS) and the local magnetization density (LMD) in the vicinity of a magnetic point-defect in a degenerate two-dimensional electron gas with a mixed Rashba-Dresselhaus spin-orbit coupling interaction (SOI). The dependence of the Friedel oscillations, which arise under these conditions, on the ratio of the SOI constants is investigated. We obtain asymptotic expressions for the oscillatory parts of the LDOS and the LMD, that are accurate for large distances from the defect. It is shown, that the Friedel oscillations are significantly anisotropic and contain several harmonics for certain ratios of the SOI constants. Period of the oscillations for directions along the symmetry axes of the Fermi contours are determined. Finally, we introduce a method for determining the values of the two SOI constants by measuring the period of the Friedel oscillations of the LDOS and the LMD for different harmonics.

  19. Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper

    Directory of Open Access Journals (Sweden)

    Hailong Zhang

    2015-01-01

    Full Text Available This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v model of magneto-rheological damper (MRD. The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.

  20. Perturbation method of studying the EI Niño oscillation with two parameters by using the delay sea-air oscillator model

    International Nuclear Information System (INIS)

    Du Zeng-Ji; Lin Wan-Tao; Mo Jia-Qi

    2012-01-01

    The EI Niño-southern oscillation (ENSO) is an interannual phenomenon involved in tropical Pacific ocean-atmosphere interactions. In this paper, we develop an asymptotic method of solving the nonlinear equation using the ENSO model. Based on a class of the oscillator of the ENSO model, a approximate solution of the corresponding problem is studied employing the perturbation method

  1. Relaxed damage threshold intensity conditions and nonlinear increase in the conversion efficiency of an optical parametric oscillator using a bi-directional pump geometry.

    Science.gov (United States)

    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.

  2. Search for νμ → νe oscillations

    International Nuclear Information System (INIS)

    Godley, A.R.

    1998-01-01

    Full text: Neutrino oscillations, the changing of neutrino flavour state from one of τ, μ or e, to another, are proof of massive neutrinos, in turn pointing to Physics beyond the Standard Model, and so are of great current interest. Solar and atmospheric neutrino results suggested evidence for neutrino oscillations. Further, a tau neutrino mass of ∼ 10 eV could supply the missing mass needed to close the Universe. To satisfy the increasing interest, CERN's Neutrino Physics Program commissioned two concurrent experiments to investigate the possibility of neutrino oscillations, one of which is NOMAD, Neutrino Oscillation Magnetic Detector. NOMAD was designed to verify or deny the earlier positive neutrino oscillations results by searching for muon to tauon neutrino oscillations in accelerator neutrinos. The LSND experiment later provided evidence for muon to electron neutrino oscillations, but due to the multi-purpose design of NOMAD, it was also possible to investigate this channel. Moreover, the area of phase space being uncovered, (related to neutrino energy and oscillation length), overlaps considerably with that of LSND. An electron neutrino oscillation search involves looking for electron neutrinos in what is primarily a muon neutrino beam, with just a small contamination of electron neutrinos. It is surmised that the excess of electron neutrinos come from oscillated muon neutrinos. This type of search is called an appearance search. The principles of such a search will be detailed herein. These include a breakdown of the CERN Neutrino Beam and a method for detecting and collating different neutrino flavours at NOMAD

  3. Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

    Science.gov (United States)

    Tobita, Miwa; Omura, Yoshiharu

    2018-03-01

    We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

  4. Microwave oscillator with 'whispering gallery' resonator

    International Nuclear Information System (INIS)

    Kirichenko, A.Ya.; Prokopenko, Yu.V.; Filippov, Yu.F.; Lonin, Yu.F.; Papkovich, V.G.; Ponomarev, A.G.; Prokopenko, Yu.V.; Uvarov, V.T.

    2010-01-01

    It was presented researches of a generation of microwave radiation into system with azimuthally periodical relativistic electron beam current that excites a high-Q quasi-optical dielectric resonator. The Eigen parameters of cylindrical Teflon resonator were determined by numerical computation. Registration of the microwave radiation realizes by a crystal set of 8-mm wavelength range. Research projects of microwave oscillators with high-Q resonators, in which 'whispering gallery' oscillations are excited by an electron flow, are presented. Multiresonator oscillators ideology is based on principles of microwave generation in klystrons with both subcritical and supercritical electron beams currents.

  5. Microwave oscillator based on an intrinsic BSCCO-type Josephson junction

    DEFF Research Database (Denmark)

    Pedersen, Niels Falsig; Madsen, Søren Peder

    2005-01-01

    . The resulting model is a set of coupled nonlinear partial differential equations. By direct numerical simulations we have demonstrated that the qualitative behavior of the combined intrinsic Josephson junction and cavity system can be understood on the basis of general concepts of nonlinear oscillators...

  6. Nonlinear bound on unstable field energy in relativistic electron beams and plasmas

    International Nuclear Information System (INIS)

    Davidson, R.C.; Yoon, P.H.

    1989-01-01

    This paper makes use of Fowler's method [J. Math Phys. 4, 559 (1963)] to determine the nonlinear thermodynamic bound on field energy in unstable plasmas or electron beams in which the electrons are relativistic. Treating the electrons as the only active plasma component, the nonlinear Vlasov--Maxwell equations and the associated global conservation constraints are used to calculate the lowest upper bound on the field energy [ΔE-script/sub F/]/sub max/ that can evolve for the general initial electron distribution function f/sub b//sub / 0 equivalentf/sub b/(x,p,0). The results are applied to three choices of the initial distribution function f/sub b//sub / 0 . Two of the distribution functions have an inverted population in momentum p/sub perpendicular/ perpendicular to the magnetic field B 0 e/sub z/, and the third distribution function reduces to a bi-Maxwellian in the nonrelativistic limit. The lowest upper bound on the efficiency of radiation generation, eta/sub max/ = [ΔE-script/sub F/]/sub max//[V -1 ∫ d 3 x∫ d 3 p(γ-1)mc 2 f/sub b//sub / 0 ], is calculated numerically over a wide range of system parameters for varying degrees of initial anisotropy

  7. Effects of electron scattering on the oscillations of an X-ray source

    International Nuclear Information System (INIS)

    Kylafis, N.D.; Klimis, G.S.

    1987-01-01

    The time variability observed at infinity due to a variable point source at the center of a spherical cloud of radius R and optical depth to electron scattering tau is analytically determined. The emissin pattern of the source and its time variability are assumed to be of the following three forms: (1) isotropic emission with intensity varying sinusoidally in time with angular frequency Omega(L), (2) emission in the form of a delta-function beam rotating with angular frequency Omega(R) about a fixed axis and with intensity constant in time, and (3) emission in the form of a delta-function beam rotating with angular frequency Omega(R) about a fixed axis and with intensity varying sinusoidally in time with angular frequency Omega(L). More complicated source emissions and variabilities are studied by superposing the above forms. The results of our calculations reveal the conditions under which quasi-periodic oscillations can be observed from X-ray sources, while periodic oscillations are completely smeared out. Furthermore, these results can be used to study the X-ray oscillations of such sources as Her X-1, Cyg X-3, and the Vela pulsar, which are believed to be embedded in scattering clouds. 35 references

  8. Implementing a memristive Van der Pol oscillator coupled to a linear oscillator: synchronization and application to secure communication

    International Nuclear Information System (INIS)

    Megam Ngouonkadi, E B; Fotsin, H B; Louodop Fotso, P

    2014-01-01

    This paper investigates the dynamics of a memristor-based Van der Pol oscillator coupled to a linear circuit (VDPCL). This chaotic oscillator is a modification of the classical Van der Pol coupled to a linear circuit, and is obtained by replacing the classical cubic nonlinearity by the memristive one. The memristive VDPCL oscillator, in addition to having a very special stability property, exhibits interesting spectral characteristics, which makes it suitable for chaos-based secure communication applications. The memristor is realized by using off-the-shelf components. The basic properties of the circuit are analyzed by means of bifurcation analysis. Chaotic attractors from numerical and experimental analysis are presented, followed by a comparison of results obtained from the modified VDPCL oscillator and those from the classical VDPCL oscillator. An application to synchronization and chaos secure communication is also presented. (paper)

  9. Oscillating electromagnetic soliton in an anisotropic ferromagnetic medium

    Energy Technology Data Exchange (ETDEWEB)

    Sathishkumar, P., E-mail: perumal_sathish@yahoo.co.in [Department of Physics, K.S.R. College of Engineering (Autonomous), Tiruchengode 637215, Tamilnadu (India); Senjudarvannan, R. [Department of Physics, Jansons Institute of Technology, Karumathampatty, Coimbatore 641659 (India)

    2017-05-01

    We investigate theoretically the propagation of electromagnetic oscillating soliton in the form of breather in an anisotropic ferromagnetic medium. The interaction of magnetization with the magnetic field component of the electromagnetic (EM) wave has been studied by solving Maxwell's equations coupled with a Landau–Lifshitz equation for the magnetization of the medium. We made a small perturbation on the magnetization and magnetic field along the direction of propagation of EM wave in the framework of reductive perturbation method and the associated nonlinear magnetization dynamics is governed by a generalized derivative nonlinear Schrödinger (DNLS) equation. In order to understand the dynamics of the concerned system, we employ the Jacobi elliptic function method to solve the DNLS equation and deduce breatherlike soliton modes for the EM wave in the medium. - Highlights: • The propagation of electromagnetic oscillating soliton in an anisotropic ferromagnetic medium is investigated in the presence of varying external magnetic field. • The magnetization and electromagnetic wave modulates in the form of breathing like oscillating solitons. • The governing nonlinear spin dynamical equation is studied through a reductive perturbation method. • The magnetization components of the ferromagnetic medium are derived using Jacobi elliptic functions method with the aid of symbolic computation.

  10. The Duffing oscillator with damping

    DEFF Research Database (Denmark)

    Johannessen, Kim

    2015-01-01

    An analytical solution to the differential equation describing the Duffing oscillator with damping is presented. The damping term of the differential equation and the initial conditions satisfy an algebraic equation, and thus the solution is specific for this type of damping. The nonlinear term...... of the differential equation is allowed to be considerable compared to the linear term. The solution is expressed in terms of the Jacobi elliptic functions by including a parameter-dependent elliptic modulus. The analytical solution is compared to the numerical solution, and the agreement is found to be very good....... It is established that the period of oscillation is shorter compared to that of a linearized model but increasing with time and asymptotically approaching the period of oscillation of the linear damped model. An explicit expression for the period of oscillation has been derived, and it is found to be very accurate....

  11. The effect of loss of immunity on noise-induced sustained oscillations in epidemics.

    Science.gov (United States)

    Chaffee, J; Kuske, R

    2011-11-01

    The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nearly regular oscillations in a system that is quiescent without noise. In this context the criteria indicate how loss of immunity and other factors can lead to a significant increase in the parameter range for prevalence of the sustained oscillations, without any external driving forces. Comparison of the power spectral densities of the full model and the approximation confirms that the multiple scales analysis captures nonlinear features of the oscillations.

  12. Modal analysis of inter-area oscillations using the theory of normal modes

    Energy Technology Data Exchange (ETDEWEB)

    Betancourt, R.J. [School of Electromechanical Engineering, University of Colima, Manzanillo, Col. 28860 (Mexico); Barocio, E. [CUCEI, University of Guadalajara, Guadalajara, Jal. 44480 (Mexico); Messina, A.R. [Graduate Program in Electrical Engineering, Cinvestav, Guadalajara, Jal. 45015 (Mexico); Martinez, I. [State Autonomous University of Mexico, Toluca, Edo. Mex. 50110 (Mexico)

    2009-04-15

    Based on the notion of normal modes in mechanical systems, a method is proposed for the analysis and characterization of oscillatory processes in power systems. The method is based on the property of invariance of modal subspaces and can be used to represent complex power system modal behavior by a set of decoupled, two-degree-of-freedom nonlinear oscillator equations. Using techniques from nonlinear mechanics, a new approach is outlined, for determining the normal modes (NMs) of motion of a general n-degree-of-freedom nonlinear system. Equations relating the normal modes and the physical velocities and displacements are developed from the linearized system model and numerical issues associated with the application of the technique are discussed. In addition to qualitative insight, this method can be utilized in the study of nonlinear behavior and bifurcation analyses. The application of these procedures is illustrated on a planning model of the Mexican interconnected system using a quadratic nonlinear model. Specifically, the use of normal mode analysis as a basis for identifying modal parameters, including natural frequencies and damping ratios of general, linear systems with n degrees of freedom is discussed. Comparisons to conventional linear analysis techniques demonstrate the ability of the proposed technique to extract the different oscillation modes embedded in the oscillation. (author)

  13. Nonlinear optical interactions in silicon waveguides

    Directory of Open Access Journals (Sweden)

    Kuyken B.

    2017-03-01

    Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

  14. Chemical event chain model of coupled genetic oscillators.

    Science.gov (United States)

    Jörg, David J; Morelli, Luis G; Jülicher, Frank

    2018-03-01

    We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

  15. Chemical event chain model of coupled genetic oscillators

    Science.gov (United States)

    Jörg, David J.; Morelli, Luis G.; Jülicher, Frank

    2018-03-01

    We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

  16. 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...

  17. 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

  18. Measuring $\\theta_{13}$ via Muon Neutrino to Electron Neutrino Oscillations in the MINOS Experiment

    Energy Technology Data Exchange (ETDEWEB)

    Toner, Ruth B. [Univ. of Cambridge (United Kingdom). Pembroke College

    2011-01-01

    One of the primary goals in neutrino physics at the present moment is to make a measurement of the neutrino oscillation parameter $\\theta_{13}$. This parameter, in addition to being unknown, could potentially allow for the introduction of CP violation into the lepton sector. The MINOS long-baseline neutrino oscillation experiment has the ability to make a measurement of this parameter, by looking for the oscillation of muon neutrinos to electron neutrinos between a Near and Far Detector over a distance of 735 km. This thesis discusses the development of an analysis framework to search for this oscillation mode. Two major improvements to pre-existing analysis techniques have been implemented by the author. First, a novel particle ID technique based on strip topology, known as the Library Event Matching (LEM) method, is optimized for use in MINOS. Second, a multiple bin likelihood method is developed to fit the data. These two improvements, when combined, increase MINOS' sensitivity to $\\sin^2(2\\theta_{13})$ by 27\\% over previous analyses. This thesis sees a small excess over background in the Far Detector. A Frequentist interpretation of the data rules out $\\theta_{13}=0$ at 91\\%. A Bayesian interpretation of the data is also presented, placing the most stringent upper boundary on the oscillation parameter to date, at $\\sin^2(2\\theta_{13})<0.09(0.015)$ for the Normal (Inverted) Hierarchy and $\\delta_{CP}=0$.

  19. Quantum oscillations and the electronic transport properties in multichain nanorings

    International Nuclear Information System (INIS)

    Racolta, D.

    2009-01-01

    We consider a system of multichain nanorings in static electric and magnetic field. The magnetic field induces characteristic phase changes. These phase shifts produce interference phenomena in the case of nanosystems for which the coherence length is larger than the sample dimension. We obtain energy solutions that are dependent on the number of sites N α characterizing a chain, of phase on the phase φ α and on the applied voltage. We found rich oscillations structures exhibited by the magnetic flux and we established the transmission probability. This proceeds by applying Landauer conductance formulae which opens the way to study electronic transport properties. (authors)

  20. The nonlinear dynamics of the Oklo natural reactor

    International Nuclear Information System (INIS)

    Bilanovic, Z.; Harms, A.A.

    1985-01-01

    An analysis of the Oklo natural reactor, a self-sustaining and self-regulating critical assembly that existed some 2 billion years ago in Gabon, Africa, is presented. Nonlinear continuous dif ferential and nonlinear discrete iterative formulations are established and selected parameter characterizations identified. Conceivable power oscillations are calculated and discussed. Some implications of nonlinear mappings for nuclear simulation are suggested