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Sample records for mode nonlinear stabilization

  1. Nonlinear drift tearing mode. Strong mode of excitation and stabilization mechanisms

    International Nuclear Information System (INIS)

    Galeev, A.A.; Zelenyj, L.M.; Kuznetsova, M.M.

    1985-01-01

    A nonlinear theory of magnetic disturbance development in collisionless configurations with magnetic field shear is considered. The instability evolution is investigated with account for the dynamics of ions and potential electric fields which determine the mode stabilization. It has been found that the drift tearing mode possesses metastable properties: in a nonlinear mode even the growth of linearly stable disturbances of the finite amplitude is possible

  2. Stabilization of switched nonlinear systems with unstable modes

    CERN Document Server

    Yang, Hao; Cocquempot, Vincent

    2014-01-01

    This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...

  3. Nonlinear ω*-stabilization of the m = 1 mode in tokamaks

    International Nuclear Information System (INIS)

    Rogers, B.; Zakharov, L.

    1995-08-01

    Earlier studies of sawtooth oscillations in Tokamak Fusion Test Reactor supershots (Levinton et al, Phys. Rev. Lett. 72, 2895 (1994); Zakharov, et al, Plasma Phys. and Contr. Nucl. Fus. Res., Proc. 15th Int. Conf., Seville 1994, Vienna) have found an apparent contradiction between conventional linear theory and experiment: even in sawtooth-free discharges, the theory typically predicts instability due to a nearly ideal m = 1 mode. Here, the nonlinear evolution of such mode is analyzed using numerical simulations of a two-fluid magnetohydrodynamic (MHD) model. We find the mode saturates nonlinearly at a small amplitude provided the ion and electron drift-frequencies ω* i,e are somewhat above the linear stability threshold of the collisionless m = 1 reconnecting mode. The comparison of the simulation results to m = 1 mode activity in TFTR suggests additional, stabilizing effects outside the present model are also important

  4. Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

    DEFF Research Database (Denmark)

    Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

    2001-01-01

    We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....

  5. Controlling the stability of nonlinear optical modes via electromagnetically induced transparency

    Science.gov (United States)

    Zhang, Kun; Liang, Yi-zeng; Lin, Ji; Li, Hui-jun

    2018-02-01

    We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having Λ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schrödinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.

  6. Nonlinear Diamagnetic Stabilization of Double Tearing Modes in Cylindrical MHD Simulations

    Science.gov (United States)

    Abbott, Stephen; Germaschewski, Kai

    2014-10-01

    Double tearing modes (DTMs) may occur in reversed-shear tokamak configurations if two nearby rational surfaces couple and begin reconnecting. During the DTM's nonlinear evolution it can enter an ``explosive'' growth phase leading to complete reconnection, making it a possible driver for off-axis sawtooth crashes. Motivated by similarities between this behavior and that of the m = 1 kink-tearing mode in conventional tokamaks we investigate diamagnetic drifts as a possible DTM stabilization mechanism. We extend our previous linear studies of an m = 2 , n = 1 DTM in cylindrical geometry to the fully nonlinear regime using the MHD code MRC-3D. A pressure gradient similar to observed ITB profiles is used, together with Hall physics, to introduce ω* effects. We find the diamagnetic drifts can have a stabilizing effect on the nonlinear DTM through a combination of large scale differential rotation and mechanisms local to the reconnection layer. MRC-3D is an extended MHD code based on the libMRC computational framework. It supports nonuniform grids in curvilinear coordinates with parallel implicit and explicit time integration.

  7. Nonlinear drift tearing mode

    International Nuclear Information System (INIS)

    Zelenyj, L.M.; Kuznetsova, M.M.

    1989-01-01

    Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed

  8. A theorem for non-linear stability to tearing modes

    International Nuclear Information System (INIS)

    Avinash, K.

    1992-12-01

    Within the reduced MHD approximation it is shown that dJ z /dΨ≤0 [J z is z component of the current density and Ψ is the helical flux] is a sufficient condition for the equilibrium to be non-linearly stable to tearing mode. It is further shown that this is also a sufficient condition for an equilibrium to be axisymmetric, hence helical equilibrium consistent with this condition cannot be constructed. However a class of axisymmetric equilibrium with hollow current profile is shown to satisfy the stability criterion. (author). 16 refs, 2 figs

  9. Nonlinear surface elastic modes in crystals

    Science.gov (United States)

    Gorentsveig, V. I.; Kivshar, Yu. S.; Kosevich, A. M.; Syrkin, E. S.

    1990-03-01

    The influence of nonlinearity on shear horizontal surface elastic waves in crystals is described on the basis of the effective nonlinear Schrödinger equation. It is shown that the corresponding solutions form a set of surface modes and the simplest mode coincides with the solution proposed by Mozhaev. The higher order modes have internal frequencies caused by the nonlinearity. All these modes decay in the crystal as uoexp(- z/ zo) atz≫ zo- u o-1 ( z is the distance from the crystal surface, uo the wave amplitude at the surface). The creation of the modes from a localized surface excitation has a threshold. The stability of the modes is discussed.

  10. Linear stability and nonlinear dynamics of the fishbone mode in spherical tokamaks

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Feng; Liu, J. Y. [School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024 (China); Fu, G. Y.; Breslau, J. A. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States)

    2013-10-15

    Extensive linear and nonlinear simulations have been carried out to investigate the energetic particle-driven fishbone instability in spherical tokamak plasmas with weakly reversed q profile and the q{sub min} slightly above unity. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that a fishbone instability is excited by energetic beam ions preferentially at higher q{sub min} values, consistent with the observed appearance of the fishbone before the “long-lived mode” in MAST and NSTX experiments. In contrast, at lower q{sub min} values, the fishbone tends to be stable. In this case, the beam ion effects are strongly stabilizing for the non-resonant kink mode. Nonlinear simulations show that the fishbone saturates with strong downward frequency chirping as well as radial flattening of the beam ion distribution. An (m, n) = (2, 1) magnetic island is found to be driven nonlinearly by the fishbone instability, which could provide a trigger for the (2, 1) neoclassical tearing mode sometimes observed after the fishbone instability in NSTX.

  11. Nonlinear saturation of the trapped-ion mode by mode coupling in two dimensions

    International Nuclear Information System (INIS)

    Cohen, B.I.; Tang, W.M.

    1977-01-01

    A study of the nonlinear saturation by mode coupling of the dissipative trapped-ion mode is presented in which both radial and poloidal variations are considered. The saturation mechanism consists of the nonlinear coupling via E x B convection of energy from linearly unstable modes to stable modes. Stabilization is provided at short poloidal wavelengths by Landau damping from trapped and circulating ions, at short radial wavelengths by effects associated with the finite ion banana excursions and at long wavelengths by ion collisions. A one-dimensional, nonlinear partial differential equation for the electrostatic potential derived in earlier work is extended to two dimensions and to third order in amplitude. Included systematically are kinetic effects, e.g., Landau damping and its spatial dependence due to magnetic shear. The stability and accessibility of equilibria are considered in detail for cases far from as well as close to marginal stability. In the first case three-wave interactions are found to be important when the spectrum of unstable modes is sufficiently narrow. In the latter case, it is found that for a single unstable mode, a four-wave interaction can provide the dominant saturation mechanism. Cross-field transport is calculated, and the scaling of results is considered for tokamak parameters

  12. Robust Stability for Nonlinear Systems with Time-Varying Delay and Uncertainties via the H∞ Quasi-Sliding Mode Control

    Directory of Open Access Journals (Sweden)

    Yi-You Hou

    2014-01-01

    Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.

  13. Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

    Science.gov (United States)

    Whelan, G. G.; Pueschel, M. J.; Terry, P. W.

    2018-04-01

    The physical causes for the strong stabilizing effect of finite plasma β on ion-temperature-gradient-driven turbulence, which far exceeds quasilinear estimates, are identified from nonlinear gyrokinetic simulations. The primary contribution stems from a resonance of frequencies in the dominant nonlinear interaction between the unstable mode, the stable mode, and zonal flows, which maximizes the triplet correlation time and therefore the energy transfer efficiency. A modification to mixing-length transport estimates is constructed, which reproduces nonlinear heat fluxes throughout the examined β range.

  14. Threshold condition for nonlinear tearing modes in tokamaks

    Energy Technology Data Exchange (ETDEWEB)

    Zabiego, M.F. [Association Euratom-CEA, Centre d`Etudes de Cadarache, 13 - Saint-Paul-lez-Durance (France). Dept. de Recherches sur la Fusion Controlee; Callen, J.D. [Wisconsin Univ., Madison, WI (United States). Dept. of Nuclear Engineering and Engineering Physics

    1996-04-01

    Low-mode-number tearing mode nonlinear evolution is analyzed emphasizing the need for a threshold condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. Introducing a threshold condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space. (author). 19 refs.

  15. Threshold condition for nonlinear tearing modes in tokamaks

    International Nuclear Information System (INIS)

    Zabiego, M.F.; Callen, J.D.

    1996-04-01

    Low-mode-number tearing mode nonlinear evolution is analyzed emphasizing the need for a threshold condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. Introducing a threshold condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space. (author)

  16. Stability and nonlinear dynamics of gyrotrons at cyclotron harmonics

    International Nuclear Information System (INIS)

    Saraph, G.P.; Nusinovich, G.S.; Antonsen, T.M. Jr.; Levush, B.

    1992-01-01

    Gyrotrons operating at higher harmonics of the cyclotron frequency can overcome the frequency limitations caused by achievable strength of the magnetic field. However, the excitation of modes at the fundamental frequency exhibit a major problem for stable operation of harmonic gyrotron at high power with high efficiency. Therefore the issues of stability of gyrotron operation at the cyclotron harmonics and nonlinear dynamics of mode interaction are of great importance. The results of the authors stability analysis and multimode simulation are presented here. A detailed nonlinear theory of steady state single mode operation at cyclotron harmonics has been presented previously, taking into account beam-wave coupling and nonlinear gain function at cyclotron harmonics. A set of equations describing low gain regime interaction of modes resonant at different cyclotron harmonics was studied before. The multifrequency time-dependent nonlinear analysis presented here is based on previous gyrotron studies and beam-wave interaction at cyclotron harmonics. The authors have determined the parameter space for stable single mode operation at the second harmonic. The nonlinear dynamics of mode evolution and mode interaction for a harmonic gyrotron is presented. A new nonlinear effect in which the parasite at the fundamental harmonic helps excite the operating mode at the second harmonic has been demonstrated

  17. Non-linear effects in electron cyclotron current drive applied for the stabilization of neoclassical tearing modes

    NARCIS (Netherlands)

    Ayten, B.; Westerhof, E.; ASDEX Upgrade team,

    2014-01-01

    Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived

  18. Sliding mode control for uncertain unified chaotic systems with input nonlinearity

    International Nuclear Information System (INIS)

    Chiang, T.-Y.; Hung, M.-L.; Yan, J.-J.; Yang, Y.-S.; Chang, J.-F.

    2007-01-01

    This paper investigates the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Using the sliding mode control technique, a robust control law is established which stabilizes the uncertain unified chaotic systems even when the nonlinearity in the actuators is present. A novel adaptive switching surface is introduced to simplify the task of assigning the stability of the closed-loop system in the sliding mode motion. An illustrative example is given to demonstrate the effectiveness of the proposed sliding mode control design

  19. Nonlinear dynamics of a driven mode near marginal stability

    International Nuclear Information System (INIS)

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

    1995-09-01

    The nonlinear dynamics of a linearly unstable mode in a driven kinetic system is investigated to determine scaling of the saturated fields near the instability threshold. To leading order, this problem reduces to solving an integral equation with a temporally nonlocal cubic term. This equation can exhibit a self-similar solution that blows up in a finite time. When the blow-up occurs, higher nonlinearities become important and the mode saturates due to plateau formation arising from particle trapping in the wave. Otherwise, the simplified equation gives a regular solution that leads to a different saturation scaling reflecting the closeness to the instability threshold

  20. Spiraling solitons and multipole localized modes in nonlocal nonlinear media

    International Nuclear Information System (INIS)

    Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.; Bang, Ole; Krolikowski, Wieslaw; Kivshar, Yuri S.

    2007-01-01

    We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form

  1. Spiralling solitons and multipole localized modes in nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan

    2007-01-01

    We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form....

  2. 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.)

  3. Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators

    KAUST Repository

    Amin, Muhammad

    2013-09-01

    A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.

  4. Effect of modes interaction on the resistive wall mode stability

    International Nuclear Information System (INIS)

    Chen Longxi; Wu Bin

    2013-01-01

    Effects of modes interaction on the resistive wall mode (RWM) stability are studied. When considering the modes interaction effects, the linear growth rate of the most unstable (3, 1) mode decreases. After linear evolution, the RWM saturates at the nonlinear phase. The saturation can be attributed to flux piling up on the resistive wall. When some modes exist, the (3, 1) mode saturates at lower level compared with single mode evolution. Meanwhile, the magnetic energy of the (5, 2) mode increases correspondingly, but the magnetic energy saturation level of the (2, 1) mode changes weakly. (authors)

  5. Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications

    Science.gov (United States)

    Kuehl, Joseph J.

    2017-02-01

    A new "wave packet" formulation of the parabolized stability equations method is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening, and results in disturbance representation more consistent with the experiment than traditional formulations. A Mach 6 flared-cone example is presented.

  6. Threshold condition for nonlinear tearing modes in tokamaks

    International Nuclear Information System (INIS)

    Zabiego, M.F.; Callen, J.D.

    1996-03-01

    Low-mode-number tearing, mode nonlinear evolution is analyzed emphasizing the need for a threshold condition, to account for observations in tokamaks. The discussion is illustrated by two models recently introduced in the literature. The models can be compared with the available data and/or serve as a basis for planning some experiments in order to either test theory (by means of beta-limit scaling laws, as proposed in this paper) or attempt to control undesirable tearing modes. Introducing a threshold condition in the tearing mode stability analysis is found to reveal some bifurcation points and thus domains of intrinsic stability in the island dynamics operational space

  7. Nonlinear simulation of edge-localized mode in spherical tokamak

    International Nuclear Information System (INIS)

    Mizuguchi, N.; Hayashi, T.; Nakajima, N.; Khan, R.

    2006-10-01

    A numerical modeling for the dynamics of an edge-localized mode (ELM) crash in the spherical tokamak is proposed with a consecutive scenario which is initiated by the spontaneous growth of the ballooning mode instability by means of a three-dimensional nonlinear magnetohydrodynamic simulation. The simulation result shows a two-step relaxation process which is induced by the intermediate-n ballooning instability followed by the m/n=1/1 internal kink mode, where m and n represent the poloidal and toroidal mode numbers, respectively. By comparing with the experimental observations, we have found that the simulation result can reproduce several characteristic features of the so-called type-I ELM in an appropriate time scale: (1) relation to the ballooning instability, (2) intermediate-n precursors, (3) low-n structure on the crash, (4) formation and separation of the filament, and (5) considerable amount of loss of plasma. Furthermore, the model is verified by examining the effect of diamagnetic stabilization and comparing the nonlinear behavior with that of the peeling modes. The ion diamagnetic drift terms are found to stabilize some specific components linearly; nevertheless they are not so effective in the nonlinear dynamics such as the filament formation and the amount of loss. For the peeling mode case, no prominent filament structure is formed in contrast to the ballooning case. (author)

  8. Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2017-01-01

    The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

  9. Linear and nonlinear stability in resistive magnetohydrodynamics

    International Nuclear Information System (INIS)

    Tasso, H.

    1994-01-01

    A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its open-quotes nearnessclose quotes to necessity is analysed. It is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. This, together with hermiticity makes its analytical and numerical evaluation worthwhile for the optimization of magnetic configurations. Physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimization more tractable. In the case of special force-free fields the simplified functional reduces to a good approximation of the exact stability functional derived by other means. It turns out that in this case the condition is also sufficient for nonlinear stability. Nonlinear stability in hydrodynamics and magnetohydrodynamics is discussed especially in connection with open-quotes unconditionalclose quotes stability and with severe limitations on the Reynolds number. Two examples in magnetohydrodynamics show that the limitations on the Reynolds numbers can be removed but unconditional stability is preserved. Practical stability needs to be treated for limited levels of perturbations or for conditional stability. This implies some knowledge of the basin of attraction of the unperturbed solution, which is a very difficult problem. Finally, a special inertia-caused Hopf bifurcation is identified and the nature of the resulting attractors is discussed. 23 refs

  10. Nonlinear Predictive Sliding Mode Control for Active Suspension System

    Directory of Open Access Journals (Sweden)

    Dazhuang Wang

    2018-01-01

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

  11. Nonlinear localized modes in dipolar Bose-Einstein condensates in optical lattices

    International Nuclear Information System (INIS)

    Rojas-Rojas, S.; Vicencio, R. A.; Molina, M. I.; Abdullaev, F. Kh.

    2011-01-01

    Modulational instability and discrete matter wave solitons in dipolar BECs, loaded into a deep optical lattice, are investigated analytically and numerically. The process of modulational instability of nonlinear plane matter waves in a dipolar nonlinear lattice is studied and the regions of instability are established. The existence and stability of bulk discrete solitons are analyzed analytically and confirmed by numerical simulations. In marked contrast with the usual discrete nonlinear Schroedinger behavior (no dipolar interactions), we found a region where the two fundamental modes are simultaneously unstable, allowing enhanced mobility across the lattice for large norm values. To study the existence and properties of surface discrete solitons, an analysis of the dimer configuration is performed. The properties of symmetric and antisymmetric modes including stability diagrams and bifurcations are investigated in closed form. For the case of a bulk medium, properties of fundamental on-site and intersite localized modes are analyzed. On-site and intersite surface localized modes are studied, and we find that they do not exist when nonlocal interactions predominate with respect to local ones.

  12. Nonlinear dynamics of tearing modes in the reversed field pinch

    International Nuclear Information System (INIS)

    Holmes, J.A.; Carreras, B.A.; Diamond, P.H.; Lynch, V.E.

    1988-01-01

    The results of investigations of nonlinear tearing-mode dynamics in reversed field pinch plasmas are described. The linear instabilities have poloidal mode number m = 1 and toroidal mode numbers 10approx. < napprox. <20, and the resonant surfaces are therefore in the plasma core. The nonlinear dynamics result in dual cascade processes. The first process is a rapid m = 1 spectral broadening toward high n, with a simultaneous spreading of magnetic turbulence radially outward toward the field-reversal surface. Global m = 0 perturbations, which are driven to large amplitudes by the m = 1 instabilities, in turn trigger the m = 1 spectral broadening by back coupling to the higher n. The second process is a cascade toward large m and is mediated by m = 2 modes. The m = 2 perturbations have the structure of localized, driven current sheets and nonlinearly stabilize the m = 1 modes by transferring m = 1 energy to small-scale dissipation. The calculated spectrum has many of the qualitative features observed in experiments

  13. Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes

    Energy Technology Data Exchange (ETDEWEB)

    Becar, Ramon [Universidad Cato lica de Temuco, Departamento de Ciencias Matematicas y Fisicas, Temuco (Chile); Gonzalez, P.A. [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Vasquez, Yerko [Universidad de La Serena, Departamento de Fisica, Facultad de Ciencias, La Serena (Chile)

    2016-02-15

    We study scalar perturbations of four- dimensional topological nonlinear charged Lifshitz black holes with spherical and plane transverse sections, and we find numerically the quasinormal modes for scalar fields. Then we study the stability of these black holes under massive and massless scalar field perturbations. We focus our study on the dependence of the dynamical exponent, the nonlinear exponent, the angular momentum, and the mass of the scalar field in the modes. It is found that the modes are overdamped, depending strongly on the dynamical exponent and the angular momentum of the scalar field for a spherical transverse section. In contrast, for plane transverse sections the modes are always overdamped. (orig.)

  14. Nonlinear stability of supersonic jets

    Science.gov (United States)

    Tiwari, S. N. (Principal Investigator); Bhat, T. R. S. (Principal Investigator)

    1996-01-01

    The stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations are presented. In this analysis the large scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.

  15. On the asymptotic stability of nonlinear mechanical switched systems

    Science.gov (United States)

    Platonov, A. V.

    2018-05-01

    Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

  16. A robust nonlinear stabilizer as a controller for improving transient stability in micro-grids.

    Science.gov (United States)

    Azimi, Seyed Mohammad; Afsharnia, Saeed

    2017-01-01

    This paper proposes a parametric-Lyapunov approach to the design of a stabilizer aimed at improving the transient stability of micro-grids (MGs). This strategy is applied to electronically-interfaced distributed resources (EI-DRs) operating with a unified control configuration applicable to all operational modes (i.e. grid-connected mode, islanded mode, and mode transitions). The proposed approach employs a simple structure compared with other nonlinear controllers, allowing ready implementation of the stabilizer. A new parametric-Lyapunov function is proposed rendering the proposed stabilizer more effective in damping system transition transients. The robustness of the proposed stabilizer is also verified based on both time-domain simulations and mathematical proofs, and an ultimate bound has been derived for the frequency transition transients. The proposed stabilizer operates by deploying solely local information and there are no needs for communication links. The deteriorating effects of the primary resource delays on the transient stability are also treated analytically. Finally, the effectiveness of the proposed stabilizer is evaluated through time-domain simulations and compared with the recently-developed stabilizers performed on a multi-resource MG. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  17. Nonlinear dynamics of tearing modes in the reversed field pinch

    International Nuclear Information System (INIS)

    Holmes, J.A.; Carreras, B.A.; Diamond, P.H.; Lynch, V.E.

    1987-05-01

    The results of investigations of nonlinear tearing-mode dynamics in reversed field pinch plasmas are described. The linear instabilities have poloidal mode number m = 1 and toroidal mode numbers 10 ≤ n ≤ 20, and the resonant surfaces are therefore in the plasma core. The nonlinear dynamics result in dual cascade processes. The first process is a rapid m = 1 spectral broadening toward high n, with a simultaneous spreading of magnetic turbulence radially outward toward the field-reversal surface. Global m = 0 perturbations, which are driven to large amplitudes by the m = 1 instabilities, in turn trigger the m = 1 spectral broadening by back-coupling to the higher n. The second process is a cascade toward large m and is mediated by m = 2 modes. The m = 2 perturbations have the structure of localized, driven current sheets and nonlinearly stabilize the m = 1 modes by transferring m = 1 energy to small-scale dissipation. The calculated spectrum has many of the qualitative features observed in experiments. 13 refs., 21 figs., 1 tab

  18. Nonlinear Stability and Structure of Compressible Reacting Mixing Layers

    Science.gov (United States)

    Day, M. J.; Mansour, N. N.; Reynolds, W. C.

    2000-01-01

    The parabolized stability equations (PSE) are used to investigate issues of nonlinear flow development and mixing in compressible reacting shear layers. Particular interest is placed on investigating the change in flow structure that occurs when compressibility and heat release are added to the flow. These conditions allow the 'outer' instability modes- one associated with each of the fast and slow streams-to dominate over the 'central', Kelvin-Helmholtz mode that unaccompanied in incompressible nonreacting mixing layers. Analysis of scalar probability density functions in flows with dominant outer modes demonstrates the ineffective, one-sided nature of mixing that accompany these flow structures. Colayer conditions, where two modes have equal growth rate and the mixing layer is formed by two sets of vortices, offer some opportunity for mixing enhancement. Their extent, however, is found to be limited in the mixing layer's parameter space. Extensive validation of the PSE technique also provides a unique perspective on central- mode vortex pairing, further supporting the view that pairing is primarily governed perspective sheds insight on how linear stability theory is able to provide such an accurate prediction of experimentally-observed, fully nonlinear flow phenomenon.

  19. Improved algorithm for solving nonlinear parabolized stability equations

    International Nuclear Information System (INIS)

    Zhao Lei; Zhang Cun-bo; Liu Jian-xin; Luo Ji-sheng

    2016-01-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. (paper)

  20. Implications of a wavepacket formulation for the nonlinear parabolized stability equations to hypersonic boundary layers

    Science.gov (United States)

    Kuehl, Joseph

    2016-11-01

    The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.

  1. Strongly nonlinear theory of rapid solidification near absolute stability

    Science.gov (United States)

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

    2017-10-01

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

  2. Improved algorithm for solving nonlinear parabolized stability equations

    Science.gov (United States)

    Zhao, Lei; Zhang, Cun-bo; Liu, Jian-xin; Luo, Ji-sheng

    2016-08-01

    Due to its high computational efficiency and ability to consider nonparallel and nonlinear effects, nonlinear parabolized stability equations (NPSE) approach has been widely used to study the stability and transition mechanisms. However, it often diverges in hypersonic boundary layers when the amplitude of disturbance reaches a certain level. In this study, an improved algorithm for solving NPSE is developed. In this algorithm, the mean flow distortion is included into the linear operator instead of into the nonlinear forcing terms in NPSE. An under-relaxation factor for computing the nonlinear terms is introduced during the iteration process to guarantee the robustness of the algorithm. Two case studies, the nonlinear development of stationary crossflow vortices and the fundamental resonance of the second mode disturbance in hypersonic boundary layers, are presented to validate the proposed algorithm for NPSE. Results from direct numerical simulation (DNS) are regarded as the baseline for comparison. Good agreement can be found between the proposed algorithm and DNS, which indicates the great potential of the proposed method on studying the crossflow and streamwise instability in hypersonic boundary layers. Project supported by the National Natural Science Foundation of China (Grant Nos. 11332007 and 11402167).

  3. On the nonlinear stability of mKdV breathers

    Science.gov (United States)

    Alejo, Miguel A.; Muñoz, Claudio

    2012-11-01

    Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under a class of small perturbations. Our proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.

  4. Curvature effects in the nonlinear growth of the cylindrical tearing mode

    International Nuclear Information System (INIS)

    Somon, J. P.

    1984-01-01

    The full set of the usual resistive massless equations is used to investigate the nonlinear growth of the helical perturbation to a cylindrical equilibrium with tokamak ordering. There is a curvature dependant critical magnetic island width xsub(T)sup(*) α set containing D/Δ' above which the Rutherford solution is recovered for the tearing mode as well as for the linear slow interchange modes with Δ' > 0. Non linearity stabilizes at this critical width the linearly unstable slow interchange modes with Δ' > 0

  5. H-mode edge stability of Alcator C-mod plasmas

    International Nuclear Information System (INIS)

    Mossessian, D.A.; Hubbard, A.; Hughes, J.W.; Greenwald, M.; LaBombard, B.; Snipes, J.A.; Wolfe, S.; Snyder, P.; Wilson, H.; Xu, X.; Nevins, W.

    2003-01-01

    For steady state H-mode operation, a relaxation mechanism is required to limit build-up of the edge gradient and impurity content. C-Mod sees two such mechanisms - EDA and grassy ELMs, but not large type I ELMs. In EDA the edge relaxation is provided by an edge localized quasi coherent electromagnetic mode that exists at moderate pedestal temperature T 3.5 and does not limit the build up of the edge pressure gradient. The mode is not observed in the ideal MHD stability analysis, but is recorded in the nonlinear real geometry fluctuations modeling based on fluid equations and is thus tentatively identified as a resistive ballooning mode. At high edge pressure gradients and temperatures the mode is replaced by broadband fluctuations (f< 50 kHz) and small irregular ELMs are observed. Based on ideal MHD calculations that include the effects of edge bootstrap current, these ELMs are identified as medium n (10 < n < 50) coupled peeling/ballooning modes. The stability thresholds, its dependence on the plasma shape and the modes structure are studied experimentally and with the linear MHD stability code ELITE. (author)

  6. Nonlinear magnetohydrodynamics of edge localized mode precursors

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)

    2015-02-15

    A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.

  7. Stability of the n = 1 internal kink mode in equilibria with flows

    International Nuclear Information System (INIS)

    Aydemir, A.Y.; Waelbroeck, F.L.

    1996-01-01

    Stabilizing influence of mass flows, either directly or through their shearing action, on various modes is now generally recognized. Here we examine linear and nonlinear stability of the n = 1 internal kink mode in equilibria with toroidal rotation, using our nonlinear, initial-value MHD code CTD, which can be used to generate self-consistent equilibria with flows in arbitrary geometries. It is well known that equilibrium mass flows introduce complications in determination of MHD equilibria and their stability properties, such as the loss of self-adjointness and an increase in the number of conditions required to uniquely determine the equilibria. Thus, even with purely toroidal flows, an implicit statement about the equation of state is needed, in addition to a knowledge of the magnetic field and velocity profiles; rotation in an adiabatic plasma leads to a different equilibrium than, for example, in an isothermal one, with possibly quite different stability properties. We find that the expected stabilizing influence of toroidal rotation on n = 1 is generally absent in adiabatically generated equilibria in which, of all the relevant thermodynamic variables, only the specific entropy is a flux function, s = s (ψ). Fortunately, physically more relevant isothermal case where the temperature is constant on flux surfaces, T = T(ψ), has more favorable stability characteristics. On the other hand, an inconsistent but common practice of ignoring density perturbations, a benign omission for static equilibria, leads to overly optimistic results when equilibrium flows axe present, predicting stability when there may not be any. The crucial role played by the equation of state in determining equilibrium raises questions regarding the role of parallel transport in stability calculations; this and other nonideal effects, along with the role of plasma β vs. the rotational β, and nonlinear stability when the mode is pushed beyond marginality, will be discussed

  8. Linear and non-linear amplification of high-mode perturbations at the ablation front in HiPER targets

    Energy Technology Data Exchange (ETDEWEB)

    Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)

    2011-01-15

    The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

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

    Science.gov (United States)

    Mobayen, Saleh

    2018-06-01

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

  10. Linear and nonlinear stability analysis in BWRs applying a reduced order model

    Energy Technology Data Exchange (ETDEWEB)

    Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)

    2016-09-15

    Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

  11. Linear and nonlinear stability analysis in BWRs applying a reduced order model

    International Nuclear Information System (INIS)

    Olvera G, O. A.; Espinosa P, G.; Prieto G, A.

    2016-09-01

    Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

  12. Stationary localized modes of the quintic nonlinear Schroedinger equation with a periodic potential

    International Nuclear Information System (INIS)

    Alfimov, G. L.; Konotop, V. V.; Pacciani, P.

    2007-01-01

    We consider localized modes (bright solitons) of the one-dimensional quintic nonlinear Schroedinger equation with a periodic potential, describing several mean-field models of low-dimensional condensed gases. In the case of attractive nonlinearity we deduce sufficient conditions for collapse. We show that there exist spatially localized modes with arbitrarily large numbers of particles. We study such solutions in the semi-infinite gap (attractive case) and in the first gap (attractive and repulsive cases), and show that a nonzero minimum value of the number of particles is necessary for a localized mode to be created. In the limit of large negative frequencies (attractive case) we observe quantization of the number of particles of the stationary modes. Such solutions can be interpreted as coupled Townes solitons and appear to be stable. The modes in the first gap have numbers of particles infinitely growing with frequencies approaching one of the gap edges, which is explained by the power decay of the modes. Stability of the localized modes is discussed

  13. Nonlinear Vibration and Mode Shapes of FG Cylindrical Shells

    Directory of Open Access Journals (Sweden)

    Saeed Mahmoudkhani

    Full Text Available Abstract The nonlinear vibration and normal mode shapes of FG cylindrical shells are investigated using an efficient analytical method. The equations of motion of the shell are based on the Donnell’s non-linear shallow-shell, and the material is assumed to be gradually changed across the thickness according to the simple power law. The solution is provided by first discretizing the equations of motion using the multi-mode Galerkin’s method. The nonlinear normal mode of the system is then extracted using the invariant manifold approach and employed to decouple the discretized equations. The homotopy analysis method is finally used to determine the nonlinear frequency. Numerical results are presented for the backbone curves of FG cylindrical shells, nonlinear mode shapes and also the nonlinear invariant modal surfaces. The volume fraction index and the geometric properties of the shell are found to be effective on the type of nonlinear behavior and also the nonlinear mode shapes of the shell. The circumferential half-wave numbers of the nonlinear mode shapes are found to change with time especially in a thinner cylinder.

  14. Nonlinear gyrokinetic simulations of the I-mode high confinement regime and comparisons with experiment

    Energy Technology Data Exchange (ETDEWEB)

    White, A. E., E-mail: whitea@mit.edu; Howard, N. T.; Creely, A. J.; Chilenski, M. A.; Greenwald, M.; Hubbard, A. E.; Hughes, J. W.; Marmar, E.; Rice, J. E.; Sierchio, J. M.; Sung, C.; Walk, J. R.; Whyte, D. G. [MIT Plasma Science and Fusion Center, Cambridge, Massachusetts 02139 (United States); Mikkelsen, D. R.; Edlund, E. M.; Kung, C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08540 (United States); Holland, C. [University of California, San Diego (UCSD) San Diego, California 92093 (United States); Candy, J.; Petty, C. C. [General Atomics, P.O. Box 85608, San Diego, California 92186 (United States); Reinke, M. L. [York University, Heslington, York YO10 5DD (United Kingdom); and others

    2015-05-15

    For the first time, nonlinear gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separation between heat and particle transport, I-mode exhibits several favorable characteristics compared to H-mode. The nonlinear gyrokinetic code GYRO [J. Candy and R. E. Waltz, J Comput. Phys. 186, 545 (2003)] is used to explore the effects of E × B shear and profile stiffness in I-mode and compare with L-mode. The nonlinear GYRO simulations show that I-mode core ion temperature and electron temperature profiles are more stiff than L-mode core plasmas. Scans of the input E × B shear in GYRO simulations show that E × B shearing of turbulence is a stronger effect in the core of I-mode than L-mode. The nonlinear simulations match the observed reductions in long wavelength density fluctuation levels across the L-I transition but underestimate the reduction of long wavelength electron temperature fluctuation levels. The comparisons between experiment and gyrokinetic simulations for I-mode suggest that increased E × B shearing of turbulence combined with increased profile stiffness are responsible for the reductions in core turbulence observed in the experiment, and that I-mode resembles H-mode plasmas more than L-mode plasmas with regards to marginal stability and temperature profile stiffness.

  15. Linear and nonlinear kinetic-stability studies in tokamaks

    International Nuclear Information System (INIS)

    Tang, W.M.; Chance, M.S.; Chen, L.; Krommes, J.A.; Lee, W.W.; Rewoldt, G.

    1982-09-01

    This paper presents results of theoretical investigations on important linear kinetic properties of low frequency instabilities in toroidal systems and on nonlinear processes which could significantly influence their impact on anomalous transport. Analytical and numerical methods and also particle simulations have been employed to carry out these studies. In particular, the following subjects are considered: (1) linear stability analysis of kinetic instabilities for realistic tokamak equilibria and the application of such calculations to the PDX and PLT tokamak experiments including the influence of a hot beam-ion component; (2) determination of nonlinearly saturated, statistically steady states of three interacting drift modes; and (3) gyrokinetic particle simulation of drift instabilities

  16. Nonlinear defect localized modes and composite gray and anti-gray solitons in one-dimensional waveguide arrays with dual-flip defects

    Science.gov (United States)

    Liu, Yan; Guan, Yefeng; Li, Hai; Luo, Zhihuan; Mai, Zhijie

    2017-08-01

    We study families of stationary nonlinear localized modes and composite gray and anti-gray solitons in a one-dimensional linear waveguide array with dual phase-flip nonlinear point defects. Unstaggered fundamental and dipole bright modes are studied when the defect nonlinearity is self-focusing. For the fundamental modes, symmetric and asymmetric nonlinear modes are found. Their stable areas are studied using different defect coefficients and their total power. For the nonlinear dipole modes, the stability conditions of this type of mode are also identified by different defect coefficients and the total power. When the defect nonlinearity is replaced by the self-defocusing one, staggered fundamental and dipole bright modes are created. Finally, if we replace the linear waveguide with a full nonlinear waveguide, a new type of gray and anti-gray solitons, which are constructed by a kink and anti-kink pair, can be supported by such dual phase-flip defects. In contrast to the usual gray and anti-gray solitons formed by a single kink, their backgrounds on either side of the gray hole or bright hump have the same phase.

  17. Reconstructed phase spaces of intrinsic mode functions. Application to postural stability analysis.

    Science.gov (United States)

    Snoussi, Hichem; Amoud, Hassan; Doussot, Michel; Hewson, David; Duchêne, Jacques

    2006-01-01

    In this contribution, we propose an efficient nonlinear analysis method characterizing postural steadiness. The analyzed signal is the displacement of the centre of pressure (COP) collected from a force plate used for measuring postural sway. The proposed method consists of analyzing the nonlinear dynamics of the intrinsic mode functions (IMF) of the COP signal. The nonlinear properties are assessed through the reconstructed phase spaces of the different IMFs. This study shows some specific geometries of the attractors of some intrinsic modes. Moreover, the volume spanned by the geometric attractors in the reconstructed phase space represents an efficient indicator of the postural stability of the subject. Experiments results corroborate the effectiveness of the method to blindly discriminate young subjects, elderly subjects and subjects presenting a risk of falling.

  18. Modulation stability and dispersive optical soliton solutions of higher order nonlinear Schrödinger equation and its applications in mono-mode optical fibers

    Science.gov (United States)

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

    2018-01-01

    In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.

  19. Nonlinear Slewing Spacecraft Control Based on Exergy, Power Flow, and Static and Dynamic Stability

    Science.gov (United States)

    Robinett, Rush D.; Wilson, David G.

    2009-10-01

    This paper presents a new nonlinear control methodology for slewing spacecraft, which provides both necessary and sufficient conditions for stability by identifying the stability boundaries, rigid body modes, and limit cycles. Conservative Hamiltonian system concepts, which are equivalent to static stability of airplanes, are used to find and deal with the static stability boundaries: rigid body modes. The application of exergy and entropy thermodynamic concepts to the work-rate principle provides a natural partitioning through the second law of thermodynamics of power flows into exergy generator, dissipator, and storage for Hamiltonian systems that is employed to find the dynamic stability boundaries: limit cycles. This partitioning process enables the control system designer to directly evaluate and enhance the stability and performance of the system by balancing the power flowing into versus the power dissipated within the system subject to the Hamiltonian surface (power storage). Relationships are developed between exergy, power flow, static and dynamic stability, and Lyapunov analysis. The methodology is demonstrated with two illustrative examples: (1) a nonlinear oscillator with sinusoidal damping and (2) a multi-input-multi-output three-axis slewing spacecraft that employs proportional-integral-derivative tracking control with numerical simulation results.

  20. Integral sliding mode-based formation control of multiple unertain robots via nonlinear disturbane observer

    Directory of Open Access Journals (Sweden)

    Dianwei Qian

    2016-11-01

    Full Text Available This article proposes a control scheme for formation of maneuvers of a team of mobile robots. The control scheme integrates the integral sliding mode control method with the nonlinear disturbance observer technique. The leader–follower formation dynamics suffer from uncertainties originated from the individual robots. The uncertainties challenge the formation control of such robots. Assuming that the uncertainties are unknown but bounded, an nonlinear disturbance observer-based observer is utilized to approximate them. The observer outputs feed on an integral sliding mode control-based controller. The controller and observer are integrated into the control scheme to realize formation maneuvers despite uncertainties. The formation stability is analyzed by means of the Lyapunov’s theorem. In the sense of Lyapunov, not only the convergence of the approximation errors is guaranteed but also such a control scheme can asymptotically stabilize the formation system. Compared to the results by the sole integral sliding mode control, some simulations are presented to demonstrate the feasibility and performance of the control scheme.

  1. Measurement of nonlinear mode coupling of tearing fluctuations

    International Nuclear Information System (INIS)

    Assadi, S.; Prager, S.C.; Sidikman, K.L.

    1992-03-01

    Three-wave nonlinear coupling of spatial Fourier modes is measured in the MST reversed field pinch by applying bi-spectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 polodial modes and 32 toroidal modes. Comparison to bi-spectra predicted by MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomittant with a broadened (presumably nonlinearly generated) k-spectrum

  2. Calculating electron cyclotron current drive stabilization of resistive tearing modes in a nonlinear magnetohydrodynamic model

    International Nuclear Information System (INIS)

    Jenkins, Thomas G.; Schnack, Dalton D.; Kruger, Scott E.; Hegna, C. C.; Sovinec, Carl R.

    2010-01-01

    A model which incorporates the effects of electron cyclotron current drive (ECCD) into the magnetohydrodynamic equations is implemented in the NIMROD code [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)] and used to investigate the effect of ECCD injection on the stability, growth, and dynamical behavior of magnetic islands associated with resistive tearing modes. In addition to qualitatively and quantitatively agreeing with numerical results obtained from the inclusion of localized ECCD deposition in static equilibrium solvers [A. Pletzer and F. W. Perkins, Phys. Plasmas 6, 1589 (1999)], predictions from the model further elaborate the role which rational surface motion plays in these results. The complete suppression of the (2,1) resistive tearing mode by ECCD is demonstrated and the relevant stabilization mechanism is determined. Consequences of the shifting of the mode rational surface in response to the injected current are explored, and the characteristic short-time responses of resistive tearing modes to spatial ECCD alignments which are stabilizing are also noted. We discuss the relevance of this work to the development of more comprehensive predictive models for ECCD-based mitigation and control of neoclassical tearing modes.

  3. Structure, stability and ELM dynamics of the H-mode pedestal in DIII-D

    International Nuclear Information System (INIS)

    Fenstermacher, M.E.; Leonard, A.W.; Osborne, T.H.

    2005-01-01

    Experiments are described that have increased understanding of the transport and stability physics that set the H-mode edge pedestal width and height, determine the onset of Type-I edge localized modes (ELMs), and produce the nonlinear dynamics of the ELM perturbation in the pedestal and scrape-off layer (SOL). Predictive models now exist for the n e pedestal profile and the p e height at the onset of Type-I ELMs, and progress has been made toward predictive models of the T e pedestal width and nonlinear ELM evolution. Similarity experiments between DIII-D and JET suggested that neutral penetration physics dominates in the relationship between the width and height of the n e pedestal while plasma physics dominates in setting the T e pedestal width. Measured pedestal conditions including edge current at ELM onset agree with intermediate-n peeling-ballooning (P-B) stability predictions. Midplane ELM dynamics data show the predicted (P-B) structure at ELM onset, large rapid variations of the SOL parameters, and fast radial propagation in later phases, similar to features in nonlinear ELM simulations. (author)

  4. Stabilization of long wavelength sausage and kink modes of a Z-pinch by nonlinear radial oscillations

    International Nuclear Information System (INIS)

    Bud'ko, A.B.; Karlson, E.T.; Liberman, M.A.

    1992-01-01

    A number of experiments with fiber-initiated dense Z-pinches, with compressional and gas-embedded Z-pinches, with imploding gas-puff Z-pinches and the straight Extrap configuration performed in the last decade demonstrated sufficiently improved stability of Z-pinch configurations. The striking stability with respect to the sausage modes can be explained, in principle, by ideal MHD theory as well as by finite plasma conductivity effects. The global kink mode can not be stabilized by the appropriate choice of the unperturbed profiles neither within the scope of the ideal MHD nor taking into account finite ion Larmor radius and viscous damping effects. In this report we shall demonstrate that stabilization of the global kink modes can be explained by the assumption that pinch is not in a stationary but in a dynamic equilibrium. (author) 12 refs., 2 figs

  5. 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

  6. Nonlinear coupling of low-n modes in PBX-M

    International Nuclear Information System (INIS)

    Sesnic, S.; Kaita, R.; Kaye, S.; Okabayashi, M.; Bell, R.E.; Kugel, H.W.; Leblanc, B.; Takahashi, H.; Gammel, G.M.; Holland, A.; Levinton, F.M.; Powers, E.J.; Im, S.

    1994-03-01

    In many of the medium and high beta discharges in PBX-M low-n modes with different n-numbers are observed. The probability of a low-n mode to be excited decreases with increasing n-number. If two modes of different frequency and n-number (ω 1 and ω 2 ; k 1 and k 2 ) are simultaneously present in the plasma, these modes interact nonlinearly and create sidebands in frequency (ω 2 ±ω 1 ) and wave-number (k 2 ±k 1 or n 2 ±n 1 and m 2 ±m 1 ). If these fundamental modes, ω 1 /k 1 and ω 2 /k 2 , contain strong harmonics, the harmonics also interact nonlinearly, creating more nonlinear products: kω 2 ±lω 1 and kk 2 ±lk 1 , where k and l are integers describing the harmonics. These modes, the products of nonlinear interaction between two fundamental modes, most probably have a kink character. During this three-wave coupling interaction, a decrease in neutron rate and an enhanced loss of medium energy ions are observed

  7. Beam Stability and Nonlinear Dynamics. Proceedings

    International Nuclear Information System (INIS)

    Parsa, Z.

    1997-01-01

    These proceedings represent papers presented at the Beam Stability and Nonlinear Dynamics symposium held in Santa Barbara in December 1996. The symposium was sponsored by the National Science Foundation as part of the United States long term accelerator research. The focus of this symposium was on nonlinear dynamics and beam stability. The topics included single-particle and many-particle dynamics, and stability in large circular accelerators such as the Large Hadron Collider(LHC). Other subjects covered were spin dynamics, nonlinear aberration correction, collective effects in the LHC, sawtooth instability and Landau damping in the presence of strong nonlinearity. There were presentations concerning plasma physics including the effect of beam echo. There are 17 papers altogether in these proceedings and 8 of them have been abstracted for the Energy Science and Technology database

  8. Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Minh-Duc Tran

    2015-01-01

    Full Text Available This paper presents a high-performance nonsingular terminal sliding mode control method for uncertain second-order nonlinear systems. First, a nonsingular terminal sliding mode surface is introduced to eliminate the singularity problem that exists in conventional terminal sliding mode control. By using this method, the system not only can guarantee that the tracking errors reach the reference value in a finite time with high-precision tracking performance but also can overcome the complex-value and the restrictions of the exponent (the exponent should be fractional number with an odd numerator and an odd denominator in traditional terminal sliding mode. Then, in order to eliminate the chattering phenomenon, a super-twisting higher-order nonsingular terminal sliding mode control method is proposed. The stability of the closed-loop system is established using the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

  9. Adaptive Actor-Critic Design-Based Integral Sliding-Mode Control for Partially Unknown Nonlinear Systems With Input Disturbances.

    Science.gov (United States)

    Fan, Quan-Yong; Yang, Guang-Hong

    2016-01-01

    This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.

  10. Linear stability of tearing modes

    International Nuclear Information System (INIS)

    Cowley, S.C.; Kulsrud, R.M.; Hahm, T.S.

    1986-05-01

    This paper examines the stability of tearing modes in a sheared slab when the width of the tearing layer is much smaller than the ion Larmor radius. The ion response is nonlocal, and the quasineutrality retains its full integal form. An expansion procedure is introduced to solve the quasineutrality equation in powers of the width of the tearing layer over the ion Larmor radius. The expansion procedure is applied to the collisionless and semi-collisional tearing modes. The first order terms in the expansion we find to be strongly stabilizing. The physics of the mode and of the stabilization is discussed. Tearing modes are observed in experiments even though the slab theory predicts stability. It is proposed that these modes grow from an equilibrium with islands at the rational surfaces. If the equilibrium islands are wider than the ion Larmor radius, the mode is unstable when Δ' is positive

  11. Nonlinear effects on mode-converted lower-hybrid waves

    International Nuclear Information System (INIS)

    Kuehl, H.H.

    1976-01-01

    Nonlinear ponderomotive force effects on mode-converted lower-hybrid waves are considered. The nonlinear distortion of these waves is shown to be governed by the cubic nonlinear Schroedinger equation. The threshold condition for self-focusing and filamentation is derived

  12. Linear and nonlinear studies of resistive-ballooning modes in a tokamak edge plasma with scrape-off layer

    International Nuclear Information System (INIS)

    Lau, Y.T.; Novakovskii, S.V.; Drake, J.F.

    1996-01-01

    We will present 2D linear and 3D nonlinear studies of resistive-ballooning modes in tokamak edge plasmas which include a closed flux region, as well as a limiter scrape-off layer (SOL) region. These studies therefore go beyond most earlier work, where the stability of the edge in the closed flux region and in the SOL have been considered separately. A 2D linear code, 2D-BALLOON, examines the stability of these curvature driven modes and provides the complete 2D eigenfunction spanning the closed flux surface region as well the open field line region. The sheath boundary condition in the SOL introduces an important new parameter λ = (m e /m i ) 1/2 v ei qR/v Te . This parameter plays a significant role in determining the stability of these modes in both the closed flux and SOL regions because of the radial coupling across the last closed flux surface (LCFS). For small λ the spectrum of unstable modes is broad and extends into the low toroidal mode number exclamation point regime where the spatial structure is flute-like. The amplitude for these modes is larger in the SOL compared to the closed flux region. However when A is increased, the low mode numbers are strongly stabilized and the high mode numbers which are strongly ballooning are the dominant modes. In this regime the radial modes straddle the LCFS. In both these cases, the variation in the plasma density is necessary for the radial localization. In the three-dimensional nonlinear simulations, we have solved a set of fluid equations in a toroidal geometry with both the closed flux region and the SOL. The introduction of the SOL to the twisted tube for the closed flux region, has been a major addition to our 3D code. We find that the turbulent transport in the SOL drops significantly as A is increased, which is consistent with our expectations from the 2D linear code results

  13. Stability of plane wave solutions of the two-space-dimensional nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Martin, D.U.; Yuen, H.C.; Saffman, P.G.

    1980-01-01

    The stability of plane, periodic solutions of the two-dimensional nonlinear Schroedinger equation to infinitesimal, two-dimensional perturbation has been calculated and verified numerically. For standing wave disturbances, instability is found for both odd and even modes; as the period of the unperturbed solution increases, the instability associated with the odd modes remains but that associated with the even mode disappears, which is consistent with the results of Zakharov and Rubenchik, Saffman and Yuen and Ablowitz and Segur on the stability of solitons. In addition, we have identified travelling wave instabilities for the even mode perturbations which are absent in the long-wave limit. Extrapolation to the case of an unperturbed solution with infinite period suggests that these instabilities may also be present for the soliton. In other words, the soliton is unstable to odd, standing-wave perturbations, and very likely also to even, travelling-wave perturbations. (orig.)

  14. Effect of nonlinear energy transport on neoclassical tearing mode stability in tokamak plasmas

    Science.gov (United States)

    Fitzpatrick, Richard

    2017-05-01

    An investigation is made into the effect of the reduction in anomalous perpendicular electron heat transport inside the separatrix of a magnetic island chain associated with a neoclassical tearing mode in a tokamak plasma, due to the flattening of the electron temperature profile in this region, on the overall stability of the mode. The onset of the neoclassical tearing mode is governed by the ratio of the divergences of the parallel and perpendicular electron heat fluxes in the vicinity of the island chain. By increasing the degree of transport reduction, the onset of the mode, as the divergence ratio is gradually increased, can be made more and more abrupt. Eventually, when the degree of transport reduction passes a certain critical value, the onset of the neoclassical tearing mode becomes discontinuous. In other words, when some critical value of the divergence ratio is reached, there is a sudden bifurcation to a branch of neoclassical tearing mode solutions. Moreover, once this bifurcation has been triggered, the divergence ratio must be reduced by a substantial factor to trigger the inverse bifurcation.

  15. Stochastic modeling of mode interactions via linear parabolized stability equations

    Science.gov (United States)

    Ran, Wei; Zare, Armin; Hack, M. J. Philipp; Jovanovic, Mihailo

    2017-11-01

    Low-complexity approximations of the Navier-Stokes equations have been widely used in the analysis of wall-bounded shear flows. In particular, the parabolized stability equations (PSE) and Floquet theory have been employed to capture the evolution of primary and secondary instabilities in spatially-evolving flows. We augment linear PSE with Floquet analysis to formally treat modal interactions and the evolution of secondary instabilities in the transitional boundary layer via a linear progression. To this end, we leverage Floquet theory by incorporating the primary instability into the base flow and accounting for different harmonics in the flow state. A stochastic forcing is introduced into the resulting linear dynamics to model the effect of nonlinear interactions on the evolution of modes. We examine the H-type transition scenario to demonstrate how our approach can be used to model nonlinear effects and capture the growth of the fundamental and subharmonic modes observed in direct numerical simulations and experiments.

  16. Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice

    International Nuclear Information System (INIS)

    Kavitha, L.; Parasuraman, E.; Gopi, D.; Prabhu, A.; Vicencio, Rodrigo A.

    2016-01-01

    We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.

  17. Experimentally observed evolution between dynamic patterns and intrinsic localized modes in a driven nonlinear electrical cyclic lattice

    Science.gov (United States)

    Shige, S.; Miyasaka, K.; Shi, W.; Soga, Y.; Sato, M.; Sievers, A. J.

    2018-02-01

    Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor. Depending on the number of cells and electrical lattice damping an LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum the LSM can be continuously converted into ILMs and vice versa. The differences in pattern formation between simulations and experimental findings are due to a low concentration of impurities. Through this novel nonlinear excitation and switching channel in cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur. Because of the general nature of these dynamical results for nonintegrable lattices applications are to be expected. The ultimate stability of driven aero machinery containing nonlinear periodic structures may be one example.

  18. Nonlinear PCA: characterizing interactions between modes of brain activity.

    OpenAIRE

    Friston, K; Phillips, J; Chawla, D; Büchel, C

    2000-01-01

    This paper presents a nonlinear principal component analysis (PCA) that identifies underlying sources causing the expression of spatial modes or patterns of activity in neuroimaging time-series. The critical aspect of this technique is that, in relation to conventional PCA, the sources can interact to produce (second-order) spatial modes that represent the modulation of one (first-order) spatial mode by another. This nonlinear PCA uses a simple neural network architecture that embodies a spec...

  19. Transition to chaos for ballooning modes stabilized by finite Larmor radius effects

    Energy Technology Data Exchange (ETDEWEB)

    Weiland, J; Wilhelmsson, H [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Elektromagnetisk Faeltteori

    1983-08-01

    The nonlinear dynamics of interacting ballooning modes, stabilized by finite Larmor radius effects is analyzed in terms of a set of equations, which exhibit stochastic properties. These are explicitly shown to depend on the balance between shear and driving pressure force. The onset of bifurcations and chaotic behaviour are directly identified with certain values of parameters characterizing the physical system.

  20. Neural Network Based Finite-Time Stabilization for Discrete-Time Markov Jump Nonlinear Systems with Time Delays

    Directory of Open Access Journals (Sweden)

    Fei Chen

    2013-01-01

    Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.

  1. Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

    Directory of Open Access Journals (Sweden)

    Dong Zhang

    2017-03-01

    Full Text Available This article presents a new fractional-order sliding mode control (FOSMC strategy based on a linear-quadratic regulator (LQR for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.

  2. A new algebraic growth of nonlinear tearing mode

    International Nuclear Information System (INIS)

    Li, D.

    1995-01-01

    It is found that the quasilinear modification of magnetic field produces a nonlinear Lorentz force opposing the linear driving force and slowing down the vortex flow. A new algebraic growth appears due to this damping mechanism to oppose the linear growth of the tearing mode. This effect was eliminated in Rutherford's model [Phys. Fluids 16, 1903 (1973)] under the flux average operation and the assumption ∂/∂t much-lt η/δ 2 (here η is the resistivity, δ is the resistive layer width). A unified analytical model is developed by using standard perturbation theory for the linear and nonlinear growth of the tearing mode. The inertia effect and quasilinear effects of both the current density and the magnetic field have been included. A nonlinear evolution equation is analytically derived for the tearing mode to describe the linear growth, Rutherford's behavior, and the new behavior. The classical linear result is exactly recovered as the quasilinear effects are negligible. It is shown that a more slowly algebraic growth like Ψ 1 ∝t can become dominant in the nonlinear phase instead of Rutherford behavior like Ψ 1 ∝t 2 , provided the tearing mode in the linear phase is strongly unstable. Here Ψ 1 is the magnetic flux perturbation. copyright 1995 American Institute of Physics

  3. On Stabilization of Nonautonomous Nonlinear Systems

    International Nuclear Information System (INIS)

    Bogdanov, A. Yu.

    2008-01-01

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

  4. Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems

    Directory of Open Access Journals (Sweden)

    Junhai Luo

    2014-01-01

    Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.

  5. Nonlinear adaptive observer-based sliding mode control for LAMOST mount driving

    International Nuclear Information System (INIS)

    Zhou Wangping; Guo Wei; Yu Li; Yang Changsong; Zheng Yi

    2010-01-01

    Heavy disturbances caused mainly by wind and friction in the mount drive system greatly impair the pointing accuracy of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST). To overcome this negative effect, a third order Higher Order Sliding Mode (HOSM) controller is proposed. The key part of this approach is to design an appropriate observer which obtains the acceleration state. A nonlinear adaptive observer is proposed in which a novel polynomial model is applied to estimate the internal disturbances of the mount drive system. Theoretical analysis demonstrates the stability of the proposed observer. Simulation results show that this nonlinear adaptive observer can obtain a high precision acceleration signal which completes the HOSM controller. Furthermore, the HOSM approach can easily satisfy the position tracking requirements of the LAMOST mount drive system.

  6. Discrete-time nonlinear sliding mode controller

    African Journals Online (AJOL)

    user

    Keywords: Discrete-time delay system, Sliding mode control, nonlinear sliding ... of engineering systems such as chemical process control, delay in the actuator ...... instrumentation from Motilal Nehru National Institute of Technology (MNNIT),.

  7. Robust stabilization of nonlinear systems: The LMI approach

    Directory of Open Access Journals (Sweden)

    Šiljak D. D.

    2000-01-01

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

  8. Ideal MHD stability and characteristics of edge localized modes on CFETR

    Science.gov (United States)

    Li, Ze-Yu; Chan, V. S.; Zhu, Yi-Ren; Jian, Xiang; Chen, Jia-Le; Cheng, Shi-Kui; Zhu, Ping; Xu, Xue-Qiao; Xia, Tian-Yang; Li, Guo-Qiang; Lao, L. L.; Snyder, P. B.; Wang, Xiao-Gang; the CFETR Physics Team

    2018-01-01

    Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for the China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario (R  =  5.7 m, B T  =  5 T) derived from multi-code integrated modeling, with key parameters {{β }N},{{β }T},{{β }p} varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for the engineering design. The long wavelength low-n global ideal MHD stability of the CFETR baseline scenario, including the wall stabilization effect, is evaluated by GATO. It is found that the low-n core modes are stable with a wall at r/a  =  1.2. An investigation of intermediate wavelength ideal MHD modes (peeling ballooning modes) is also carried out by multi-code benchmarking, including GATO, ELITE, BOUT++ and NIMROD. A good agreement is achieved in predicting edge-localized instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT++. A mix of grassy and type I ELMs is identified. When the size and magnetic field of CFETR are increased (R  =  6.6 m, B T  =  6 T), collisionality correspondingly increases and the instability is expected to shift to grassy ELMs.

  9. Nonlinear physical systems spectral analysis, stability and bifurcations

    CERN Document Server

    Kirillov, Oleg N

    2013-01-01

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

  10. Nonlinear coupling of kink modes in Tokamaks

    International Nuclear Information System (INIS)

    Dagazian, R.Y.

    1975-07-01

    The m = 2, n = 1 kink mode is shown to be capable of destabilizing the m = 1, n = 1 internal kink. A nonlinear Lagrangian theory is developed for the coupling of modes of different pitch, and it is applied to the interaction of these modes. The coupling to the m = 2 mode provides sufficient additional destabilization to the internal mode to permit it to account even quantitatively (where it had failed when considered by itself) for many of the features of the disruptive instability. (U.S.)

  11. Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates

    International Nuclear Information System (INIS)

    He, Y J; Wang, H Z; Malomed, Boris A; Mihalache, Dumitru

    2008-01-01

    We demonstrate that by spatially modulating the Bessel optical lattice where a Bose-Einstein condensate is loaded, we get tunable rotary orbits of nonlinear lattice modes. We show that the radially expanding or shrinking Bessel lattice can drag the nonlinear localized modes to orbits of either larger or smaller radii and the rotary velocity of nonlinear modes can be changed accordingly. The localized modes can even be transferred to the Bessel lattice core when the localized modes' rotations are stopped. Effects beyond the quasi-particle approximation such as destruction of the nonlinear modes by nonadiabatic dragging are also explored

  12. Structural stability of nonlinear population dynamics.

    Science.gov (United States)

    Cenci, Simone; Saavedra, Serguei

    2018-01-01

    In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

  13. Structural stability of nonlinear population dynamics

    Science.gov (United States)

    Cenci, Simone; Saavedra, Serguei

    2018-01-01

    In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

  14. Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars

    International Nuclear Information System (INIS)

    Schenk, A.K.; Arras, P.; Flanagan, E.E.; Teukolsky, S.A.; Wasserman, I.

    2002-01-01

    We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars, assuming that the mode amplitudes are only mildly nonlinear. The formalism is simpler than previous treatments of mode-mode interactions for spherical stars, and simplifies and corrects previous treatments for rotating stars. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings, which suffices for moderate amplitude modal excitations; the formalism is easy to extend to higher order couplings. We describe a new, efficient way to compute the modal coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. The formalism is general enough to allow computation of the initial trends in the evolution of the spin frequency and differential rotation of the background star. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. First, we clarify some aspects of the expansion in stellar rotation frequency Ω that is often used to compute approximate mode functions. We show that, in zero-buoyancy stars, the rotational modes (those modes whose frequencies vanish as Ω→0) are orthogonal to zeroth order in Ω. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r modes to other rotational modes are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in Ω or in compressibility. In particular, in zero-buoyancy stars, the coupling of three r modes is forbidden

  15. Optimal Sliding Mode Controllers for Attitude Stabilization of Flexible Spacecraft

    Directory of Open Access Journals (Sweden)

    Chutiphon Pukdeboon

    2011-01-01

    Full Text Available The robust optimal attitude control problem for a flexible spacecraft is considered. Two optimal sliding mode control laws that ensure the exponential convergence of the attitude control system are developed. Integral sliding mode control (ISMC is applied to combine the first-order sliding mode with optimal control and is used to control quaternion-based spacecraft attitude manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state-dependent Riccati equation (SDRE and optimal Lyapunov techniques are employed to solve the infinite-time nonlinear optimal control problem. The second method of Lyapunov is used to guarantee the stability of the attitude control system under the action of the proposed control laws. An example of multiaxial attitude manoeuvres is presented and simulation results are included to verify the usefulness of the developed controllers.

  16. High-mode-number ballooning modes in a heliotron/torsatron system. II. Stability

    International Nuclear Information System (INIS)

    Nakajima, N.

    1996-01-01

    In heliotron/torsatron systems that have a large Shafranov shift, the local magnetic shear is found to have no stabilizing effect on high-mode-number ballooning modes at the outer side of the torus, even in the region where the global shear is stellarator-like in nature. The disappearance of this stabilization, in combination with the compression of the flux surfaces at the outer side of the torus, leads at relatively low values of the plasma pressure to significant modifications of the stabilizing effect due to magnetic field-line bending on high-mode-number ballooning modes-specifically, that the field-line bending stabilization can be remarkably suppressed or enhanced. In an equilibrium that is slightly Mercier-unstable or completely Mercier-stable due to peaked pressure profiles, such as those used in standard stability calculations, high-mode-number ballooning modes are destabilized due to these modified stability effects, with their eigenfunctions highly localized along the field line. Highly localized mode structures such as these cause the ballooning mode eigenvalues ω 2 to have a strong field line dependence (i.e., α-variation) through the strong dependence of the local magnetic curvature, such that the level surfaces of ω 2 (ψ,θ k ,α) (≤0) become spheroids in (ψ,θ k ,α) space, where ψ labels flux surfaces and θ k is the radial wave number. Because the spheroidal level surfaces for unstable eigenvalues are surrounded by level surfaces for stable eigenvalues of high-mode-number toroidal Alfvacute en eigenmodes, those high-mode-number ballooning modes never lead to low-mode-number modes. In configuration space, these high-mode-number modes are localized in a single toroidal pitch of the helical coils, and hence they may experience substantial stabilization due to finite Larmor radius effects. copyright 1996 American Institute of Physics

  17. Squeezing in multi-mode nonlinear optical state truncation

    International Nuclear Information System (INIS)

    Said, R.S.; Wahiddin, M.R.B.; Umarov, B.A.

    2007-01-01

    In this Letter, we show that multi-mode qubit states produced via nonlinear optical state truncation driven by classical external pumpings exhibit squeezing condition. We restrict our discussions to the two- and three-mode cases

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

    International Nuclear Information System (INIS)

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

    1985-09-01

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

  19. Stability, Nonlinearity and Reliability of Electrostatically Actuated MEMS Devices

    Directory of Open Access Journals (Sweden)

    Di Chen

    2007-05-01

    Full Text Available Electrostatic micro-electro-mechanical system (MEMS is a special branch with a wide range of applications in sensing and actuating devices in MEMS. This paper provides a survey and analysis of the electrostatic force of importance in MEMS, its physical model, scaling effect, stability, nonlinearity and reliability in detail. It is necessary to understand the effects of electrostatic forces in MEMS and then many phenomena of practical importance, such as pull-in instability and the effects of effective stiffness, dielectric charging, stress gradient, temperature on the pull-in voltage, nonlinear dynamic effects and reliability due to electrostatic forces occurred in MEMS can be explained scientifically, and consequently the great potential of MEMS technology could be explored effectively and utilized optimally. A simplified parallel-plate capacitor model is proposed to investigate the resonance response, inherent nonlinearity, stiffness softened effect and coupled nonlinear effect of the typical electrostatically actuated MEMS devices. Many failure modes and mechanisms and various methods and techniques, including materials selection, reasonable design and extending the controllable travel range used to analyze and reduce the failures are discussed in the electrostatically actuated MEMS devices. Numerical simulations and discussions indicate that the effects of instability, nonlinear characteristics and reliability subjected to electrostatic forces cannot be ignored and are in need of further investigation.

  20. Eddy Heat Conduction and Nonlinear Stability of a Darcy Lapwood System Analysed by the Finite Spectral Method

    Directory of Open Access Journals (Sweden)

    Jónas Elíasson

    2014-01-01

    Full Text Available A finite Fourier transform is used to perform both linear and nonlinear stability analyses of a Darcy-Lapwood system of convective rolls. The method shows how many modes are unstable, the wave number instability band within each mode, the maximum growth rate (most critical wave numbers on each mode, and the nonlinear growth rates for each amplitude as a function of the porous Rayleigh number. Single amplitude controls the nonlinear growth rates and thereby the physical flow rate and fluid velocity, on each mode. They are called the flak amplitudes. A discrete Fourier transform is used for numerical simulations and here frequency combinations appear that the traditional cut-off infinite transforms do not have. The discrete show a stationary solution in the weak instability phase, but when carried past 2 unstable modes they show fluctuating motion where all amplitudes except the flak may be zero on the average. This leads to a flak amplitude scaling process of the heat conduction, producing an eddy heat conduction coefficient where a Nu-RaL relationship is found. It fits better to experiments than previously found solutions but is lower than experiments.

  1. Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

    Science.gov (United States)

    Balsa, Thomas F.; Gartside, James

    1995-01-01

    The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

  2. Nonlinear behavior of multiple-helicity resistive interchange modes near marginally stable states

    International Nuclear Information System (INIS)

    Sugama, Hideo; Nakajima, Noriyoshi; Wakatani, Masahiro.

    1991-05-01

    Nonlinear behavior of resistive interchange modes near marginally stable states is theoretically studied under the multiple-helicity condition. Reduced fluid equations in the sheared slab configuration are used in order to treat a local transport problem. With the use of the invariance property of local reduced fluid model equations under a transformation between the modes with different rational surfaces, weakly nonlinear theories for single-helicity modes by Hamaguchi and Nakajima are extended to the multiple-helicity case and applied to the resistive interchange modes. We derive the nonlinear amplitude equations of the multiple-helicity modes, from which the convective transport in the saturated state is obtained. It is shown how the convective transport is enhanced by nonlinear interaction between modes with different rational surfaces compared with the single-helicity case. We confirm that theoretical results are in good agreement with direct numerical simulations. (author)

  3. Nonlinear Mirror and Weibel modes: peculiarities of quasi-linear dynamics

    Directory of Open Access Journals (Sweden)

    O. A. Pokhotelov

    2010-12-01

    Full Text Available A theory for nonlinear evolution of the mirror modes near the instability threshold is developed. It is shown that during initial stage the major instability saturation is provided by the flattening of the velocity distribution function in the vicinity of small parallel ion velocities. The relaxation scenario in this case is accompanied by rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic BGK modes. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by relevant numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode. The similarity with resonant Weibel instability is discussed.

  4. Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability

    DEFF Research Database (Denmark)

    Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar

    2017-01-01

    technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness....... CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic......To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation...

  5. Non-linear sliding mode control of the lower extremity exoskeleton based on human–robot cooperation

    Directory of Open Access Journals (Sweden)

    Shiqiang Zhu

    2016-10-01

    Full Text Available This article presents a human–robot cooperation controller towards the lower extremity exoskeleton which aims to improve the tracking performance of the exoskeleton and reduce the human–robot interaction force. Radial basis function neural network is introduced to model the human–machine interaction which can better approximate the non-linear relationship than the general impedance model. A new method to calculate the inverse Jacobian matrix is presented. Compared to traditional damped least squares method, the novel method is proved to be able to avoid the orientation change of the velocity of the human–robot interaction point by the simulation result. This feature is very important in human–robot system. Then, an improved non-linear robust sliding mode controller is designed to promote the tracking performance considering system uncertainties and model errors, where a new non-linear integral sliding surface is given. The stability analysis of the proposed controller is performed using Lyapunov stability theory. Finally, the novel methods are applied to the swing leg control of the lower extremity exoskeleton, its effectiveness is validated by simulation and comparative experiments.

  6. Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities

    International Nuclear Information System (INIS)

    Itasse, Maxime; Brazier, Jean-Philippe; Léon, Olivier; Casalis, Grégoire

    2015-01-01

    Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m 1 , n 1 ), (m 2 , n 2 ), such that the difference in azimuth and in frequency matches the desired “target” mode (m 1 − m 2 , n 1 − n 2 ). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes

  7. Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities

    Energy Technology Data Exchange (ETDEWEB)

    Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr; Casalis, Grégoire, E-mail: Gregoire.Casalis@onera.fr [Onera - The French Aerospace Lab, F-31055 Toulouse (France)

    2015-08-15

    Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequency matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.

  8. Stability analysis of embedded nonlinear predictor neural generalized predictive controller

    Directory of Open Access Journals (Sweden)

    Hesham F. Abdel Ghaffar

    2014-03-01

    Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.

  9. Adaptive Neural-Sliding Mode Control of Active Suspension System for Camera Stabilization

    Directory of Open Access Journals (Sweden)

    Feng Zhao

    2015-01-01

    Full Text Available The camera always suffers from image instability on the moving vehicle due to the unintentional vibrations caused by road roughness. This paper presents a novel adaptive neural network based on sliding mode control strategy to stabilize the image captured area of the camera. The purpose is to suppress vertical displacement of sprung mass with the application of active suspension system. Since the active suspension system has nonlinear and time varying characteristics, adaptive neural network (ANN is proposed to make the controller robustness against systematic uncertainties, which release the model-based requirement of the sliding model control, and the weighting matrix is adjusted online according to Lyapunov function. The control system consists of two loops. The outer loop is a position controller designed with sliding mode strategy, while the PID controller in the inner loop is to track the desired force. The closed loop stability and asymptotic convergence performance can be guaranteed on the basis of the Lyapunov stability theory. Finally, the simulation results show that the employed controller effectively suppresses the vibration of the camera and enhances the stabilization of the entire camera, where different excitations are considered to validate the system performance.

  10. Aircraft nonlinear stability analysis and multidimensional stability region estimation under icing conditions

    Directory of Open Access Journals (Sweden)

    Liang QU

    2017-06-01

    Full Text Available Icing is one of the crucial factors that could pose great threat to flight safety, and thus research on stability and stability region of aircraft safety under icing conditions is significant for control and flight. Nonlinear dynamical equations and models of aerodynamic coefficients of an aircraft are set up in this paper to study the stability and stability region of the aircraft under an icing condition. Firstly, the equilibrium points of the iced aircraft system are calculated and analyzed based on the theory of differential equation stability. Secondly, according to the correlation theory about equilibrium points and the stability region, this paper estimates the multidimensional stability region of the aircraft, based on which the stability regions before and after icing are compared. Finally, the results are confirmed by the time history analysis. The results can give a reference for stability analysis and envelope protection of the nonlinear system of an iced aircraft.

  11. Asymptotic stabilization of nonlinear systems using state feedback

    International Nuclear Information System (INIS)

    D'Attellis, Carlos

    1990-01-01

    This paper studies the design of state-feedback controllers for the stabilization of single-input single-output nonlinear systems x = f(x) + g(x)u, y = h(x). Two approaches for the stabilization problem are given; the asymptotic stability is achieved by means of: a) nonlinear state feedback: two nonlinear feedbacks are used; the first separates the system in a controllable linear part and in the zeros-dynamic part. The second feedback generates an asymptotically stable equilibrium on the manifold where this dynamics evolves; b) nonlinear dynamic feedback: conditions are established under which the system can follow the output of a completely controllable bilinear system which uses bounded controls. This fact enables the system to reach, using bounded controls too, a desired output value in finite time. As this value corresponds to a state that lays in the attraction basin of a stable equilibrium with the same output, the system evolves to that point. The two methods are illustrated by examples. (Author) [es

  12. Nonlinear Equilibrium and Stability Analysis of Axially Loaded Piles Under Bilateral Contact Constraints

    Directory of Open Access Journals (Sweden)

    Ricardo A. da Mota Silveira

    Full Text Available AbstractThis paper presents a nonlinear stability analysis of piles under bilateral contact constraints imposed by a geological medium (soil or rock. To solve this contact problem, the paper proposes a general numerical methodology, based on the finite element method (FEM. In this context, a geometrically nonlinear beam-column element is used to model the pile while the geological medium can be idealized as discrete (spring or continuum (Winkler and Pasternak foundation elements. Foundation elements are supposed to react under tension and compression, so during the deformation process the structural elements are subjected to bilateral contact constraints. The errors along the equilibrium paths are minimized and the convoluted nonlinear equilibrium paths are made traceable through the use of an updated Lagrangian formulation and a Newton-Raphson scheme working with the generalized displacement technique. The study offers stability analyses of three problems involving piles under bilateral contact constraints. The analyses show that in the evaluation of critical loads a great influence is wielded by the instability modes. Also, the structural system stiffness can be highly influenced by the representative model of the soil.

  13. Increase of nonlinear signal distortions due to linear mode coupling in space division multiplexed systems

    DEFF Research Database (Denmark)

    Kutluyarov, Ruslan V.; Bagmanov, Valeriy Kh; Antonov, Vyacheslav V.

    2017-01-01

    This paper is focused on the analysis of linear and nonlinear mode coupling in space division multiplexed (SDM) optical communications over step-index fiber in few-mode regime. Linear mode coupling is caused by the fiber imperfections, while the nonlinear coupling is caused by the Kerr......-nonlinearities. Therefore, we use the system of generalized coupled nonlinear Schrödinger equations (GCNLSE) to describe the signal propagation. We analytically show that the presence of linear mode coupling may cause increasing of the nonlinear signal distortions. For the detailed study we solve GCNLSE numerically...... for the standard step index fiber at the wavelength of 850 nm in the basis of spatial modes with helical phase front (vortex modes) and for a special kind of few-mode fiber with enlarged core, providing propagation of five spatial modes at 1550 nm. Simulation results confirm that the linear mode coupling may lead...

  14. Nonlinear process in the mode transition in typical strut-based and cavity-strut based scramjet combustors

    Science.gov (United States)

    Yan, Li; Liao, Lei; Huang, Wei; Li, Lang-quan

    2018-04-01

    The analysis of nonlinear characteristics and control of mode transition process is the crucial issue to enhance the stability and reliability of the dual-mode scramjet engine. In the current study, the mode transition processes in both strut-based combustor and cavity-strut based combustor are numerically studied, and the influence of the cavity on the transition process is analyzed in detail. The simulations are conducted by means of the Reynolds averaged Navier-Stokes (RANS) equations coupled with the renormalization group (RNG) k-ε turbulence model and the single-step chemical reaction mechanism, and this numerical approach is proved to be valid by comparing the predicted results with the available experimental shadowgraphs in the open literature. During the mode transition process, an obvious nonlinear property is observed, namely the unevenly variations of pressure along the combustor. The hysteresis phenomenon is more obvious upstream of the flow field. For the cavity-strut configuration, the whole flow field is more inclined to the supersonic state during the transition process, and it is uneasy to convert to the ramjet mode. In the scram-to-ram transition process, the process would be more stable, and the hysteresis effect would be reduced in the ram-to-scram transition process.

  15. Nonlinear stability of ideal fluid equilibria

    International Nuclear Information System (INIS)

    Holm, D.D.

    1988-01-01

    The Lyapunov method for establishing stability is related to well- known energy principles for nondissipative dynamical systems. A development of the Lyapunov method for Hamiltonian systems due to Arnold establishes sufficient conditions for Lyapunov stability by using the energy plus other conserved quantities, together with second variations and convexity estimates. When treating the stability of ideal fluid dynamics within the Hamiltonian framework, a useful class of these conserved quantities consists of the Casimir functionals, which Poisson-commute with all functionals of the dynamical fluid variables. Such conserved quantities, when added to the energy, help to provide convexity estimates that bound the growth of perturbations. These convexity estimates, in turn, provide norms necessary for establishing Lyapunov stability under the nonlinear evolution. In contrast, the commonly used second variation or spectral stability arguments only prove linearized stability. As ideal fluid examples, in these lectures we discuss planar barotropic compressible fluid dynamics, the three-dimensional hydrostatic Boussinesq model, and a new set of shallow water equations with nonlinear dispersion due to Basdenkov, Morosov, and Pogutse[1985]. Remarkably, all three of these samples have the same Hamiltonian structure and, thus, possess the same Casimir functionals upon which their stability analyses are based. We also treat stability of modified quasigeostrophic flow, a problem whose Hamiltonian structure and Casimirs closely resemble Arnold's original example. Finally, we discuss some aspects of conditional stability and the applicability of Arnold's development of the Lyapunov technique. 100 refs

  16. The non-linear evolution of edge localized modes

    International Nuclear Information System (INIS)

    Wenninger, Ronald

    2013-01-01

    Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal

  17. The non-linear evolution of edge localized modes

    Energy Technology Data Exchange (ETDEWEB)

    Wenninger, Ronald

    2013-01-09

    Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal

  18. Spatiotemporal light-beam compression from nonlinear mode coupling

    Science.gov (United States)

    Krupa, Katarzyna; Tonello, Alessandro; Couderc, Vincent; Barthélémy, Alain; Millot, Guy; Modotto, Daniele; Wabnitz, Stefan

    2018-04-01

    We experimentally demonstrate simultaneous spatial and temporal compression in the propagation of light pulses in multimode nonlinear optical fibers. We reveal that the spatial beam self-cleaning recently discovered in graded-index multimode fibers is accompanied by significant temporal reshaping and up to fourfold shortening of the injected subnanosecond laser pulses. Since the nonlinear coupling among the modes strongly depends on the instantaneous power, we explore the entire range of the nonlinear dynamics with a single optical pulse, where the optical power is continuously varied across the pulse profile.

  19. Mode coupling in nonlinear Rayleigh--Taylor instability

    International Nuclear Information System (INIS)

    Ofer, D.; Shvarts, D.; Zinamon, Z.; Orszag, S.A.

    1992-01-01

    This paper studies the interaction of a small number of modes in the two-fluid Rayleigh--Taylor instability at relatively late stages of development, i.e., the nonlinear regime, using a two-dimensional hydrodynamic code incorporating a front-tracking scheme. It is found that the interaction of modes can greatly affect the amount of mixing and may even reduce the width of the mixing region. This interaction is both relatively long range in wave-number space and also acts in both directions, i.e., short wavelengths affect long wavelengths and vice versa. Three distinct stages of interaction have been identified, including substantial interaction among modes some of which may still be in their classical (single mode) ''linear'' phase

  20. Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion.

    Science.gov (United States)

    Siminos, Evangelos; Bénisti, Didier; Gremillet, Laurent

    2011-05-01

    We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed. © 2011 American Physical Society

  1. Nonlinear evolution of Mack modes in a hypersonic boundary layer

    Science.gov (United States)

    Chokani, Ndaona

    2005-01-01

    In hypersonic boundary layer flows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layer transition. In the case of low-level freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Cross-bicoherence measurements, derived from hot-wire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phase-locked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, cross-bicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the low-frequency, phase-locked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.

  2. Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer.

    Science.gov (United States)

    Wedin, Håkan; Cherubini, Stefania; Bottaro, Alessandro

    2015-07-01

    The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K̂ of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K̂=0). This leads to a Reynolds number of approximately Re(c)=54400 for the onset of linearly unstable waves, and close to Re(g)=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985); J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Re(c)=796 and Re(g)=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re(-ρ), where the value of ρ depends on the permeability coefficient K̂. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for

  3. Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay

    Directory of Open Access Journals (Sweden)

    S. J. Sadati

    2010-01-01

    Full Text Available Fractional calculus started to play an important role for analysis of the evolution of the nonlinear dynamical systems which are important in various branches of science and engineering. In this line of taught in this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative, and we proved two theorems for Mittag-Leffler stability of the fractional nonlinear time delay systems.

  4. Resistive wall mode stabilization in slowly rotating high beta plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Reimerdes, H [Columbia University, New York, NY 10027 (United States); Garofalo, A M [Columbia University, New York, NY 10027 (United States); Okabayashi, M [Princeton Plasma Physics Laboratory, Princeton, NJ 08543-0451 (United States); Strait, E J [General Atomics, San Diego, CA 92186-5608 (United States); Betti, R [University of Rochester, Rochester, NY 14627 (United States); Chu, M S [General Atomics, San Diego, CA 92186-5608 (United States); Hu, B [University of Rochester, Rochester, NY 14627 (United States); In, Y [FAR-TECH, Inc., San Diego, CA 92121 (United States); Jackson, G L [General Atomics, San Diego, CA 92186-5608 (United States); La Haye, R J [General Atomics, San Diego, CA 92186-5608 (United States); Lanctot, M J [Columbia University, New York, NY 10027 (United States); Liu, Y Q [Chalmers University of Technology, S-412 96 Goeteborg (Sweden); Navratil, G A [Columbia University, New York, NY 10027 (United States); Solomon, W M [Princeton Plasma Physics Laboratory, Princeton, NJ 08543-0451 (United States); Takahashi, H [Princeton Plasma Physics Laboratory, Princeton, NJ 08543-0451 (United States); Groebner, R J [General Atomics, San Diego, CA 92186-5608 (United States)

    2007-12-15

    DIII-D experiments show that the resistive wall mode (RWM) can remain stable in high {beta} scenarios despite a low net torque from nearly balanced neutral beam injection heating. The minimization of magnetic field asymmetries is essential for operation at the resulting low plasma rotation of less than 20 krad s{sup -1} (measured with charge exchange recombination spectroscopy using C VI emission) corresponding to less than 1% of the Alfven velocity or less than 10% of the ion thermal velocity. In the presence of n = 1 field asymmetries the rotation required for stability is significantly higher and depends on the torque input and momentum confinement, which suggests that a loss of torque-balance can lead to an effective rotation threshold above the linear RWM stability threshold. Without an externally applied field the measured rotation can be too low to neglect the diamagnetic rotation. A comparison of the instability onset in plasmas rotating with and against the direction of the plasma current indicates the importance of the toroidal flow driven by the radial electric field in the stabilization process. Observed rotation thresholds are compared with predictions for the semi-kinetic damping model, which generally underestimates the rotation required for stability. A more detailed modeling of kinetic damping including diamagnetic and precession drift frequencies can lead to stability without plasma rotation. However, even with corrected error fields and fast plasma rotation, plasma generated perturbations, such as edge localized modes, can nonlinearly destabilize the RWM. In these cases feedback control can increase the damping of the magnetic perturbation and is effective in extending the duration of high {beta} discharges.

  5. Stability of one-step methods in transient nonlinear heat conduction

    International Nuclear Information System (INIS)

    Hughes, J.R.

    1977-01-01

    The purpose of the present work is to ascertain practical stability conditions for one-step methods commonly used in transient nonlinear heat conduction analyses. In this paper the concepts of stability, appropriate to the nonlinear problem, are thoroughly discussed. They of course reduce to the usual stability critierion for the linear, constant coefficient case. However, for nonlinear problems there are differences and theses ideas are of key importance in obtaining practical stability conditions. Of particular importance is a recent result which indicates that, in a sense, the trapezoidal and midpoint families are equivalent. Thus, stability results for one family may be translated into a result for the other. The main results obtained are: The stability behaviour of the explicit Euler method in the nonlinear regime is analogous to that for linear problems. In particular, an a priori step size restriction may be determined for each time step. The precise time step restriction on implicit conditionally stable members of the trapezoidal and midpoint families is shown not to be determinable a priori. Of considerable practical significance, unconditionally stable members of the trapezoidal and midpoint families are identified. All notions of stability employed are motivated and defined, and their interpretations in practical computing are indicated. (Auth.)

  6. Oblique non-neutral solitary Alfven modes in weakly nonlinear pair plasmas

    International Nuclear Information System (INIS)

    Verheest, Frank; Lakhina, G S

    2005-01-01

    The equal charge-to-mass ratio for both species in pair plasmas induces a decoupling of the linear eigenmodes between waves that are charge neutral or non-neutral, also at oblique propagation with respect to a static magnetic field. While the charge-neutral linear modes have been studied in greater detail, including their weakly and strongly nonlinear counterparts, the non-neutral mode has received less attention. Here the nonlinear evolution of a solitary non-neutral mode at oblique propagation is investigated in an electron-positron plasma. Employing the framework of reductive perturbation analysis, a modified Korteweg-de Vries equation (with cubic nonlinearity) for the lowest-order wave magnetic field is obtained. In the linear approximation, the non-neutral mode has its magnetic component orthogonal to the plane spanned by the directions of wave propagation and of the static magnetic field. The linear polarization is not maintained at higher orders. The results may be relevant to the microstructure in pulsar radiation or to the subpulses

  7. A vehicle stability control strategy with adaptive neural network sliding mode theory based on system uncertainty approximation

    Science.gov (United States)

    Ji, Xuewu; He, Xiangkun; Lv, Chen; Liu, Yahui; Wu, Jian

    2018-06-01

    Modelling uncertainty, parameter variation and unknown external disturbance are the major concerns in the development of an advanced controller for vehicle stability at the limits of handling. Sliding mode control (SMC) method has proved to be robust against parameter variation and unknown external disturbance with satisfactory tracking performance. But modelling uncertainty, such as errors caused in model simplification, is inevitable in model-based controller design, resulting in lowered control quality. The adaptive radial basis function network (ARBFN) can effectively improve the control performance against large system uncertainty by learning to approximate arbitrary nonlinear functions and ensure the global asymptotic stability of the closed-loop system. In this paper, a novel vehicle dynamics stability control strategy is proposed using the adaptive radial basis function network sliding mode control (ARBFN-SMC) to learn system uncertainty and eliminate its adverse effects. This strategy adopts a hierarchical control structure which consists of reference model layer, yaw moment control layer, braking torque allocation layer and executive layer. Co-simulation using MATLAB/Simulink and AMESim is conducted on a verified 15-DOF nonlinear vehicle system model with the integrated-electro-hydraulic brake system (I-EHB) actuator in a Sine With Dwell manoeuvre. The simulation results show that ARBFN-SMC scheme exhibits superior stability and tracking performance in different running conditions compared with SMC scheme.

  8. Simplex sliding mode control for nonlinear uncertain systems via chaos optimization

    International Nuclear Information System (INIS)

    Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P.

    2005-01-01

    As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method

  9. Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

    Directory of Open Access Journals (Sweden)

    Minsong Zhang

    2014-01-01

    Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

  10. NOLB: Nonlinear Rigid Block Normal Mode Analysis Method

    OpenAIRE

    Hoffmann , Alexandre; Grudinin , Sergei

    2017-01-01

    International audience; We present a new conceptually simple and computationally efficient method for nonlinear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a nonlinear extrapolation of motion out of these veloci...

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

    CERN Document Server

    Chen, Zhiyong

    2015-01-01

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

  12. Stability charts for uniform slopes in soils with nonlinear failure envelopes

    OpenAIRE

    Eid, Hisham T.

    2014-01-01

    Based on the results of an extensive parametric study, charts were developed for assessment of the stability of uniform slopes in soils with nonlinear shear strength failure envelopes. The study was conducted using envelopes formed to represent the realistic shapes of soil nonlinear drained strength envelopes and the associated different degrees of nonlinearity. The introduction of a simple methodology to describe the nonlinear envelopes and a stability parameter, the value of which depends o...

  13. Nonlinear spatial mode imaging of hybrid photonic crystal fibers

    DEFF Research Database (Denmark)

    Petersen, Sidsel Rübner; Alkeskjold, Thomas Tanggaard; Laurila, Marko

    2013-01-01

    Degenerate spontaneous four wave mixing is studied for the rst time in a large mode area hybrid photonic crystal ber, where light con nement is achieved by combined index- and bandgap guiding. Four wave mixing products are generated on the edges of the bandgaps, which is veri ed by numerical and ...... and experimental results. Since the core mode is in resonance with cladding modes near the bandedges an unconventional measurement technique is used, in this work named nonlinear spatial mode imaging....

  14. Continuous-wave to pulse regimes for a family of passively mode-locked lasers with saturable nonlinearity

    Science.gov (United States)

    Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

    2017-10-01

    The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

  15. Extracting Leading Nonlinear Modes of Changing Climate From Global SST Time Series

    Science.gov (United States)

    Mukhin, D.; Gavrilov, A.; Loskutov, E. M.; Feigin, A. M.; Kurths, J.

    2017-12-01

    Data-driven modeling of climate requires adequate principal variables extracted from observed high-dimensional data. For constructing such variables it is needed to find spatial-temporal patterns explaining a substantial part of the variability and comprising all dynamically related time series from the data. The difficulties of this task rise from the nonlinearity and non-stationarity of the climate dynamical system. The nonlinearity leads to insufficiency of linear methods of data decomposition for separating different processes entangled in the observed time series. On the other hand, various forcings, both anthropogenic and natural, make the dynamics non-stationary, and we should be able to describe the response of the system to such forcings in order to separate the modes explaining the internal variability. The method we present is aimed to overcome both these problems. The method is based on the Nonlinear Dynamical Mode (NDM) decomposition [1,2], but takes into account external forcing signals. An each mode depends on hidden, unknown a priori, time series which, together with external forcing time series, are mapped onto data space. Finding both the hidden signals and the mapping allows us to study the evolution of the modes' structure in changing external conditions and to compare the roles of the internal variability and forcing in the observed behavior. The method is used for extracting of the principal modes of SST variability on inter-annual and multidecadal time scales accounting the external forcings such as CO2, variations of the solar activity and volcanic activity. The structure of the revealed teleconnection patterns as well as their forecast under different CO2 emission scenarios are discussed.[1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016

  16. Methods of stability analysis in nonlinear mechanics

    International Nuclear Information System (INIS)

    Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.

    1989-01-01

    We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs

  17. Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode

    International Nuclear Information System (INIS)

    Zhang Wei-Ya; Li Yong-Li; Chang Xiao-Yong; Wang Nan

    2013-01-01

    In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system (FESS) with a permanent magnet (PM) brushless direct-current (DC) motor (BLDCM) is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments. (interdisciplinary physics and related areas of science and technology)

  18. Effects of intermode nonlinearity and intramode nonlinearity on modulation instability in randomly birefringent two-mode optical fibers

    Science.gov (United States)

    Li, Jin Hua; Xu, Hui; Sun, Ting Ting; Pei, Shi Xin; Ren, Hai Dong

    2018-05-01

    We analyze in detail the effects of the intermode nonlinearity (IEMN) and intramode nonlinearity (IRMN) on modulation instability (MI) in randomly birefringent two-mode optical fibers (RB-TMFs). In the anomalous dispersion regime, the MI gain enhances significantly as the IEMN and IRMN coefficients increases. In the normal dispersion regime, MI can be generated without the differential mode group delay (DMGD) effect, as long as the IEMN coefficient between two distinct modes is above a critical value, or the IRMN coefficient inside a mode is below a critical value. This critical IEMN (IRMN) coefficient depends strongly on the given IRMN (IEMN) coefficient and DMGD for a given nonlinear RB-TMF structure, and is independent on the input total power, the power ratio distribution and the group velocity dispersion (GVD) ratio between the two modes. On the other hand, in contrast to the MI band arising from the pure effect of DMGD in the normal dispersion regime, where MI vanishes after a critical total power, the generated MI band under the combined effects of IEMN and IRMN without DMGD exists for any total power and enhances with the total power. The MI analysis is verified numerically by launching perturbed continuous waves (CWs) with wave propagation method.

  19. On the Stability of Three-Dimensional Boundary Layers. Part 1; Linear and Nonlinear Stability

    Science.gov (United States)

    Janke, Erik; Balakumar, Ponnampalam

    1999-01-01

    The primary stability of incompressible three-dimensional boundary layers is investigated using the Parabolized Stability Equations (PSE). We compute the evolution of stationary and traveling disturbances in the linear and nonlinear region prior to transition. As model problems, we choose Swept Hiemenz Flow and the DLR Transition Experiment. The primary stability results for Swept Hiemenz Flow agree very well with computations by Malik et al. For the DLR Experiment, the mean flow profiles are obtained by solving the boundary layer equations for the measured pressure distribution. Both linear and nonlinear results show very good agreement with the experiment.

  20. Kinetic stability of internal kink mode

    International Nuclear Information System (INIS)

    Romanelli, F.; Fogaccia, G.

    1993-01-01

    With reference to studies of the attainment of ignited operations on devices like ITER (International Thermonuclear Experimental Reactor), the stability of the internal kink mode is re-investigated by taking into account the contribution of perpendicular compressibility, obtained by solving the drift kinetic equation. The resulting stability condition yields threshold values typically larger than the conventional Bussac criterion. For the case of ultra-flat safety factor profiles, the mode can be stable also in the absence of line-bending

  1. Stability of short wavelength tearing and twisting modes

    International Nuclear Information System (INIS)

    Waelbroeck, F.L.

    1998-01-01

    The stability and mutual interaction of tearing and twisting modes in a torus is governed by matrices that generalize the well-known Δ' stability index. The diagonal elements of these matrices determine the intrinsic stability of modes that reconnect the magnetic field at a single resonant surface. The off-diagonal elements indicate the strength of the coupling between the different modes. The author shows how the elements of these matrices can be evaluated, in the limit of short wavelength, from the free energy driving radially extended ballooning modes. The author applies the results by calculating the tearing and twisting Δ' for a model high-beta equilibrium with circular flux surfaces

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

    Science.gov (United States)

    Liu, Xian; Du, Jiajia; Gao, Qing

    2014-01-01

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

  3. Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

    Directory of Open Access Journals (Sweden)

    Xian Liu

    2014-01-01

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

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

    Directory of Open Access Journals (Sweden)

    Yu Wang

    2014-01-01

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

  5. Linear instability and nonlinear motion of rotating plasma

    International Nuclear Information System (INIS)

    Liu, J.

    1985-01-01

    Two coupled nonlinear equations describing the flute dynamics of the magnetically confined low-β collisionless rotating plasma are derived. The linear instability and nonlinear dynamics of the rotating column are analyzed theoretically. In the linear stability analysis, a new sufficient condition of stability is obtained. From the exact solution of eigenvalue equation for Gaussian density profile and uniform rotation of the plasma, the stability of the system strongly depends on the direction of plasma rotation, FLR effect and the location of the conducting wall. An analytic expression showing the finite wall effect on different normal modes is obtained and it explains the different behavior of (1,0) normal mode from other modes. The sheared rotation driven instability is investigated by using three model equilibrium profiles, and the analytic expressions of eigenvalues which includes the wall effect are obtained. The analogy between shear rotation driven instability and the instability driven by sheared plane parallel flow in the inviscid fluid is analyzed. Applying the linear analysis to the central cell of tandem mirror system, the trapped particle instability with only passing electronics is analyzed. For uniform rotation and Gaussian density profile, an analytic expression that determines the stability boundary is found. The nonlinear analysis shows that the nonlinear equations have a solitary vortex solution which is very similar to the vortex solution of nonlinear Rossby wave equation

  6. Stability of one-step methods in transient nonlinear heat conduction

    International Nuclear Information System (INIS)

    Hughes, J.R.

    1977-01-01

    The purpose of the present work is to ascertain practical stability conditions for one-step methods commonly used in transient nonlinear heat conduction analyses. The class of problems considered is governed by a temporally continuous, spatially discrete system involving the capacity matrix C, conductivity matrix K, heat supply vector, temperature vector and time differenciation. In the linear case, in which K and C are constant, the stability behavior of one-step methods is well known. But in this paper the concepts of stability, appropriate to the nonlinear problem, are thoroughly discussed. They of course reduce to the usual stability criterion for the linear, constant coefficient case. However, for nonlinear problems there are differences and these ideas are of key importance in obtaining practical stability conditions. Of particular importance is a recent result which indicates that, in a sense, the trapezoidal and midpoint families are quivalent. Thus, stability results for one family may be translated into a result for the other. The main results obtained are summarized as follows. The stability behavior of the explicit Euler method in the nonlinear regime is analogous to that for linear problems. In particular, an a priori step size restriction may be determined for each time step. The precise time step restriction on implicit conditionally stable members of the trapezoidal and midpoint families is shown not to be determinable a priori. Of considerable practical significance, unconditionally stable members of the trapezoidal and midpoint families are identified

  7. Design of Robust Supertwisting Algorithm Based Second-Order Sliding Mode Controller for Nonlinear Systems with Both Matched and Unmatched Uncertainty

    Directory of Open Access Journals (Sweden)

    Marwa Jouini

    2017-01-01

    Full Text Available This paper proposes a robust supertwisting algorithm (STA design for nonlinear systems where both matched and unmatched uncertainties are considered. The main contributions reside primarily to conceive a novel structure of STA, in order to ensure the desired performance of the uncertain nonlinear system. The modified algorithm is formed of double closed-loop feedback, in which two linear terms are added to the classical STA. In addition, an integral sliding mode switching surface is proposed to construct the attractiveness and reachability of sliding mode. Sufficient conditions are derived to guarantee the exact differentiation stability in finite time based on Lyapunov function theory. Finally, a comparative study for a variable-length pendulum system illustrates the robustness and the effectiveness of the proposed approach compared to other STA schemes.

  8. Stability of Microturbulent Drift Modes during Internal Transport Barrier Formation in the Alcator C-Mod Radio Frequency Heated H-mode

    International Nuclear Information System (INIS)

    Redi, M.H.; Fiore, C.L.; Dorland, W.; Mikkelsen, D.R.; Rewoldt, G.; Bonoli, P.T.; Ernst, D.R.; Rice, J.E.; Wukitch, S.J.

    2003-01-01

    Recent H-mode experiments on Alcator C-Mod [I.H. Hutchinson, et al., Phys. Plasmas 1 (1994) 1511] which exhibit an internal transport barrier (ITB), have been examined with flux tube geometry gyrokinetic simulations, using the massively parallel code GS2 [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88 (1995) 128]. The simulations support the picture of ion/electron temperature gradient (ITG/ETG) microturbulence driving high xi/ xe and that suppressed ITG causes reduced particle transport and improved ci on C-Mod. Nonlinear calculations for C-Mod confirm initial linear simulations, which predicted ITG stability in the barrier region just before ITB formation, without invoking E x B shear suppression of turbulence. Nonlinear fluxes are compared to experiment, which both show low heat transport in the ITB and higher transport within and outside of the barrier region

  9. Rotational stabilization of q < 1 modes

    International Nuclear Information System (INIS)

    Waelbroeck, F.L.; Aydemir, A.Y.

    1996-01-01

    Analyses of high performance discharges with central safety factor below unity have shown that the ideal Magnetohydrodynamic stability threshold for the n=1 kink mode is often violated with impunity. For TFTR (Tokamak Fusion Test Reactor) supershots, the experimental observations can be explained by diamagnetic stabilization of the reconnecting model provided that the fluid free energy is suitably reduced by trapped particle effects. For the broader profiles typical of other high confinement regimes, however, diamagnetic effects cannot account for the experimental results. Furthermore, there is evidence that the Mercier stability condition can also be violated in some cases. Here, we show that toroidal rotation of the plasma can stabilize the kink mode even in the presence of resistivity in configurations that would otherwise be ideally unstable. Two effects can be distinguished. The first effect consists in a reduction of the ideal driving energy. This can be understood in view of the fact that, to a good approximation, the internal kink is a rigid body displacement combining a tilt of the plasma inside the q = 1 surface with a translation along the tilt axis. In the presence of rotation, this displacement must be accompanied by a precessional motion so as to conserve angular momentum. The kinetic energy of the precessional motion must be extracted from the energy driving the displacement. The second effect of rotation is to resolve the Alfven singularity. This is a consequence of the pressure perturbation caused by the equilibrium variation of the entropy within the flux surfaces. It results in the stabilization of resistive as well as weak ideal instabilities, including Mercier modes. For rotationally stabilized equilibria, it also implies the presence of a neutrally stable mode with frequency of the order of the growth rate of the internal kink

  10. The influence of toroidicity, pressure and local profile changes on tearing mode stability

    International Nuclear Information System (INIS)

    Connor, J.W.; Hastie, R.J.; Martin, T.J.; Cowley, S.C.

    1992-01-01

    Tearing modes appear to play a significant role in determining Tokamak behaviour. In high temperature plasmas realistic plasma models for the response at the resonant magnetic surfaces necessitate the use of asymptotic matching methods (the Δ' formulation) in calculations of linear stability and non-linear saturation. These calculations are complicated by toroidal and surface shape effects which cause coupling of different poloidal harmonics in a tearing mode. This leads to coupling of tearing modes centred on different resonant surfaces. However, when diamagnetic effects and sheared equilibrium flows are taken into account theory predicts that tearing will occur at only one surface. At all other surfaces the plasma response is determined by the ideal inertial equations. As a first approximation we treat this as infinite, and calculate the scalar Δ' m/n associated with one resonant surface at a time. (author) 8 refs., 2 figs., 2 tabs

  11. Nonlinear Stability Analysis of a Composite Girder Cable-Stayed Bridge with Three Pylons during Construction

    Directory of Open Access Journals (Sweden)

    Xiaoguang Deng

    2015-01-01

    Full Text Available Based on the nonlinear stability analysis method, the 3D nonlinear finite element model of a composite girder cable-stayed bridge with three pylons is established to research the effect of factors including geometric nonlinearity, material nonlinearity, static wind load, and unbalanced construction load on the structural stability during construction. Besides, the structural nonlinear stability in different construction schemes and the determination of temporary pier position are also studied. The nonlinear stability safety factors are calculated to demonstrate the rationality and safety of construction schemes. The results show that the nonlinear stability safety factors of this bridge during construction meet the design requirement and the minimum value occurs in the maximum double cantilever stage. Besides, the nonlinear stability of the structure in the side of edge-pylon meets the design requirement in the two construction schemes. Furthermore, the temporary pier can improve the structure stability, effectively, and the actual position is reasonable. In addition, the local buckling of steel girder occurs earlier than overall instability under load in some cable tension stages. Finally, static wind load and the unbalanced construction load should be considered in the stability analysis for the adverse impact.

  12. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    Science.gov (United States)

    Xiong, G. Z.; Wang, L.; Li, X. Q.; Liu, H. F.; Tang, C. J.; Huang, J.; Zhang, X.; Wang, X. Q.

    2017-06-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet-Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs.

  13. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    International Nuclear Information System (INIS)

    Xiong, G Z; Liu, H F; Huang, J; Wang, X Q; Wang, L; Li, X Q; Tang, C J; Zhang, X

    2017-01-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet–Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs. (paper)

  14. Nonlinear evolution of the mode structure of ELMs in realistic ASDEX Upgrade geometry

    Energy Technology Data Exchange (ETDEWEB)

    Krebs, Isabel; Hoelzl, Matthias; Lackner, Karl; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Boltzmannstr. 2, Garching (Germany); Collaboration: The ASDEX Upgrade Team

    2013-07-01

    Edge-localized modes (ELMs) are edge instabilities in H-mode plasmas, which eject particles and energy. The suitability of the H-mode for future fusion reactors depends crucially on the exact ELM dynamics as they can damage plasma facing components if too large. We have simulated ELMs in ASDEX Upgrade geometry using the nonlinear MHD code JOREK. Emphasis was put on the mode structure evolution in the early ELM phase which is characterized by the exponential growth of the unstable toroidal Fourier harmonics followed by a phase of saturation. In the linear phase, toroidal harmonics grow independently, whereas at larger amplitudes, the nonlinear interaction between the toroidal harmonics influences their growth and structure. Prior to mode saturation, the evolution of the mode structure can be reproduced well by a simple quadratic mode-interaction model, which yields a possible explanation for the strong n=1 component of type-I ELMs observed in ASDEX Upgrade. In the linear phase of the simulations, intermediate toroidal mode numbers (n 6-14) are most unstable as predicted by the peeling-ballooning model. But non-linearly, the n=1 component becomes important due to an energy transfer from pairs of linearly dominant toroidal harmonics with neighboring mode numbers to the n=1. The latter thereby changes its spatial structure.

  15. Compressible stability of growing boundary layers using parabolized stability equations

    Science.gov (United States)

    Chang, Chau-Lyan; Malik, Mujeeb R.; Erlebacher, Gordon; Hussaini, M. Y.

    1991-01-01

    The parabolized stability equation (PSE) approach is employed to study linear and nonlinear compressible stability with an eye to providing a capability for boundary-layer transition prediction in both 'quiet' and 'disturbed' environments. The governing compressible stability equations are solved by a rational parabolizing approximation in the streamwise direction. Nonparallel flow effects are studied for both the first- and second-mode disturbances. For oblique waves of the first-mode type, the departure from the parallel results is more pronounced as compared to that for the two-dimensional waves. Results for the Mach 4.5 case show that flow nonparallelism has more influence on the first mode than on the second. The disturbance growth rate is shown to be a strong function of the wall-normal distance due to either flow nonparallelism or nonlinear interactions. The subharmonic and fundamental types of breakdown are found to be similar to the ones in incompressible boundary layers.

  16. Stability of non-linear constitutive formulations for viscoelastic fluids

    CERN Document Server

    Siginer, Dennis A

    2014-01-01

    Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities.

  17. Diode array pumped, non-linear mirror Q-switched and mode-locked

    Indian Academy of Sciences (India)

    A non-linear mirror consisting of a lithium triborate crystal and a dichroic output coupler are used to mode-lock (passively) an Nd : YVO4 laser, pumped by a diode laser array. The laser can operate both in cw mode-locked and simultaneously Q-switched and mode-locked (QML) regime. The peak power of the laser while ...

  18. On the stability and compressive nonlinearity of a physiologically based model of the cochlea

    Energy Technology Data Exchange (ETDEWEB)

    Nankali, Amir [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Grosh, Karl [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan (United States); Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan (United States)

    2015-12-31

    Hearing relies on a series of coupled electrical, acoustical (fluidic) and mechanical interactions inside the cochlea that enable sound processing. A positive feedback mechanism within the cochlea, called the cochlear amplifier, provides amplitude and frequency selectivity in the mammalian auditory system. The cochlear amplifier and stability are studied using a nonlinear, micromechanical model of the Organ of Corti (OoC) coupled to the electrical potentials in the cochlear ducts. It is observed that the mechano-electrical transduction (MET) sensitivity and somatic motility of the outer hair cell (OHC), control the cochlear stability. Increasing MET sensitivity beyond a critical value, while electromechanical coupling coefficient is within a specific range, causes instability. We show that instability in this model is generated through a supercritical Hopf bifurcation. A reduced order model of the system is approximated and it is shown that the tectorial membrane (TM) transverse mode effect on the dynamics is significant while the radial mode can be simplified from the equations. The cochlear amplifier in this model exhibits good agreement with the experimental data. A comprehensive 3-dimensional model based on the cross sectional model is simulated and the results are compared. It is indicated that the global model qualitatively inherits some characteristics of the local model, but the longitudinal coupling along the cochlea shifts the stability boundary (i.e., Hopf bifurcation point) and enhances stability.

  19. Nonlinear theory of collisionless trapped ion modes

    International Nuclear Information System (INIS)

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

    1996-01-01

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

  20. Nonlinear stability, bifurcation and resonance in granular plane Couette flow

    Science.gov (United States)

    Shukla, Priyanka; Alam, Meheboob

    2010-11-01

    A weakly nonlinear stability theory is developed to understand the effect of nonlinearities on various linear instability modes as well as to unveil the underlying bifurcation scenario in a two-dimensional granular plane Couette flow. The relevant order parameter equation, the Landau-Stuart equation, for the most unstable two-dimensional disturbance has been derived using the amplitude expansion method of our previous work on the shear-banding instability.ootnotetextShukla and Alam, Phys. Rev. Lett. 103, 068001 (2009). Shukla and Alam, J. Fluid Mech. (2010, accepted). Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary linear instabilities, respectively, are analysed using the first Landau coefficient. It is shown that the subcritical instability can appear in the linearly stable regime. The present bifurcation theory shows that the flow is subcritically unstable to disturbances of long wave-lengths (kx˜0) in the dilute limit, and both the supercritical and subcritical states are possible at moderate densities for the dominant stationary and traveling instabilities for which kx=O(1). We show that the granular plane Couette flow is prone to a plethora of resonances.ootnotetextShukla and Alam, J. Fluid Mech. (submitted, 2010)

  1. General description and understanding of the nonlinear dynamics of mode-locked fiber lasers.

    Science.gov (United States)

    Wei, Huai; Li, Bin; Shi, Wei; Zhu, Xiushan; Norwood, Robert A; Peyghambarian, Nasser; Jian, Shuisheng

    2017-05-02

    As a type of nonlinear system with complexity, mode-locked fiber lasers are known for their complex behaviour. It is a challenging task to understand the fundamental physics behind such complex behaviour, and a unified description for the nonlinear behaviour and the systematic and quantitative analysis of the underlying mechanisms of these lasers have not been developed. Here, we present a complexity science-based theoretical framework for understanding the behaviour of mode-locked fiber lasers by going beyond reductionism. This hierarchically structured framework provides a model with variable dimensionality, resulting in a simple view that can be used to systematically describe complex states. Moreover, research into the attractors' basins reveals the origin of stochasticity, hysteresis and multistability in these systems and presents a new method for quantitative analysis of these nonlinear phenomena. These findings pave the way for dynamics analysis and system designs of mode-locked fiber lasers. We expect that this paradigm will also enable potential applications in diverse research fields related to complex nonlinear phenomena.

  2. Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

    Science.gov (United States)

    Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

    2017-12-01

    We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

  3. Edge kink/ballooning mode stability in tokamaks with separatrix

    International Nuclear Information System (INIS)

    Medvedev, S Yu; Martynov, A A; Martin, Y R; Sauter, O; Villard, L

    2006-01-01

    Stability limits against external kink modes driven by large current density and pressure gradient values in the pedestal region are investigated for tokamak plasmas with separatrix. Stability diagrams for modes with different toroidal wave numbers under variations of pressure gradient and current density in the pedestal region are presented for several equilibrium configurations related to TCV. A scaling for the toroidal wave number of the most unstable mode is proposed. The influence of the plasma cross-section geometry on the stability limits is discussed

  4. Stabilization of ballooning modes with sheared toroidal rotation

    International Nuclear Information System (INIS)

    Miller, R.L.; Waelbroeck, F.W.; Lao, L.L.; Taylor, T.S.

    1994-11-01

    A new code demonstrates the stabilization of MHD ballooning modes by sheared toroidal rotation. A shifted model is used to elucidate the physics and numerically reconstructed equilibria are used to analyze DIII-D discharges. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (dΩ/dq where Ω is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and, in the shifted circle model, direct stable access to the second stability regime occurs when this frequency is a fraction of the Alfven frequency ω A = V A /qR. Shear stabilization is also demonstrated for an equilibrium reconstruction of a DIII-D VH-mode

  5. Ballooning mode stabilization by moderate sheared rotation

    International Nuclear Information System (INIS)

    Hameiri, E.

    1996-01-01

    Sheared toroidal plasma rotation has been known for some time to have a stabilizing effect on the ballooning modes. A recent calculation showed that a large flow shear, with dΩ/dq of the order of the Alfven toroidal frequency, can stabilize the ballooning modes. This latest result is, in fact, not so optimistic. For observed flows with Mach number of order unity one gets dΩ/dq smaller by a factor O(√β) from the required level (if the flow shear length is of the same order as the magnetic shear length). Moreover, the calculation does not take into account a possibly large transient growth of the mode amplitude due to its Floquet structures We show here that, in fact, there is a general tendency of the ballooning mode to stabilize as soon as the flow shear dΩ/dq exceeds the (O√β smaller) open-quotes slowclose quotes magnetosonic wave frequency. Our analysis is perturbative, where the small parameter is related to the small coupling between the slow and Alfven waves-as is the case in a high aspect-ratio tokamak. (In the perturbation it is important to take the Hamiltonian nature of the governing equations into account.) Moreover, our results apply to the relevant transient growth of the mode amplitude

  6. Stabilization of nonlinear excitations by disorder

    DEFF Research Database (Denmark)

    Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.

    1998-01-01

    Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem...... are investigated. We find that otherwise unstable excitations can be stabilized by the presence of disorder in the continuum problem. For the very narrow excitations of the discrete problem we find that the disorder has no effect on the averaged behavior. Finally, we show that the disorder can be applied to induce...... a high degree of controllability of the spatial extent of the stable excitations in the continuum system....

  7. Stabilization of ballooning modes with sheared toroidal rotation

    International Nuclear Information System (INIS)

    Miller, R.L.; Waelbroeck, F.L.; Hassam, A.B.; Waltz, R.E.

    1995-01-01

    Stabilization of magnetohydrodynamic ballooning modes by sheared toroidal rotation is demonstrated using a shifted circle equilibrium model. A generalized ballooning mode representation is used to eliminate the fast Alfven wave, and an initial value code solves the resulting equations. The s-α diagram (magnetic shear versus pressure gradient) of ballooning mode theory is extended to include rotational shear. In the ballooning representation, the modes shift periodically along the field line to the next point of unfavorable curvature. The shift frequency (dΩ/dq, where Ω is the angular toroidal velocity and q is the safety factor) is proportional to the rotation shear and inversely proportional to the magnetic shear. Stability improves with increasing shift frequency and direct stable access to the second stability regime occurs when this frequency is approximately one-quarter to one-half the Alfven frequency, ω A =V A /qR. copyright 1995 American Institute of Physics

  8. Actively mode-locked diode laser with a mode spacing stability of ∼6 × 10{sup -14}

    Energy Technology Data Exchange (ETDEWEB)

    Zakharyash, V F; Kashirsky, A V; Klementyev, V M [Institute of Laser Physics, Siberian Branch, Russian Academy of Sciences, Novosibirsk (Russian Federation)

    2015-10-31

    We have studied mode spacing stability in an actively mode-locked external-cavity semiconductor laser. It has been shown that, in the case of mode spacing pulling to the frequency of a highly stable external microwave signal produced by a hydrogen standard (stability of 4 × 10{sup -14} over an averaging period τ = 10 s), this configuration ensures a mode spacing stability of 5.92 × 10{sup -14} (τ = 10 s). (control of radiation parameters)

  9. A Generalized Halanay Inequality for Stability of Nonlinear Neutral Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    Wansheng Wang

    2010-01-01

    Full Text Available This paper is devoted to generalize Halanay's inequality which plays an important rule in study of stability of differential equations. By applying the generalized Halanay inequality, the stability results of nonlinear neutral functional differential equations (NFDEs and nonlinear neutral delay integrodifferential equations (NDIDEs are obtained.

  10. A nonlinear multi-mode wideband piezoelectric vibration-based energy harvester using compliant orthoplanar spring

    Energy Technology Data Exchange (ETDEWEB)

    Dhote, Sharvari, E-mail: sharvari.dhote@mail.utoronto.ca; Zu, Jean; Zhu, Yang [Department of Mechanical and Industrial Engineering, University of Toronto, 5 King' s College Road, Toronto, Ontario M5S-3G8 (Canada)

    2015-04-20

    In this paper, a nonlinear wideband multi-mode piezoelectric vibration-based energy harvester (PVEH) is proposed based on a compliant orthoplanar spring (COPS), which has an advantage of providing multiple vibration modes at relatively low frequencies. The PVEH is made of a tri-leg COPS flexible structure, where three fixed-guided beams are capable of generating strong nonlinear oscillations under certain base excitation. A prototype harvester was fabricated and investigated through both finite-element analysis and experiments. The frequency response shows multiple resonance which corresponds to a hardening type of nonlinear resonance. By adding masses at different locations on the COPS structure, the first three vibration modes are brought close to each other, where the three hardening nonlinear resonances provide a wide bandwidth for the PVEH. The proposed PVEH has enhanced performance of the energy harvester in terms of a wide frequency bandwidth and a high-voltage output under base excitations.

  11. Maintaining the stability of nonlinear differential equations by the enhancement of HPM

    International Nuclear Information System (INIS)

    Hosein Nia, S.H.; Ranjbar, A.N.; Ganji, D.D.; Soltani, H.; Ghasemi, J.

    2008-01-01

    Homotopy perturbation method is an effective method to find a solution of a nonlinear differential equation. In this method, a nonlinear complex differential equation is transformed to a series of linear and nonlinear parts, almost simpler differential equations. These sets of equations are then solved iteratively. Finally, a linear series of the solutions completes the answer if the convergence is maintained. In this Letter, the need for stability verification is shown through some examples. Consequently, HPM is enhanced by a preliminary assumption. The idea is to keep the inherent stability of nonlinear dynamic, even the selected linear part is not

  12. Quantum Solitons and Localized Modes in a One-Dimensional Lattice Chain with Nonlinear Substrate Potential

    International Nuclear Information System (INIS)

    Li Dejun; Mi Xianwu; Deng Ke; Tang Yi

    2006-01-01

    In the classical lattice theory, solitons and localized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j 0 .

  13. Saturation and stability of nonlinear photonic crystals

    International Nuclear Information System (INIS)

    Franco-Ortiz, M; Corella-Madueño, A; Rosas-Burgos, R A; Adrian Reyes, J; Avendaño, Carlos G

    2017-01-01

    We consider a one-dimensional photonic crystal made by an infinite set of nonlinear nematic films immersed in a linear dielectric medium. The thickness of each equidistant film is negligible and its refraction index depends continuously on the electric field intensity, giving rise to all the involved nonlinear terms, which joints from a starting linear index for negligible amplitudes to a final saturation index for extremely large field intensities. We show that the nonlinear exact solutions of this system form an intensity-dependent band structure which we calculate and analyze. Next, we ponder a finite version of this system; that is, we take a finite array of linear dielectric stacks of the same size separated by the same nonlinear extremely thin nematic slabs and find the reflection coefficients for this arrangement and obtain the dependence on the wave number and intensity of the incident wave. As a final step we analyze the stability of the analytical solutions of the nonlinear crystal by following the evolution of an additive amplitude to the analytical nonlinear solution we have found here. We discuss our results and state our conclusions. (paper)

  14. Forty-five degree backscattering-mode nonlinear absorption imaging in turbid media.

    Science.gov (United States)

    Cui, Liping; Knox, Wayne H

    2010-01-01

    Two-color nonlinear absorption imaging has been previously demonstrated with endogenous contrast of hemoglobin and melanin in turbid media using transmission-mode detection and a dual-laser technology approach. For clinical applications, it would be generally preferable to use backscattering mode detection and a simpler single-laser technology. We demonstrate that imaging in backscattering mode in turbid media using nonlinear absorption can be obtained with as little as 1-mW average power per beam with a single laser source. Images have been achieved with a detector receiving backscattered light at a 45-deg angle relative to the incoming beams' direction. We obtain images of capillary tube phantoms with resolution as high as 20 microm and penetration depth up to 0.9 mm for a 300-microm tube at SNR approximately 1 in calibrated scattering solutions. Simulation results of the backscattering and detection process using nonimaging optics are demonstrated. A Monte Carlo-based method shows that the nonlinear signal drops exponentially as the depth increases, which agrees well with our experimental results. Simulation also shows that with our current detection method, only 2% of the signal is typically collected with a 5-mm-radius detector.

  15. Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonlinear Sliding Surface

    OpenAIRE

    Yong-Kun Lu

    2015-01-01

    An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The ...

  16. Basic mode of nonlinear spin-wave resonance in normally magnetized ferrite films

    International Nuclear Information System (INIS)

    Gulyaev, Yu.V.; Zil'berman, P.E.; Timiryazev, A.G.; Tikhomirova, M.P.

    2000-01-01

    Modes of nonlinear and spin-wave resonance (SWR) in the normally magnetized ferrite films were studied both theoretically and experimentally. The particular emphasis was placed on the basic mode of SWR. One showed theoretically that with the growth of the precession amplitude the profile of the basic mode changed. The nonlinear shift of the resonance field depends on the parameters of fixing of the surface spins. Films of ferroyttrium garnet (FYG) with strong gradient of the single-axis anisotropy field along the film thickness, as well as, FYG films of the submicron thickness where investigated experimentally. With the intensification of Uhf-power one observed the sublinear shift of the basic mode resonance field following by the superlinear growth of the absorbed power. That kind of behaviour is explained by variation of the profile of the varying magnetization space distribution [ru

  17. Stability of n = 1 kink modes in bean-shaped tokamaks

    International Nuclear Information System (INIS)

    Manickam, J.; Grimm, R.C.; Okabayashi, M.

    1983-08-01

    Numerical studies show that by indenting the small-major-radius side of conventional finite-aspect-ratio tokamaks, significant improvements to the stability of pressure-driven ideal MHD modes can be achieved. The internal n - 1 kink mode can be stabilized completely with quite modest indentation. Kink-ballooning mode stability is also improved, and, in the presence of a nearby conducting wall, accessibility to a second stable region at high plasma β is possible

  18. 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)

  19. Three-dimensional boundary layer stability and transition

    Science.gov (United States)

    Malik, M. R.; Li, F.

    1992-01-01

    Nonparallel and nonlinear stability of a three-dimensional boundary layer, subject to crossflow instability, is investigated using parabolized stability equations (PSEs). Both traveling and stationary disturbances are considered and nonparallel effect on crossflow instability is found to be destabilizing. Our linear PSE results for stationary disturbances agree well with the results from direct solution of Navier-Stokes equations obtained by Spalart (1989). Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble remarkably well with the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in our nonlinear calculations. Nonlinear interaction of the stationary amplitude of the stationary vortex is large as compared to the traveling mode, and the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the traveling mode dominates the downstream development owing to its higher growth rate, and there is a tendency for the stationary mode to be suppressed. The effect of nonlinear wave development on the skin-friction coefficient is also computed.

  20. Nonlinear dynamical modes of climate variability: from curves to manifolds

    Science.gov (United States)

    Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander

    2016-04-01

    The necessity of efficient dimensionality reduction methods capturing dynamical properties of the system from observed data is evident. Recent study shows that nonlinear dynamical mode (NDM) expansion is able to solve this problem and provide adequate phase variables in climate data analysis [1]. A single NDM is logical extension of linear spatio-temporal structure (like empirical orthogonal function pattern): it is constructed as nonlinear transformation of hidden scalar time series to the space of observed variables, i. e. projection of observed dataset onto a nonlinear curve. Both the hidden time series and the parameters of the curve are learned simultaneously using Bayesian approach. The only prior information about the hidden signal is the assumption of its smoothness. The optimal nonlinearity degree and smoothness are found using Bayesian evidence technique. In this work we do further extension and look for vector hidden signals instead of scalar with the same smoothness restriction. As a result we resolve multidimensional manifolds instead of sum of curves. The dimension of the hidden manifold is optimized using also Bayesian evidence. The efficiency of the extension is demonstrated on model examples. Results of application to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

  1. Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability

    International Nuclear Information System (INIS)

    Yan, R.; Aluie, H.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.

    2016-01-01

    The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume

  2. Dynamics of Nonlinear Excitation of the High-Order Mode in a Single-Mode Step-Index Optical Fiber

    Science.gov (United States)

    Burdin, V.; Bourdine, A.

    2018-04-01

    This work is concerned with approximate model of higher-order mode nonlinear excitation in a singlemode silica optical fiber. We present some results of simulation for step-index optical fiber under femtosecond optical pulse launching, which confirm ability of relatively stable higher-order mode excitation in such singlemode optical fiber over sufficiently narrow range of launched optical power variation.

  3. Ideal MHD stability analysis of KSTAR target AT mode

    International Nuclear Information System (INIS)

    Yi, S.M.; Kim, J.H.; You, K.I.; Kim, J.Y.

    2009-01-01

    Full text: A main research objective of KSTAR (Korea Superconducting Tokamak Advanced Research) device is to demonstrate the steady-state operation capability of high-performance AT (Advanced Tokamak) mode. To meet this goal, it is critical for KSTAR to have a good MHD stability boundary, particularly against the high-beta ideal instabilities such as the external kink and the ballooning modes. To support this MHD stability KSTAR has been designed to have a strong plasma shape and a close interval between plasma and passive- plate wall. During the conceptual design phase of KSTAR, a preliminary study was performed to estimate the high beta MHD stability limit of KSTAR target AT mode using PEST and VACUUM codes and it was shown that the target AT mode can be stable up to β N ∼ 5 with a well-defined plasma pressure and current profiles. Recently, a new calculation has been performed to estimate the ideal stability limit in various KSTAR operating conditions using DCON code, and it has been observed that there is some difference between the new and old calculation results, particularly in the dependence of the maximum β N value on the toroidal mode number. Here, we thus present a more detailed analysis of the ideal MHD stability limit of KSTAR target AT mode using various codes, which include GATO as well as PEST and DCON, in the comparison of calculation results among the three codes. (author)

  4. On the stability of non-linear systems

    International Nuclear Information System (INIS)

    Guelman, M.

    1968-09-01

    A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [fr

  5. Large Signal Stabilization of Hybrid AC/DC Micro-Grids Using Nonlinear Robust Controller

    Directory of Open Access Journals (Sweden)

    Reza Pejmanfar

    2017-12-01

    Full Text Available This paper presents a robust nonlinear integrated controller to improve stability of hybrid AC/DC micro-grids under islanding mode. The proposed controller includes two independent controllers where each one is responsible to control one part of the system. First controller will improve the stability of input DC/DC converter. Using this controller, the voltage of DC bus is fully stabilized such that when a large disturbance occurs, its voltage will become constant without any significant dynamic. The necessity of DC bus regulation which has not been considered in previous studies, is imminent as it not only improves voltage stability of the micro-grid but also protects consumers which are directly connected to the DC bus, against voltage variations. Frequency stability of the micro-grid is provided by the second proposed controller which is applied to output DC/AC converter of the micro-grid. Adaptive method is used to make the controllers proposed in this paper, robust. Duty cycle of converters switches are adjusted such that voltage and frequency of the micro-grid are set on the desired value in minimum possible time under transient disturbances and uncertainty of the loads as well as micro-sources characteristics.

  6. Stability of Nonlinear Neutral Stochastic Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    Minggao Xue

    2010-01-01

    Full Text Available Neutral stochastic functional differential equations (NSFDEs have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.

  7. Deciphering the imprint of topology on nonlinear dynamical network stability

    International Nuclear Information System (INIS)

    Nitzbon, J; Schultz, P; Heitzig, J; Kurths, J; Hellmann, F

    2017-01-01

    Coupled oscillator networks show complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these relations by incorporating sampling-based measures of the transient behaviour of the system, its survivability, as well as its asymptotic behaviour, its basin stability. By combining basin stability and survivability we uncover novel, previously unknown asymptotic states with solitary, desynchronized oscillators which are rotating with a frequency different from their natural one. They occur almost exclusively after perturbations at nodes with specific topological properties. More generally we confirm and significantly refine the results on the distinguished role tree-shaped appendices play for nonlinear stability. We find a topological classification scheme for nodes located in such appendices, that exactly separates them according to their stability properties, thus establishing a strong link between topology and dynamics. Hence, the results can be used for the identification of vulnerable nodes in power grids or other coupled oscillator networks. From this classification we can derive general design principles for resilient power grids. We find that striving for homogeneous network topologies facilitates a better performance in terms of nonlinear dynamical network stability. While the employed second-order Kuramoto-like model is parametrised to be representative for power grids, we expect these insights to transfer to other critical infrastructure systems or complex network dynamics appearing in various other fields. (paper)

  8. Nonlinear stability research on the hydraulic system of double-side rolling shear

    Science.gov (United States)

    Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

    2015-10-01

    This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

  9. Spread F bubbles - Nonlinear Rayleigh-Taylor mode in two dimensions

    Science.gov (United States)

    Hudson, M. K.

    1978-01-01

    The paper discusses long-wavelength developed bottomside spread F which has been attributed to the Rayleigh-Taylor instability. The nonlinear saturation amplitude and the k spectrum of the inertia-dominated Rayleigh-Taylor instability is found in two directions: east-west and vertical. As in the collisional case (Chaturvedi and Ossakow, 1977), the dominant nonlinearity is found to be two-dimensional. It is found that the linearly most unstable modes, which are primarily horizontal, saturate by the nonlinear generation of vertical spatial harmonics. The harmonics are damped by diffusion or recombination. The resulting amplitude spectrum indicates that bubbles are vertically elongated in both inertial and collisional regimes.

  10. Linear and nonlinear electrostatic modes in a nonuniform magnetized electron plasma

    International Nuclear Information System (INIS)

    Vranjes, J.; Shukla, P.K.; Kono, M.; Poedts, S.

    2001-01-01

    Linear and nonlinear low-frequency modes in a magnetized electron plasma are studied, taking into account a proper description of the equilibrium plasma state that is inhomogeneous. Assuming a homogeneous magnetic field and sheared plasma flows, flute-like perturbations are studied in the presence of density and potential gradients. Linear analysis reveals the presence of a streaming instability and depicts conditions for global linear spiral mode. In the nonlinear domain, a tripolar vortex, which is driven and carried by the flow, is found. Also investigated are the consequences of a magnetic shear as well as nonuniformities along the magnetic field lines, which are shown to be responsible for the possible annulment of the magnetic shear effects. Streaming along the lines of the sheared magnetic field is also studied. A variety of nonlinear structures (viz. global multipolar vortices, local vortex chains, and tripolar vortices) is shown to be the consequence of the simultaneous action of the parallel and perpendicular flows

  11. Non-linear self-reinforced growth of tearing modes with multiple rational surfaces

    International Nuclear Information System (INIS)

    Maschke, E.K.; Persson, M.; Dewar, R.L.; Australian National Univ., Canberra, ACT

    1993-06-01

    The non-linear evolution of tearing modes with multiple rational surfaces is discussed. It is demonstrated that, in the presence of small differential rotation, the non-linear growth might be faster than exponential. This growth occurs as the rotation frequencies of the plasma at the different rational surfaces go into equilibrium

  12. Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators

    International Nuclear Information System (INIS)

    Eriksson, A M; Midtvedt, D; Croy, A; Isacsson, A

    2013-01-01

    We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings. (paper)

  13. Absolute stability of nonlinear systems with time delays and applications to neural networks

    Directory of Open Access Journals (Sweden)

    Xinzhi Liu

    2001-01-01

    Full Text Available In this paper, absolute stability of nonlinear systems with time delays is investigated. Sufficient conditions on absolute stability are derived by using the comparison principle and differential inequalities. These conditions are simple and easy to check. In addition, exponential stability conditions for some special cases of nonlinear delay systems are discussed. Applications of those results to cellular neural networks are presented.

  14. 110 GHz hybrid mode-locked fiber laser with enhanced extinction ratio based on nonlinear silicon-on-insulator micro-ring-resonator (SOI MRR)

    International Nuclear Information System (INIS)

    Liu, Yang; Hsu, Yung; Chow, Chi-Wai; Yang, Ling-Gang; Lai, Yin-Chieh; Yeh, Chien-Hung; Tsang, Hon-Ki

    2016-01-01

    We propose and experimentally demonstrate a new 110 GHz high-repetition-rate hybrid mode-locked fiber laser using a silicon-on-insulator microring-resonator (SOI MRR) acting as the optical nonlinear element and optical comb filter simultaneously. By incorporating a phase modulator (PM) that is electrically driven at a fraction of the harmonic frequency, an enhanced extinction ratio (ER) of the optical pulses can be produced. The ER of the optical pulse train increases from 3 dB to 10 dB. As the PM is only electrically driven by the signal at a fraction of the harmonic frequency, in this case 22 GHz (110 GHz/5 GHz), a low bandwidth PM and driving circuit can be used. The mode-locked pulse width and the 3 dB spectral bandwidth of the proposed mode-locked fiber laser are measured, showing that the optical pulses are nearly transform limited. Moreover, stability evaluation for an hour is performed, showing that the proposed laser can achieve stable mode-locking without the need for optical feedback or any other stabilization mechanism. (letter)

  15. Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability:A Comparative Analysis with CPL Power Variation

    OpenAIRE

    Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar; Mihet-Popa, Lucian; Blaabjerg, Frede; Ramachandaramurthy, Vigna K.

    2017-01-01

    To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear...

  16. Tearing mode stability of tokamak plasmas with elliptical cross section

    International Nuclear Information System (INIS)

    Carreras, B.A.; Holmes, J.A.; Hicks, H.R.; Lynch, V.E.

    1981-02-01

    The effect of the ellipticity of the plasma cross section on tearing mode stability is investigated. The induced coupling between modes is shown to be destabilizing; however, the modification of the equilibrium tends to stabilize the tearing modes. The net effect depends on the manner in which the equilibrium is modified as the plasma cross-section shape is changed

  17. Non-linear coupling of drift modes in a quadrupole

    International Nuclear Information System (INIS)

    Elliott, J.A.; Sandeman, J.C.; Tessema, G.Y.

    1990-01-01

    We report continuing experimental studies of non-linear interactions of drift waves, with direct evidence of a growth saturation mechanism by transfer of energy to lower frequency modes. Wave launching experiments show that the decay rate of drift waves can be strongly amplitude dependent. (author) 9 refs., 5 figs

  18. Nonlinear optics in the LP(02) higher-order mode of a fiber.

    Science.gov (United States)

    Chen, Y; Chen, Z; Wadsworth, W J; Birks, T A

    2013-07-29

    The distinct disperion properties of higher-order modes in optical fibers permit the nonlinear generation of radiation deeper into the ultraviolet than is possible with the fundamental mode. This is exploited using adiabatic, broadband mode convertors to couple light efficiently from an input fundamental mode and also to return the generated light to an output fundamental mode over a broad spectral range. For example, we generate visible and UV supercontinuum light in the LP(02) mode of a photonic crystal fiber from sub-ns pulses with a wavelength of 532 nm.

  19. Output Feedback Stabilization with Nonlinear Predictive Control: Asymptotic properties

    Directory of Open Access Journals (Sweden)

    Lars Imsland

    2003-07-01

    Full Text Available State space based nonlinear model predictive control (NM PC needs the state for the prediction of the system behaviour. Unfortunately, for most applications, not all states are directly measurable. To recover the unmeasured states, typically a stable state observer is used. However, this implies that the stability of the closed-loop should be examined carefully, since no general nonlinear separation principle exists. Recently semi-global practical stability results for output feedback NMPC using a high-gain observer for state estimation have been established. One drawback of this result is that (in general the observer gain must be increased, if the desired set the state should converge to is made smaller. We show that under slightly stronger assumptions, not only practical stability, but also convergence of the system states and observer error to the origin for a sufficiently large but bounded observer gain can be achieved.

  20. Computational study of axisymmetric modes in noncircular cross section tokamaks

    International Nuclear Information System (INIS)

    Johnson, J.L.; Chance, M.S.; Greene, J.M.; Grimm, R.C.; Jardin, S.C.; Kerner, W.; Manickam, J.; Weimer, K.E.

    1976-09-01

    A major computational program to investigate the MHD equilibrium, stability, and nonlinear evolution properties of realistic tokamak configurations is proceeding. Preliminary application is made to the Princeton PDX device. Both axisymmetric (n = 0) modes and kink (n = 1) modes are found; the growth rates depend sensitively on the configuration. A study of the nonlinear evolution of axisymmetric modes in such a device shows that flux conservation in the vacuum region can limit their growth

  1. Turbulent transport stabilization by ICRH minority fast ions in low rotating JET ILW L-mode plasmas

    Science.gov (United States)

    Bonanomi, N.; Mantica, P.; Di Siena, A.; Delabie, E.; Giroud, C.; Johnson, T.; Lerche, E.; Menmuir, S.; Tsalas, M.; Van Eester, D.; Contributors, JET

    2018-05-01

    The first experimental demonstration that fast ion induced stabilization of thermal turbulent transport takes place also at low values of plasma toroidal rotation has been obtained in JET ILW (ITER-like wall) L-mode plasmas with high (3He)-D ICRH (ion cyclotron resonance heating) power. A reduction of the gyro-Bohm normalized ion heat flux and higher values of the normalized ion temperature gradient have been observed at high ICRH power and low NBI (neutral beam injection) power and plasma rotation. Gyrokinetic simulations indicate that ITG (ion temperature gradient) turbulence stabilization induced by the presence of high-energetic 3He ions is the key mechanism in order to explain the experimental observations. Two main mechanisms have been identified to be responsible for the turbulence stabilization: a linear electrostatic wave-fast particle resonance mechanism and a nonlinear electromagnetic mechanism. The dependence of the stabilization on the 3He distribution function has also been studied.

  2. Nonlinear growth of strongly unstable tearing modes

    International Nuclear Information System (INIS)

    Waelbroeck, F.L.

    1993-11-01

    Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect-ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded

  3. Global kink and ballooning modes in high-beta systems and stability of toroidal drift modes

    International Nuclear Information System (INIS)

    Galvao, R.M.O.; Goedbloed, J.P.; Rem, J.; Sakanaka, P.H.; Schep, T.J.; Venema, M.

    1983-01-01

    A numerical code (HBT) has been developed which solves for the equilibrium, global stability and high-n stability of plasmas with arbitrary cross-section. Various plasmas are analysed for their stability to these modes in the high-beta limit. Screw-pinch equilibria are stable to high-n ballooning modes up to betas of 18%. The eigenmode equation for drift waves is analysed numerically. The toroidal branch is shown to be destabilized by the non-adiabatic response of trapped and circulating particles. (author)

  4. On the Nonlinear Structural Analysis of Wind Turbine Blades using Reduced Degree-of-Freedom Models

    DEFF Research Database (Denmark)

    Holm-Jørgensen, Kristian; Larsen, Jesper Winther; Nielsen, Søren R.K.

    2008-01-01

    , modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based...... on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response...... of the small number of included modes. The qualitative erratic response and stability prediction of the reduced order models take place at frequencies slightly above normal operation. However, for normal operation of the wind turbine without resonance excitation 4 modes in the reduced-degree-of-freedom model...

  5. Stabilization of the external kink and the resistive wall mode

    International Nuclear Information System (INIS)

    Chu, M S; Okabayashi, M

    2010-01-01

    The pursuit of steady-state economic production of thermonuclear fusion energy has led to research on the stabilization of the external kink and the resistive wall mode. Advances in both experiment and theory, together with improvements in diagnostics, heating and feedback methods have led to substantial and steady progress in the understanding and stabilization of these instabilities. Many of the theory and experimental techniques and results that have been developed are useful not only for the stabilization of the resistive wall mode. They can also be used to improve the general performance of fusion confinement devices. The conceptual foundations and experimental results on the stabilization of the external kink and the resistive wall mode are reviewed. (topical review)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2017-03-18

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

  7. Three dimensional nonlinear simulations of edge localized modes on the EAST tokamak using BOUT++ code

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Z. X., E-mail: zxliu316@ipp.ac.cn; Xia, T. Y.; Liu, S. C.; Ding, S. Y. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China); Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Xu, X. Q.; Joseph, I.; Meyer, W. H. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Gao, X.; Xu, G. S.; Shao, L. M.; Li, G. Q.; Li, J. G. [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031 (China)

    2014-09-15

    Experimental measurements of edge localized modes (ELMs) observed on the EAST experiment are compared to linear and nonlinear theoretical simulations of peeling-ballooning modes using the BOUT++ code. Simulations predict that the dominant toroidal mode number of the ELM instability becomes larger for lower current, which is consistent with the mode structure captured with visible light using an optical CCD camera. The poloidal mode number of the simulated pressure perturbation shows good agreement with the filamentary structure observed by the camera. The nonlinear simulation is also consistent with the experimentally measured energy loss during an ELM crash and with the radial speed of ELM effluxes measured using a gas puffing imaging diagnostic.

  8. Local effect of equilibrium current on tearing mode stability

    International Nuclear Information System (INIS)

    Cozzani, F.

    1985-12-01

    The local effect of the equilibrium current on the linear stability of low poloidal number tearing modes in tokamaks is investigated analytically. The plasma response inside the tearing layer is derived from fluid theory and the local equilibrium current is shown to couple to the mode dynamics through its gradient, which is proportional to the local electron temperature gradient under the approximations used in the analysis. The relevant eigenmode equations, expressing Ampere's law and the plasma quasineutrality condition, respectively, are suitably combined in a single integral equation, from which a variational principle is formulated to derive the mode dispersion relations for several cases of interest. The local equilibrium current is treated as a small perturbation of the known results for the m greater than or equal to 2 and the m = 1 tearing modes in the collisional regime, and the m greater than or equal to 2 tearing mode in the semicollisional regime; its effect is found to enhance stabilization for the m greater than or equal to 2 drift-tearing mode in the collisional regime, whereas the m = 1 growth rate is very slightly increased and the stabilizing effect of the parallel thermal conduction on the m greater than or equal to 2 mode in the semicollisional regime is slightly reduced

  9. Mode-selective mapping and control of vectorial nonlinear-optical processes in multimode photonic-crystal fibers.

    Science.gov (United States)

    Hu, Ming-Lie; Wang, Ching-Yue; Song, You-Jian; Li, Yan-Feng; Chai, Lu; Serebryannikov, Evgenii; Zheltikov, Aleksei

    2006-02-06

    We demonstrate an experimental technique that allows a mapping of vectorial nonlinear-optical processes in multimode photonic-crystal fibers (PCFs). Spatial and polarization modes of PCFs are selectively excited in this technique by varying the tilt angle of the input beam and rotating the polarization of the input field. Intensity spectra of the PCF output plotted as a function of the input field power and polarization then yield mode-resolved maps of nonlinear-optical interactions in multimode PCFs, facilitating the analysis and control of nonlinear-optical transformations of ultrashort laser pulses in such fibers.

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

    Czech Academy of Sciences Publication Activity Database

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

    2009-01-01

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

  11. Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas

    International Nuclear Information System (INIS)

    Perelomova, A.

    2010-01-01

    Two dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place, are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into thermal mode and internal vibrational degrees of freedom of a relaxing gas. The final dynamic equations are instantaneous; they include a quadratic nonlinear acoustic source, reflecting the nonlinear character of interaction of low-frequency acoustic and non-acoustic motions of the fluid. All types of sound, periodic or aperiodic, may serve as an acoustic source of both phenomena. The low-frequency sound is considered in this study. Some conclusions about temporal behavior of non-acoustic modes caused by periodic and aperiodic sound are made. Under certain conditions, acoustic cooling takes place instead of heating. (author)

  12. Convergence of numerical schemes suitable for two dimensional nonlinear convection: application to the coupling of modes in a plasma

    International Nuclear Information System (INIS)

    Boukadida, T.

    1988-01-01

    The compatibility between accuracy and stability of the quasilinear equations is studied. Three stuations are analyzed: the discontinuous P-1 approximation of the first order quasilinear equation, the two dimensional version of the Lax-Friedrichs scheme and the coupling of modes in a plasma. For the one dimensional case, the proposed scheme matches the available data. In the two dimensional case, tests to show the explosion condition are performed. This investigation can be applied in laser-matter interactions, nonlinear optics and in many fields of physics [fr

  13. Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

    Institute of Scientific and Technical Information of China (English)

    LI Shoufu

    2005-01-01

    A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

  14. Stabilization and tracking controller for a class of nonlinear discrete-time systems

    International Nuclear Information System (INIS)

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

    2011-01-01

    Highlights: → We present recursive design of stabilizing controller for nonlinear discrete-time systems. → Problem of stabilizing and tracking control of single link manipulator system is addressed. → We extend the proposed results to output tracking problems. → The proposed methodology is applied satisfactorily to discrete-time chaotic maps. - Abstract: In this paper, stabilization and tracking control problem for parametric strict feedback class of discrete time systems is addressed. Recursive design of control function based on contraction theory framework is proposed instead of traditional Lyapunov based method. Explicit structure of controller is derived for the addressed class of nonlinear discrete-time systems. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics. Problem of stabilization and output tracking control in case of single link manipulator system with actuator dynamics is analyzed using the proposed strategy. The proposed results are further extended to stabilization of discrete time chaotic systems. Numerical simulations presented in the end show the effectiveness of the proposed approach.

  15. Kovasznay modes in the linear stability analysis of self-similar ablation flows

    International Nuclear Information System (INIS)

    Lombard, V.

    2008-12-01

    Exact self-similar solutions of gas dynamics equations with nonlinear heat conduction for semi-infinite slabs of perfect gases are used for studying the stability of ablative flows in inertial confinement fusion, when a shock wave propagates in front of a thermal front. Both the similarity solutions and their linear perturbations are numerically computed with a dynamical multi-domain Chebyshev pseudo-spectral method. Laser-imprint results, showing that maximum amplification occurs for a laser-intensity modulation of zero transverse wavenumber have thus been obtained (Abeguile et al. (2006); Clarisse et al. (2008)). Here we pursue this approach by proceeding for the first time to an analysis of perturbations in terms of Kovasznay modes. Based on the analysis of two compressible and incompressible flows, evolution equations of vorticity, acoustic and entropy modes are proposed for each flow region and mode couplings are assessed. For short times, perturbations are transferred from the external surface to the ablation front by diffusion and propagate as acoustic waves up to the shock wave. For long times, the shock region is governed by the free propagation of acoustic waves. A study of perturbations and associated sources allows us to identify strong mode couplings in the conduction and ablation regions. Moreover, the maximum instability depends on compressibility. Finally, a comparison with experiments of flows subjected to initial surface defects is initiated. (author)

  16. 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

  17. Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.

    Science.gov (United States)

    Shen, Qikun; Shi, Peng; Shi, Yan

    2016-12-01

    In this paper, the problem of distributed adaptive fuzzy control is investigated for high-order uncertain nonlinear multiagent systems on directed graph with a fixed topology. It is assumed that only the outputs of each follower and its neighbors are available in the design of its distributed controllers. Equivalent output injection sliding mode observers are proposed for each follower to estimate the states of itself and its neighbors, and an observer-based distributed adaptive controller is designed for each follower to guarantee that it asymptotically synchronizes to a leader with tracking errors being semi-globally uniform ultimate bounded, in which fuzzy logic systems are utilized to approximate unknown functions. Based on algebraic graph theory and Lyapunov function approach, using Filippov-framework, the closed-loop system stability analysis is conducted. Finally, numerical simulations are provided to illustrate the effectiveness and potential of the developed design techniques.

  18. Suppression and nonlinear excitation of parasitic modes in second harmonic gyrotrons operating in a very high order mode

    International Nuclear Information System (INIS)

    Nusinovich, Gregory S.; Pu, Ruifeng; Granatstein, Victor L.

    2015-01-01

    In recent years, there was an active development of high-power, sub-terahertz (sub-THz) gyrotrons for numerous applications. For example, a 0.67 THz gyrotron delivering more than 200 kW with about 20% efficiency was developed. This record high efficiency was achieved because the gyrotron operated in a high-order TE 31,8 -mode with the power of ohmic losses less than 10% of the power of outgoing radiation. That gyrotron operated at the fundamental cyclotron resonance, and a high magnetic field of about 27 T was created by a pulse solenoid. For numerous applications, it is beneficial to use gyrotrons at cyclotron harmonics which can operate in available cryomagnets with fields not exceeding 15 T. However, typically, the gyrotron operation at harmonics faces severe competition from parasitic modes at the fundamental resonance. In the present paper, we consider a similar 0.67 THz gyrotron designed for operation in the same TE 31,8 -mode, but at the second harmonic. We focus on two nonlinear effects typical for interaction between the fundamental and second harmonic modes, viz., the mode suppression and the nonlinear excitation of the mode at the fundamental harmonic by the second harmonic oscillations. Our study includes both the analytical theory and numerical simulations performed with the self-consistent code MAGY. The simulations show that stable second harmonic operation in the TE 31,8 mode is possible with only modest sacrifice of efficiency and power

  19. Stability of Nonlinear Systems with Unknown Time-varying Feedback Delay

    Science.gov (United States)

    Chunodkar, Apurva A.; Akella, Maruthi R.

    2013-12-01

    This paper considers the problem of stabilizing a class of nonlinear systems with unknown bounded delayed feedback wherein the time-varying delay is 1) piecewise constant 2) continuous with a bounded rate. We also consider application of these results to the stabilization of rigid-body attitude dynamics. In the first case, the time-delay in feedback is modeled specifically as a switch among an arbitrarily large set of unknown constant values with a known strict upper bound. The feedback is a linear function of the delayed states. In the case of linear systems with switched delay feedback, a new sufficiency condition for average dwell time result is presented using a complete type Lyapunov-Krasovskii (L-K) functional approach. Further, the corresponding switched system with nonlinear perturbations is proven to be exponentially stable inside a well characterized region of attraction for an appropriately chosen average dwell time. In the second case, the concept of the complete type L-K functional is extended to a class of nonlinear time-delay systems with unknown time-varying time-delay. This extension ensures stability robustness to time-delay in the control design for all values of time-delay less than the known upper bound. Model-transformation is used in order to partition the nonlinear system into a nominal linear part that is exponentially stable with a bounded perturbation. We obtain sufficient conditions which ensure exponential stability inside a region of attraction estimate. A constructive method to evaluate the sufficient conditions is presented together with comparison with the corresponding constant and piecewise constant delay. Numerical simulations are performed to illustrate the theoretical results of this paper.

  20. Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

    Science.gov (United States)

    Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

    2018-04-01

    The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

  1. Nonlinear damping of oblique whistler mode waves through Landau resonance

    Science.gov (United States)

    Hsieh, Y.; Omura, Y.

    2017-12-01

    Nonlinear trapping of electrons through Landau resonance is a characteristic dynamics in oblique whistler-mode wave particle interactions. The resonance velocity of the Landau resonance at quasi-parallel propagation becomes very close to the parallel group velocity of whistler-mode wave at frequency around 0.5 Ωe, causing a long distance of resonant interaction and strong acceleration of resonant electrons [1]. We demonstrate these effective accelerations for electrons with high equatorial pitch angle ( > 60°) by test particle simulations with parameters for the Earth's inner magnetosphere at L=5. In the simulations, we focus on slightly oblique whistler mode waves with wave normal angle 10.1002/2016JA023255.

  2. Stabilization of solitons under competing nonlinearities by external potentials

    Energy Technology Data Exchange (ETDEWEB)

    Zegadlo, Krzysztof B., E-mail: zegadlo@if.pw.edu.pl; Karpierz, Miroslaw A. [Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa (Poland); Wasak, Tomasz; Trippenbach, Marek [Faculty of Physics, University of Warsaw, ul. Hoza 69, PL-00-681 Warszawa (Poland); Malomed, Boris A. [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

    2014-12-15

    We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations, and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

  3. Normal mode approach to modelling of feedback stabilization of the resistive wall mode

    International Nuclear Information System (INIS)

    Chu, M.S.; Chance, M.S.; Okabayashi, M.; Glasser, A.H.

    2003-01-01

    Feedback stabilization of the resistive wall mode (RWM) of a plasma in a general feedback configuration is formulated in terms of the normal modes of the plasma-resistive wall system. The growth/damping rates and the eigenfunctions of the normal modes are determined by an extended energy principle for the plasma during its open (feedback) loop operation. A set of equations are derived for the time evolution of these normal modes with currents in the feedback coils. The dynamics of the feedback system is completed by the prescription of the feedback logic. The feasibility of the feedback is evaluated by using the Nyquist diagram method or by solving the characteristic equations. The elements of the characteristic equations are formed from the growth and damping rates of the normal modes, the sensor matrix of the perturbation fluxes detected by the sensor loops, the excitation matrix of the energy input to the normal modes by the external feedback coils, and the feedback logic. (The RWM is also predicted to be excited by an external error field to a large amplitude when it is close to marginal stability.) This formulation has been implemented numerically and applied to the DIII-D tokamak. It is found that feedback with poloidal sensors is much more effective than feedback with radial sensors. Using radial sensors, increasing the number of feedback coils from a central band on the outboard side to include an upper and a lower band can substantially increase the effectiveness of the feedback system. The strength of the RWM that can be stabilized is increased from γτ w = 1 to 30 (γ is the growth rate of the RWM in the absence of feedback and τ w is the resistive wall time constant) Using poloidal sensors, just one central band of feedback coils is sufficient for the stabilization of the RWM with γτ w = 30. (author)

  4. Stabilization of tearing modes to suppress major disruptions in tokamaks

    International Nuclear Information System (INIS)

    Holmes, J.A.; Carreras, B.; Hicks, H.R.; Lynch, S.J.; Waddell, B.V.

    1979-02-01

    It is shown, for q-profiles which lead to a disruption, that the control of the amplitude of the 2/1 tearing mode avoids the disruption. Q-profiles measured in T-4 and PLT before a major disruption were studied. Two methods of controlling the 2/1 mode amplitude have been considered: (1) Feedback stabilization with the feedback signal locked in phase with the 2/1 mode. (2) Heating slightly outside the q = 2 surface. In both cases it is only necessary to decrease the 2/1 mode amplitude to suppress the disruption. It is not always necessary to stabilize the unstable modes fully

  5. Flow shear stabilization of hybrid electron-ion drift mode in tokamaks

    International Nuclear Information System (INIS)

    Bai, L.

    1999-01-01

    In this paper, a model of sheared flow stabilization on hybrid electron-ion drift mode is proposed. At first, in the presence of dissipative trapped electrons, there exists an intrinsic oscillation mode in tokamak plasmas, namely hybrid dissipative trapped electron-ion temperature gradient mode (hereafter, called as hybrid electron-ion drift mode). This conclusion is in agreement with the observations in the simulated tokamak experiment on the CLM. Then, it is found that the coupling between the sheared flows and dissipative trapped electrons is proposed as the stabilization mechanism of both toroidal sheared flow and poloidal sheared flow on the hybrid electron-ion drift mode, that is, similar to the stabilizing effect of poloidal sheared flow on edge plasmas in tokamaks, in the presence of both dissipative trapped electrons and toroidal sheared flow, large toroidal sheared flow is always a strong stabilizing effect on the hybrid electron-ion drift mode in internal transport barrier location, too. This result is consistent with the experimental observations in JT-60U. (author)

  6. Flow shear stabilization of hybrid electron-ion drift mode in tokamaks

    International Nuclear Information System (INIS)

    Bai, L.

    2001-01-01

    In this paper, a model of sheared flow stabilization on hybrid electron-ion drift mode is proposed. At first, in the presence of dissipative trapped electrons, there exists an intrinsic oscillation mode in tokamak plasmas, namely hybrid dissipative trapped electron-ion temperature gradient mode (hereafter, called as hybrid electron-ion drift mode). This conclusion is in agreement with the observations in the simulated tokamak experiment on the CLM. Then, it is found that the coupling between the sheared flows and dissipative trapped electrons is proposed as the stabilization mechanism of both toroidal sheared flow and poloidal sheared flow on the hybrid electron-ion drift mode, that is, similar to the stabilizing effect of poloidal sheared flow on edge plasmas in tokamaks, in the presence of both dissipative trapped electrons and toroidal sheared flow, large toroidal sheared flow is always a strong stabilizing effect on the hybrid electron-ion drift mode in internal transport barrier location, too. This result is consistent with the experimental observations in JT-60U. (author)

  7. Free chattering hybrid sliding mode control for a class of non-linear systems

    DEFF Research Database (Denmark)

    Khooban, Mohammad Hassan; Niknam, Taher; Blaabjerg, Frede

    2016-01-01

    In current study, in order to find the control of general uncertain nonlinear systems, a new optimal hybrid control approach called Optimal General Type II Fuzzy Sliding Mode (OGT2FSM) is presented. In order to estimate unknown nonlinear activities in monitoring dynamic uncertainties, the benefits...... on the same topic, which are an Adaptive Interval Type-2 Fuzzy Logic Controller (AGT2FLC) and Conventional Sliding Mode Controller (CSMC), to assess the efficiency of the suggested controller. The suggested control scheme is finally used to the Electric Vehicles type as a case study. Results of simulation...

  8. 3-D nonlinear calculations of resistive tearing modes

    International Nuclear Information System (INIS)

    Hicks, H.R.; Holmes, J.A.; Lee, D.K.; Carreras, B.; Waddell, B.V.

    1981-03-01

    Recent numerical calculations of the evolution of resistive tearing modes have been central to the understanding of magnetohydrodynamic activity and disruptions in tokamaks. The nonlinear, 3-D, initial-value computer code RSF has provided many of these results. This code assumes cylindrical geometry with a Fourier series representation in the two periodic coordinates and a finite-difference representation in the radial direction. This choice makes RSF considerably more accurate and efficient than previous codes

  9. Elements of magnetohydrodynamic stability theory

    International Nuclear Information System (INIS)

    Spies, G.O.

    1976-11-01

    The nonlinear equations of ideal magnetohydrodynamics are discussed along with the following topics: (1) static equilibrium, (2) strict linear theory, (3) stability of a system with one degree of freedom, (4) spectrum and variational principles in magnetohydrodynamics, (5) elementary proof of the modified energy principle, (6) sufficient stability criteria, (7) local stability, and (8) normal modes

  10. Non-linear radial spinwave modes in thin magnetic disks

    International Nuclear Information System (INIS)

    Helsen, M.; De Clercq, J.; Vansteenkiste, A.; Van Waeyenberge, B.; Gangwar, A.; Back, C. H.; Weigand, M.

    2015-01-01

    We present an experimental investigation of radial spin-wave modes in magnetic nano-disks with a vortex ground state. The spin-wave amplitude was measured using a frequency-resolved magneto-optical spectrum analyzer, allowing for high-resolution resonance curves to be recorded. It was found that with increasing excitation amplitude up to about 10 mT, the lowest-order mode behaves strongly non-linearly as the mode frequency redshifts and the resonance peak strongly deforms. This behavior was quantitatively reproduced by micromagnetic simulations. Micromagnetic simulations showed that at higher excitation amplitudes, the spinwaves are transformed into a soliton by self-focusing, and collapse onto the vortex core, dispersing the energy in short-wavelength spinwaves. Additionally, this process can lead to switching of the vortex polarization through the injection of a Bloch point

  11. Linear and nonlinear stability analysis, associated to experimental fast reactors

    International Nuclear Information System (INIS)

    Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

    1980-07-01

    Phenomena associated to the physics of fast neutrons were analysed by linear and nonlinear Kinetics with arbitrary feedback. The theoretical foundations of linear kinetics and transfer functions aiming at the analysis of fast reactors stability, are established. These stability conditions were analitically proposed and investigated by digital and analogic programs. (E.G.) [pt

  12. High-confinement-mode edge stability of Alcator C-mod plasmas

    International Nuclear Information System (INIS)

    Mossessian, D.A.; Snyder, P.; Hubbard, A.; Hughes, J.W.; Greenwald, M.; La Bombard, B.; Snipes, J.A.; Wolfe, S.; Wilson, H.

    2003-01-01

    For steady state high-confinement-mode (H-mode) operation, a relaxation mechanism is required to limit build-up of the edge gradient and impurity content. Alcator C-Mod [Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] sees two such mechanisms--EDA (enhanced D-alpha H mode) and grassy ELMs (edge localized modes), but not large type I ELMs. In EDA the edge relaxation is provided by an edge localized quasicoherent (QC) electromagnetic mode that exists at moderate pedestal temperature T 95 >3.5, and does not limit the buildup of the edge pressure gradient. The q boundary of the operational space of the mode depends on plasma shape, with the q 95 limit moving down with increasing plasma triangularity. At high edge pressure gradients and temperatures the mode is replaced by broadband fluctuations ( f<50 kHz) and small irregular ELMs are observed. Ideal MHD (magnetohydrodynamic) stability analysis that includes both pressure and current driven edge modes shows that the discharges where the QC mode is observed are stable. The ELMs are identified as medium n (10< n<50) coupled peeling/ballooning modes. The predicted stability boundary of the modes as a function of pedestal current and pressure gradient is reproduced in experimental observations. The measured dependence of the ELMs' threshold and amplitude on plasma triangularity is consistent with the results of ideal MHD analysis performed with the linear stability code ELITE [Wilson et al., Phys. Plasmas 9, 1277 (2002)

  13. Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices

    International Nuclear Information System (INIS)

    Rojas-Rojas, Santiago; Naether, Uta; Delgado, Aldo; Vicencio, Rodrigo A.

    2016-01-01

    Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.

  14. Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices

    Energy Technology Data Exchange (ETDEWEB)

    Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)

    2016-09-16

    Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.

  15. Effects of multiple modes interaction on the resistive wall mode instability

    International Nuclear Information System (INIS)

    Chen, Longxi; Lei, Wenqing; Ma, Zhiwei; Wu, Bin

    2013-01-01

    The effects of multiple modes interaction on the resistive wall mode (RWM) are studied in a slab geometry with and without plasma flow. The modes interaction can have a large effect on both the linear growth rate and the nonlinear saturation level of the RWM. We found that modes interaction can suppress the linear growth rate for the most unstable mode. The plasma flow can also help to control the growth of the RWM. The RWM can be stabilized completely by a plasma flow when considering the modes interaction. The effect of modes interaction on the RWM is stronger for the mode rational surface in the vacuum than that in the plasma. The modes interaction results in a substantially lowered saturation level for the most unstable RWM. (paper)

  16. Naturally stable Sagnac-Michelson nonlinear interferometer.

    Science.gov (United States)

    Lukens, Joseph M; Peters, Nicholas A; Pooser, Raphael C

    2016-12-01

    Interferometers measure a wide variety of dynamic processes by converting a phase change into an intensity change. Nonlinear interferometers, making use of nonlinear media in lieu of beamsplitters, promise substantial improvement in the quest to reach the ultimate sensitivity limits. Here we demonstrate a new nonlinear interferometer utilizing a single parametric amplifier for mode mixing-conceptually, a nonlinear version of the conventional Michelson interferometer with its arms collapsed together. We observe up to 99.9% interference visibility and find evidence for noise reduction based on phase-sensitive gain. Our configuration utilizes fewer components than previous demonstrations and requires no active stabilization, offering new capabilities for practical nonlinear interferometric-based sensors.

  17. Nonlinear analysis of renal autoregulation in rats using principal dynamic modes

    DEFF Research Database (Denmark)

    Marmarelis, V Z; Chon, K H; Holstein-Rathlou, N H

    1999-01-01

    This article presents results of the use of a novel methodology employing principal dynamic modes (PDM) for modeling the nonlinear dynamics of renal autoregulation in rats. The analyzed experimental data are broadband (0-0.5 Hz) blood pressure-flow data generated by pseudorandom forcing and colle......This article presents results of the use of a novel methodology employing principal dynamic modes (PDM) for modeling the nonlinear dynamics of renal autoregulation in rats. The analyzed experimental data are broadband (0-0.5 Hz) blood pressure-flow data generated by pseudorandom forcing...... and collected in normotensive and hypertensive rats for two levels of pressure forcing (as measured by the standard deviation of the pressure fluctuation). The PDMs are computed from first-order and second-order kernel estimates obtained from the data via the Laguerre expansion technique. The results...

  18. Parameter spaces for linear and nonlinear whistler-mode waves

    International Nuclear Information System (INIS)

    Summers, Danny; Tang, Rongxin; Omura, Yoshiharu; Lee, Dong-Hun

    2013-01-01

    We examine the growth of magnetospheric whistler-mode waves which comprises a linear growth phase followed by a nonlinear growth phase. We construct time-profiles for the wave amplitude that smoothly match at the transition between linear and nonlinear wave growth. This matching procedure can only take place over a limited “matching region” in (N h /N 0 ,A T )-space, where A T is the electron thermal anisotropy, N h is the hot (energetic) electron number density, and N 0 is the cold (background) electron number density. We construct this matching region and determine how the matching wave amplitude varies throughout the region. Further, we specify a boundary in (N h /N 0 ,A T )-space that separates a region where only linear chorus wave growth can occur from the region in which fully nonlinear chorus growth is possible. We expect that this boundary should prove of practical use in performing computationally expensive full-scale particle simulations, and in interpreting experimental wave data

  19. Nonlinear dynamics near the stability margin in rotating pipe flow

    Science.gov (United States)

    Yang, Z.; Leibovich, S.

    1991-01-01

    The nonlinear evolution of marginally unstable wave packets in rotating pipe flow is studied. These flows depend on two control parameters, which may be taken to be the axial Reynolds number R and a Rossby number, q. Marginal stability is realized on a curve in the (R, q)-plane, and the entire marginal stability boundary is explored. As the flow passes through any point on the marginal stability curve, it undergoes a supercritical Hopf bifurcation and the steady base flow is replaced by a traveling wave. The envelope of the wave system is governed by a complex Ginzburg-Landau equation. The Ginzburg-Landau equation admits Stokes waves, which correspond to standing modulations of the linear traveling wavetrain, as well as traveling wave modulations of the linear wavetrain. Bands of wavenumbers are identified in which the nonlinear modulated waves are subject to a sideband instability.

  20. 4th International Conference on Structural Nonlinear Dynamics and Diagnosis

    CERN Document Server

    2018-01-01

    This book presents contributions on the most active lines of recent advanced research in the field of nonlinear mechanics and physics selected from the 4th International Conference on Structural Nonlinear Dynamics and Diagnosis. It includes fifteen chapters by outstanding scientists, covering various aspects of applications, including road tanker dynamics and stability, simulation of abrasive wear, energy harvesting, modeling and analysis of flexoelectric nanoactuator, periodic Fermi–Pasta–Ulam problems, nonlinear stability in Hamiltonian systems, nonlinear dynamics of rotating composites, nonlinear vibrations of a shallow arch, extreme pulse dynamics in mode-locked lasers, localized structures in a photonic crystal fiber resonator, nonlinear stochastic dynamics, linearization of nonlinear resonances, treatment of a linear delay differential equation, and fractional nonlinear damping. It appeals to a wide range of experts in the field of structural nonlinear dynamics and offers researchers and engineers a...

  1. 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.

  2. Integral equation based stability analysis of short wavelength drift modes in tokamaks

    International Nuclear Information System (INIS)

    Hirose, A.; Elia, M.

    2003-01-01

    Linear stability of electron skin-size drift modes in collisionless tokamak discharges has been investigated in terms of electromagnetic, kinetic integral equations in which neither ions nor electrons are assumed to be adiabatic. A slab-like ion temperature gradient mode persists in such a short wavelength regime. However, toroidicity has a strong stabilizing influence on this mode. In the electron branch, the toroidicity induced skin-size drift mode previously predicted in terms of local kinetic analysis has been recovered. The mode is driven by positive magnetic shear and strongly stabilized for negative shear. The corresponding mixing length anomalous thermal diffusivity exhibits favourable isotope dependence. (author)

  3. Digital Image Stabilization Method Based on Variational Mode Decomposition and Relative Entropy

    Directory of Open Access Journals (Sweden)

    Duo Hao

    2017-11-01

    Full Text Available Cameras mounted on vehicles frequently suffer from image shake due to the vehicles’ motions. To remove jitter motions and preserve intentional motions, a hybrid digital image stabilization method is proposed that uses variational mode decomposition (VMD and relative entropy (RE. In this paper, the global motion vector (GMV is initially decomposed into several narrow-banded modes by VMD. REs, which exhibit the difference of probability distribution between two modes, are then calculated to identify the intentional and jitter motion modes. Finally, the summation of the jitter motion modes constitutes jitter motions, whereas the subtraction of the resulting sum from the GMV represents the intentional motions. The proposed stabilization method is compared with several known methods, namely, medium filter (MF, Kalman filter (KF, wavelet decomposition (MD method, empirical mode decomposition (EMD-based method, and enhanced EMD-based method, to evaluate stabilization performance. Experimental results show that the proposed method outperforms the other stabilization methods.

  4. Stability of nonlinear waves and patterns and related topics

    Science.gov (United States)

    Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

    2018-04-01

    Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

  5. Stability of magnetic modes in tokamaks; Stabilite des modes magnetiques dans les tokamaks

    Energy Technology Data Exchange (ETDEWEB)

    Zabiego, M

    1994-06-01

    A theoretical study is carried out concerning two experimental topics: stabilization, by a suprathermal population, of the mode ``m=1, n=1`` which induces the sawtooth effect (modelling the role of suprathermal particles in the stabilization); stability, in the non linear regime, of the magnetic islands involved in magnetic turbulence problems (micro-tearing) and in disruption phenomena (tearing), and the effects of diamagnetism, excitation threshold and saturation levels. 45 figs., 97 refs.

  6. Stability of Bragg grating solitons in a cubic-quintic nonlinear medium with dispersive reflectivity

    International Nuclear Information System (INIS)

    Dasanayaka, Sahan; Atai, Javid

    2010-01-01

    We investigate the existence and stability of Bragg grating solitons in a cubic-quintic medium with dispersive reflectivity. It is found that the model supports two disjoint families of solitons. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity. On the other hand, the quintic nonlinearity is dominant in the other family. Stability regions are identified by means of systematic numerical stability analysis. In the case of the first family, the size of the stability region increases up to moderate values of dispersive reflectivity. However for the second family (i.e. region where quintic nonlinearity dominates), the size of the stability region increases even for strong dispersive reflectivity. For all values of m, there exists a subset of the unstable solitons belonging to the first family for which the instability development leads to deformation and subsequent splitting of the soliton into two moving solitons with different amplitudes and velocities.

  7. Nonlinear PT-symmetric plaquettes

    International Nuclear Information System (INIS)

    Li Kai; Kevrekidis, P G; Malomed, Boris A; Günther, Uwe

    2012-01-01

    We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT-symmetric lattices. For each configuration, we develop a dynamical model and examine its PTsymmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain–loss coefficient, γ. Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of direct simulations. In particular, stable localized modes are found in these systems, although the majority of identified solutions are unstable. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)

  8. Nonlinear dynamics of toroidal Alfvén eigenmodes in the presence of tearing modes

    Science.gov (United States)

    Zhu, J.; Ma, Z. W.; Wang, S.; Zhang, W.

    2018-04-01

    A hybrid simulation is carried out to study nonlinear dynamics of n  =  1 toroidal Alfvén eigenmodes (TAEs) with the m/n  =  2/1 tearing mode. It is found that the n  =  1 TAE is first excited by isotropic energetic particles at the linear stage and reaches the first steady state due to wave-particle interaction. After the saturation of the n  =  1 TAE, the m/n  =  2/1 tearing mode grows continuously and reaches its steady state due to nonlinear mode-mode coupling, especially, the n  =  0 component plays a very important role in the tearing mode saturation. The results suggest that the enhancement of the tearing mode activity with increase of the resistivity could weaken the TAE frequency chirping through the interaction between the p  =  1 TAE resonance and the p  =  2 tearing mode resonance for passing particles in the phase space, which is opposite to the classical physical picture of the TAE frequency chirping that is enhanced with dissipation increase.

  9. Results on stabilization of nonlinear systems under finite data-rate constraints

    NARCIS (Netherlands)

    Persis, Claudio De

    2004-01-01

    We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when

  10. Nonlinear simulation of electromagnetic current diffusive interchange mode turbulence

    International Nuclear Information System (INIS)

    Yagi, M.; Itoh, S.I.; Fukuyama, A.

    1998-01-01

    The anomalous transport in toroidal plasmas has been investigated extensively. It is pointed out that the nonlinear instability is important in driving the microturbulence[1], i.e., the self-sustained plasma turbulence. This concept is explained as follows; when the electron motion along the magnetic field line is resisted by the background turbulence, it gives rise to the effective resistivity and enhances the level of the turbulence. The nonlinear simulation of the electrostatic current diffusive interchange mode (CDIM) in the two dimensional sheared slab geometry has been performed as an example. The occurrence of the nonlinear instability and the self-sustainment of the plasma turbulence were confirmed by this simulation[2]. On the other hand, the electromagnetic turbulence is sustained in the high pressure limit. The possibility of the self-organization with more variety has been pointed out[3]. It is important to study the electromagnetic turbulence based on the nonlinear simulation. In this paper, the model equation for the electrostatic CDIM turbulence[2] is extended for both electrostatic and electromagnetic turbulence. (1) Not only E x B convective nonlinearity but also the electromagnetic nonlinearity which is related to the parallel flow are incorporated into the model equation. (2) The electron and ion pressure evolution equations are solved separately, making it possible to distinguish the electron and ion thermal diffusivities. The two dimensional nonlinear simulation of the electromagnetic CDIM is performed based on the extended fluid model. This paper is organized as follows. The model equation is explained in section II. The result of simulation is shown in section III. The conclusion and discussion are given in section IV. (author)

  11. Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

    DEFF Research Database (Denmark)

    Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk R.

    2017-01-01

    We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (V-eff). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illust...... at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics....

  12. Gradient-based optimization in nonlinear structural dynamics

    DEFF Research Database (Denmark)

    Dou, Suguang

    The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...

  13. An instability due to the nonlinear coupling of p-modes to g-modes: Implications for coalescing neutron star binaries

    International Nuclear Information System (INIS)

    Weinberg, Nevin N.; Arras, Phil; Burkart, Joshua

    2013-01-01

    A weakly nonlinear fluid wave propagating within a star can be unstable to three-wave interactions. The resonant parametric instability is a well-known form of three-wave interaction in which a primary wave of frequency ω a excites a pair of secondary waves of frequency ω b + ω c ≅ ω a . Here we consider a nonresonant form of three-wave interaction in which a low-frequency primary wave excites a high-frequency p-mode and a low-frequency g-mode such that ω b + ω c >> ω a . We show that a p-mode can couple so strongly to a g-mode of similar radial wavelength that this type of nonresonant interaction is unstable even if the primary wave amplitude is small. As an application, we analyze the stability of the tide in coalescing neutron star binaries to p-g mode coupling. We find that the equilibrium tide and dynamical tide are both p-g unstable at gravitational wave frequencies f gw ≳ 20 Hz and drive short wavelength p-g mode pairs to significant energies on very short timescales (much less than the orbital decay time due to gravitational radiation). Resonant parametric coupling to the tide is, by contrast, either stable or drives modes at a much smaller rate. We do not solve for the saturation of the p-g instability and therefore we cannot say precisely how it influences the evolution of neutron star binaries. However, we show that if even a single daughter mode saturates near its wave breaking amplitude, the p-g instability of the equilibrium tide will (1) induce significant orbital phase errors (Δφ ≳ 1 radian) that accumulate primarily at low frequencies (f gw ≲ 50 Hz) and (2) heat the neutron star core to a temperature of T ∼ 10 10 K. Since there are at least ∼100 unstable p-g daughter pairs, Δφ and T are potentially much larger than these values. Tides might therefore significantly influence the gravitational wave signal and electromagnetic emission from coalescing neutron star binaries at much larger orbital separations than previously

  14. Gyrokinetic Stability Studies of the Microtearing Mode in the National Spherical Torus Experiment H-mode

    International Nuclear Information System (INIS)

    Baumgaertel J.A., Redi M.H., Budny R.V., Rewoldt G., Dorland W.

    2005-01-01

    Insight into plasma microturbulence and transport is being sought using linear simulations of drift waves on the National Spherical Torus Experiment (NSTX), following a study of drift wave modes on the Alcator C-Mod Tokamak. Microturbulence is likely generated by instabilities of drift waves, which cause transport of heat and particles. Understanding this transport is important because the containment of heat and particles is required for the achievement of practical nuclear fusion. Microtearing modes may cause high heat transport through high electron thermal conductivity. It is hoped that microtearing will be stable along with good electron transport in the proposed low collisionality International Thermonuclear Experimental Reactor (ITER). Stability of the microtearing mode is investigated for conditions at mid-radius in a high density NSTX high performance (H-mode) plasma, which is compared to the proposed ITER plasmas. The microtearing mode is driven by the electron temperature gradient, and believed to be mediated by ion collisions and magnetic shear. Calculations are based on input files produced by TRXPL following TRANSP (a time-dependent transport analysis code) analysis. The variability of unstable mode growth rates is examined as a function of ion and electron collisionalities using the parallel gyrokinetic computational code GS2. Results show the microtearing mode stability dependence for a range of plasma collisionalities. Computation verifies analytic predictions that higher collisionalities than in the NSTX experiment increase microtearing instability growth rates, but that the modes are stabilized at the highest values. There is a transition of the dominant mode in the collisionality scan to ion temperature gradient character at both high and low collisionalities. The calculations suggest that plasma electron thermal confinement may be greatly improved in the low-collisionality ITER

  15. All-fiber nonlinearity- and dispersion-managed dissipative soliton nanotube mode-locked laser

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Z. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Nanjing University of Posts and Communications, Nanjing 210003 (China); Popa, D., E-mail: dp387@cam.ac.uk; Wittwer, V. J.; Milana, S.; Hasan, T.; Jiang, Z.; Ferrari, A. C. [Cambridge Graphene Centre, University of Cambridge, Cambridge CB3 0FA (United Kingdom); Ilday, F. Ö. [Department of Physics, Bilkent University, 06800 Ankara (Turkey); Department of Electrical and Electronics Engineering, Bilkent University, 06800 Ankara (Turkey)

    2015-12-14

    We report dissipative soliton generation from an Yb-doped all-fiber nonlinearity- and dispersion-managed nanotube mode-locked laser. A simple all-fiber ring cavity exploits a photonic crystal fiber for both nonlinearity enhancement and dispersion compensation. The laser generates stable dissipative solitons with large linear chirp in the net normal dispersion regime. Pulses that are 8.7 ps long are externally compressed to 118 fs, outperforming current nanotube-based Yb-doped fiber laser designs.

  16. Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes

    DEFF Research Database (Denmark)

    Dou, Suguang; Jensen, Jakob Søndergaard

    2016-01-01

    Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...... involving plane frame structures where the hardening/softening behavior is qualitatively and quantitatively tuned by simple changes in the geometry of the structures....

  17. Nonlinear excitation of geodesic acoustic modes by drift waves

    International Nuclear Information System (INIS)

    Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.

    2007-01-01

    In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs

  18. Nonlinear tearing modes in the reversed field pinch

    International Nuclear Information System (INIS)

    Miller, G.

    1989-01-01

    Finite-amplitude islands, which are the saturated states of tearing modes in the reversed field pinch, are calculated. These states are bifurcated noncylindrical equilibrium states. With σ(r) (σequivalentj x B/B 2 ) nonuniform across the plasma, as is consistent with experiment, a variety of m = 1 and m = 0 bifurcated equilibria are possible, instead of just the m = 1 helix calculated for uniform σ(r) by Taylor [in Pulsed High Beta Plasmas, edited by D. Evans (Pergamon, Oxford, 1976), p. 59]. Assuming the magnetic field lines in the reversed field pinch are weakly stochastic, the growth time of an unstable tearing mode is on the inertial time scale, as in the Taylor model, in constrast to growth on the resistive time scale predicted from nonlinear tearing mode theory when magnetic surfaces exist. The dependence of the saturated island width on radius of a conducting shell is investigated. Islands in the reversed field pinch often have magnetic wells in the island interior, which may result in improved confinement in the island regions

  19. Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity

    International Nuclear Information System (INIS)

    Lin Juisheng; Yan Junjuh; Liao Tehlu

    2005-01-01

    This paper is concerned with the state reconstruction of nonlinear chaotic systems with uncertainty having unknown bounds. An adaptive output feedback sliding mode observer (AOFSMO) is established from the available output measurement. Unlike most works we further consider the presence of input nonlinearity due to physical limitations and no restrictive assumption is imposed on the system. Thus, the range of applicability of the proposed method becomes broad. Finally, a hyperchaotic Roessler system is used as an illustrative example to demonstrate the effectiveness of the proposed AOFSMO design method

  20. Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping

    Directory of Open Access Journals (Sweden)

    Eleni Bisognin

    2007-01-01

    Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.

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

    International Nuclear Information System (INIS)

    Yau, H.-T.

    2008-01-01

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

  2. An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures

    DEFF Research Database (Denmark)

    Christensen, Claus Dencker; Byskov, Esben

    2010-01-01

    A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns...... with two different types of cross-section. Comparison with numerical results show that our expansion provides more accurate predictions of the behavior than usual expansions. The method is based on an extended version of the principle of virtual displacements that covers cases with auxiliary conditions...

  3. Nonlinear coupling of the resistive tearing modes under the unperturbed shear flow

    International Nuclear Information System (INIS)

    Urata, Kazuhiro

    1990-01-01

    The influence of the unperturbed shear flow on the nonlinear evolution of the tearing mode is studied. In the case of single helicity, the shear flow activates the unstable mode which finally saturates to a rigid rotor state. In the case of multiple helicity, a variety of flow patterns is created depending on parameters, and always forms the current bubble soon after the collapse of the 3/2 magnetic island. (author)

  4. On nonlinear MHD-stability of toroidal magnetized plasma

    International Nuclear Information System (INIS)

    Ilgisonis, V.I.; Pastukhov, V.P.

    1994-01-01

    The variational approach to analyze the nonlinear MHD stability of ideal plasma in toroidal magnetic field is proposed. The potential energy functional to be used is expressed in terms of complete set of independent Lagrangian invariants, that allows to take strictly into account all the restrictions inherent in the varied functions due to MHD dynamic equations. (author). 3 refs

  5. Beam stability & nonlinear dynamics. Formal report

    Energy Technology Data Exchange (ETDEWEB)

    Parsa, Z. [ed.

    1996-12-31

    his Report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report.

  6. Bifurcation and phase diagram of turbulence constituted from three different scale-length modes

    Energy Technology Data Exchange (ETDEWEB)

    Itoh, S.-I.; Kitazawa, A.; Yagi, M. [Kyushu Univ., Research Inst. for Applied Mechanics, Kasuga, Fukuoka (Japan); Itoh, K. [National Inst. for Fusion Science, Toki, Gifu (Japan)

    2002-04-01

    Cases where three kinds of fluctuations having the different typical scale-lengths coexist are analyzed, and the statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analyzed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analyzed and a phase diagram is drawn. Phase diagrams with cusp type catastrophe and butterfly type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analyzed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses. (author)

  7. Nonlinear interaction model of subsonic jet noise.

    Science.gov (United States)

    Sandham, Neil D; Salgado, Adriana M

    2008-08-13

    Noise generation in a subsonic round jet is studied by a simplified model, in which nonlinear interactions of spatially evolving instability modes lead to the radiation of sound. The spatial mode evolution is computed using linear parabolized stability equations. Nonlinear interactions are found on a mode-by-mode basis and the sound radiation characteristics are determined by solution of the Lilley-Goldstein equation. Since mode interactions are computed explicitly, it is possible to find their relative importance for sound radiation. The method is applied to a single stream jet for which experimental data are available. The model gives Strouhal numbers of 0.45 for the most amplified waves in the jet and 0.19 for the dominant sound radiation. While in near field axisymmetric and the first azimuthal modes are both important, far-field sound is predominantly axisymmetric. These results are in close correspondence with experiment, suggesting that the simplified model is capturing at least some of the important mechanisms of subsonic jet noise.

  8. The free energy principle, negative energy modes, and stability

    International Nuclear Information System (INIS)

    Morrison, P.J.; Kotschenreuther, M.

    1990-01-01

    This paper is concerned with instability of equilibria of Hamiltonian, fluid and plasma dynamical systems. Usually the dynamical equilibrium of interest is not the state of thermodynamic equilibrium, and does not correspond to a free energy minimum. The relaxation of this type of equilibrium is conventionally considered to be initiated by linear instability. However, there are many cases where linear instability is not present, but the equilibrium is nonlinearly unstable to arbitrarily small perturbations. This paper is about general free energy expressions for determining the presence of linear or nonlinear instabilities. These expressions are simple and practical, and can be obtained for all equilibria of all ideal fluid and plasma models. By free energy, we mean the energy change upon perturbations of the equilibrium that respect dynamical phase space constraints. This quantity is measured by a self-adjoint quadratic form, called δ 2 F. The free energy can result in instability when δ 2 F is indefinite; i.e. there exist accessible perturbations that lower the free energy of the system. A primary purpose of this paper is to tie together three manifestations of what we will refer to as negative energy modes. The first is the conventional plasma physics notion of negative energy mode that is based on the definition of the energy in a homogeneous dielectric medium. A negative energy mode is a normal mode of the medium (plasma) that possesses negative dielectric energy. The second manifestation occurs in finite degree-of-freedom Hamiltonian normal form theory. The quadratic part of a Hamiltonian in the vicinity of an equilibrium point, which possesses only distinct oscillatory eigenvalues, has an invariant signature. Thus in cases where the quadratic form is indefinite, it is natural to refer to the modes corresponding to the negative signature as negative energy modes

  9. Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters

    KAUST Repository

    Hajjaj, Amal Z.

    2017-01-30

    We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.

  10. The theory of stability, bistability, and instability in three-mode class-A lasers

    International Nuclear Information System (INIS)

    Jahanpanah, J; Rahdar, A A

    2014-01-01

    Instability is an inevitable and common problem in all different kinds of lasers when they are oscillating in both single-and multi-mode states. Here, the stability conditions are investigated for a three-mode class-A laser. A set of linear equations is derived for the stable oscillation of the cavity central mode together with its left and right adjacent longitudinal modes. The coefficient determinant of stability equations is Hermitian and equal to zero for the roots of two diagonal arrays. In other words, the novelty of our work is to expand the stability coefficient determinant in terms of main diagonal arrays rather than for one row or one column. These diagonal roots lead to two lower and upper boundary curves in the form of a bifurcation. The lower boundary curve mimics the single-mode laser and delimits the instability region (with no above-threshold oscillating mode) from the bistability region (with two above-threshold oscillating modes). The upper boundary curve mimics the two-mode laser and delimits the bistability region from the stability region, in which all three-longitudinal modes are simultaneously oscillating in the above-threshold state. (paper)

  11. Parameter sensitivity analysis of nonlinear piezoelectric probe in tapping mode atomic force microscopy for measurement improvement

    Energy Technology Data Exchange (ETDEWEB)

    McCarty, Rachael; Nima Mahmoodi, S., E-mail: nmahmoodi@eng.ua.edu [Department of Mechanical Engineering, The University of Alabama, Box 870276, Tuscaloosa, Alabama 35487 (United States)

    2014-02-21

    The equations of motion for a piezoelectric microcantilever are derived for a nonlinear contact force. The analytical expressions for natural frequencies and mode shapes are obtained. Then, the method of multiple scales is used to analyze the analytical frequency response of the piezoelectric probe. The effects of nonlinear excitation force on the microcantilever beam's frequency and amplitude are analytically studied. The results show a frequency shift in the response resulting from the force nonlinearities. This frequency shift during contact mode is an important consideration in the modeling of AFM mechanics for generation of more accurate imaging. Also, a sensitivity analysis of the system parameters on the nonlinearity effect is performed. The results of a sensitivity analysis show that it is possible to choose parameters such that the frequency shift minimizes. Certain parameters such as tip radius, microcantilever beam dimensions, and modulus of elasticity have more influence on the nonlinearity of the system than other parameters. By changing only three parameters—tip radius, thickness, and modulus of elasticity of the microbeam—a more than 70% reduction in nonlinearity effect was achieved.

  12. On the nonlinear stability of mKdV breathers

    DEFF Research Database (Denmark)

    Alejo Plana, Miguel Angel; Muñoz, Claudio

    2012-01-01

    Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under ...

  13. Giant enhancement of reflectance due to the interplay between surface confined wave modes and nonlinear gain in dielectric media.

    Science.gov (United States)

    Kim, Sangbum; Kim, Kihong

    2017-12-11

    We study theoretically the interplay between the surface confined wave modes and the linear and nonlinear gain of the dielectric layer in the Otto configuration. The surface confined wave modes, such as surface plasmons or waveguide modes, are excited in the dielectric-metal bilayer by obliquely incident p waves. In the purely linear case, we find that the interplay between linear gain and surface confined wave modes can generate a large reflectance peak with its value much greater than 1. As the linear gain parameter increases, the peak appears at smaller incident angles, and the associated modes also change from surface plasmons to waveguide modes. When the nonlinear gain is turned on, the reflectance shows very strong multistability near the incident angles associated with surface confined wave modes. As the nonlinear gain parameter is varied, the reflectance curve undergoes complicated topological changes and sometimes displays separated closed curves. When the nonlinear gain parameter takes an optimally small value, a giant amplification of the reflectance by three orders of magnitude occurs near the incident angle associated with a waveguide mode. We also find that there exists a range of the incident angle where the wave is dissipated rather than amplified even in the presence of gain. We suggest that this can provide the basis for a possible new technology for thermal control in the subwavelength scale.

  14. The study of 80 MHz self starting passively mode-locked Erbium-Doped Fiber Laser via nonlinear polarization rotation with SESAM

    International Nuclear Information System (INIS)

    Qamar, F.

    2013-01-01

    Erbium-Doped Fiber Laser, EDF L, passively mode-locked via only Nonlinear Polarization Rotation, NPR, and via NPR with Semiconductor Saturable Absorber Mirror, SESAM, is studied. Self start single pulse train with pulse width of 114 fs and repetition rate (PRR) of 80 MHz has been obtained when 55 cm EDFL, passively mode-locked via NPR only. Inserting SESAM in EDFL cavity leads to shorten the pulse width up to 88 fs, increases the amplitude stability up to 96% and lower the phase noise jittering to around 26 fsec. Stable second harmonic self starting passively mode-locked EDFL with pulse width of 284 fs has also been observed only when SESAM was used in the cavity. Multi-pulsed system passively mode-locked via NPR for EDFL length of 80 cm with time difference between the successive multi-pulses ranged from few picoseconds to nanoseconds, has been observed. The time difference can be controlled by the polarizer controller and the half wave plate. Further controlling of the cavity polarization leads to developing the multiple mode locking pulses train to second harmonic mode-locking pulse train with PRR of 160MHz and pulse width of 156 fs. Three harmonic superposed trains of mode locked pulse have been achieved only when SESAM added to the cavity. (author)

  15. Stability properties of cold blanket systems for current driven modes

    International Nuclear Information System (INIS)

    Ohlsson, D.

    1977-12-01

    The stability problem of the boundary regions of cold blanket systems with induced currents parallel to the lines of force is formulated. Particular interest is focused on two types of modes: first electrostatic modes driven by the combined effects of a transverse resistivity gradient due to a spatially non-uniform electron temperature and a longitudinal current, second electromagnetic kink like modes driven by the torque arising from a transverse current density gradient and magnetic field perturbations. It is found that the combination of various dissipative and neutral gas effects introduces strong stabilizing effects within specific parameter ranges. For particular steady-state models investigated it is shown that these effects become of importance in laboratory plasmas at relatively high densities, low temperatures and moderate magnetic field strengths. Stability diagrams based on specific steady-state cold plasma blanket models will be presented

  16. Neoclassical tearing mode seeding by coupling with infernal modes in low-shear tokamaks

    Science.gov (United States)

    Kleiner, A.; Graves, J. P.; Brunetti, D.; Cooper, W. A.; Halpern, F. D.; Luciani, J.-F.; Lütjens, H.

    2016-09-01

    A numerical and an analytical study of the triggering of resistive MHD modes in tokamak plasmas with low magnetic shear core is presented. Flat q profiles give rise to fast growing pressure driven MHD modes, such as infernal modes. It has been shown that infernal modes drive fast growing islands on neighbouring rational surfaces. Numerical simulations of such instabilities in a MAST-like configuration are performed with the initial value stability code XTOR-2F in the resistive frame. The evolution of magnetic islands are computed from XTOR-2F simulations and an analytical model is developed based on Rutherford’s theory in combination with a model of resistive infernal modes. The parameter {{Δ }\\prime} is extended from the linear phase to the non-linear phase. Additionally, the destabilising contribution due to a helically perturbed bootstrap current is considered. Comparing the numerical XTOR-2F simulations to the model, we find that coupling has a strong destabilising effect on (neoclassical) tearing modes and is able to seed 2/1 magnetic islands in situations when the standard NTM theory predicts stability.

  17. Shear flows induced by nonlinear evolution of double tearing modes

    International Nuclear Information System (INIS)

    Wang Zhengxiong; Kishimoto, Y.; Li, J. Q.; Wang Xiaogang; Dong, J. Q.

    2008-01-01

    Shear flows induced by nonlinear evolution of double tearing modes are investigated in a resistive magnetohydrodynamic model with slab geometry. It is found that intensive and thin poloidal shear flow layers are generated in the magnetic island region driven by coupled reconnection process at both rational surfaces. The structure of the flow layers keeps evolving after the merging of magnetic separatrices and forms a few narrow vortices along the open field lines in the final stage of magnetic reconnection. The effects of the distance between both rational surfaces and the initial magnetic shear on the nonlinear evolution of the plasma flows are also taken into consideration and the relevant mechanism is discussed

  18. Nonlinear mode conversion with chaotic soliton generation at plasma resonance

    International Nuclear Information System (INIS)

    Pietsch, H.; Laedke, E.W.; Spatschek, K.H.

    1993-01-01

    The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations

  19. Ballooning stability analysis of JET H-mode discharges

    International Nuclear Information System (INIS)

    O'Brien, D.P.; Galvao, R.; Keilhacker, M.; Lazzaro, E.; Watkins, M.L.

    1989-01-01

    Previous studies of the stability of a large aspect ratio model equilibrium to ideal MHD ballooning modes have shown that across the bulk of the plasma there exist two marginally stable values of the pressure gradient parameter α. These define an unstable zone which separates the first (small α) stable region from the second (large α) stable region. Close to the separatrix, however, the first and second regions can coalesce when the surface averaged current density, Λ, exceeds a critical value. The plasma in this region is then stable to ballooning modes at all values of the pressure gradient. In this paper we extend these results to JET H-mode equilibria using a finite aspect ratio ballooning formalism, and assess the relevance of ideal ballooning stability in these discharges. In particular we analyse shot 15894 at time 56 sec. which is 1.3 s into the H-phase. (author) 4 refs., 4 figs

  20. Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification

    Czech Academy of Sciences Publication Activity Database

    Mordukhovich, B. S.; Outrata, Jiří

    2013-01-01

    Roč. 49, č. 3 (2013), s. 446-464 ISSN 0023-5954 R&D Projects: GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : variational analysis * second-order theory * generalized differentiation * tilt stability Subject RIV: BA - General Mathematics Impact factor: 0.563, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/outrata-tilt stability in nonlinear programming under mangasarian-fromovitz constraint qualification.pdf

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

    Directory of Open Access Journals (Sweden)

    Hamed Kharrati

    2012-01-01

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

  2. Decreasing the LHC impedance with a nonlinear collimation system

    CERN Document Server

    Resta-López, J; Zimmermann, F

    2007-01-01

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

  3. Strong asymmetry for surface modes in nonlinear lattices with long-range coupling

    International Nuclear Information System (INIS)

    Martinez, Alejandro J.; Vicencio, Rodrigo A.; Molina, Mario I.

    2010-01-01

    We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increases (decreases) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.

  4. Bunched beam longitudinal stability

    International Nuclear Information System (INIS)

    Baartman, R.

    1991-05-01

    Instabilities driven by narrow-band impedances can be stabilized by Landau damping arising from the synchrotron frequency spread due to the nonlinearity of the rf wave-form. We calculate stability diagrams for various phase space distributions. We find that distributions without tails are unstable in the 'negative mass' regime (inductive impedance below transition or capacitive impedance above transition). We also find that longitudinal instability thresholds of the (usually neglected) higher order radial modes are lower than expected. For example, the next to lowest dipole mode has a lower threshold than the lowest sextupole mode even though the latter has the larger growth rate in the absence of Landau damping. (Author) 5 refs., 5 figs

  5. Chaos in toroidal ion-temperature-gradient-driven modes in dust-contaminated magnetoplasma

    Energy Technology Data Exchange (ETDEWEB)

    Qamar, Anisa; Atta-Ullah-Shah [Theoretical Plasma Physics Group, Institute of Physics and Electronics, University of Peshawar Khyber Pakhtunkhwa 25000 (Pakistan); Yaqub Khan, M; Ayub, M [Department of Mathematics, Quaid-i-Azam University, Islamabad 45320 (Pakistan); Mirza, Arshad M, E-mail: anisaqamar@gmail.com [Theoretical Plasma Physics Group, Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan)

    2011-06-01

    A new set of nonlinear equations for toroidal ion-temperature-gradient-driven (ITGD) drift-dissipative waves is derived by using Braginskii's transport model of the ion dynamics and the Boltzmann distribution of electrons in the presence of negatively charged dust grains. The temporal behaviour of the nonlinear ITGD mode is found to be governed by three nonlinear equations for the amplitudes, which is a generalization of Lorenz- and Stenflo-type equations admitting chaotic trajectories. The linear stability analysis has been presented and stationary points for our generalized mode coupling equations are also derived.

  6. Resistive toroidal stability of internal kink modes in circular and shaped tokamaks

    International Nuclear Information System (INIS)

    Bondeson, A.; Luetjens, H.; Vlad, G.

    1991-12-01

    The linear resistive magnetohydrodynamical (MHD) stability of the n=1 internal kink mode in tokamaks is studied by toroidal computations. The stabilizing influence of small aspect ratio is confirmed, but it is found that shaping of the cross section influences the internal kink mode significantly. For finite pressure and small resistivity, curvature effects at the q=1 surface make the stability sensitively dependent on shape, and ellipticity (including JET shape) is destabilizing. Only a very restricted set of finite pressure equilibria is completely stable for q 0 <1. A typical result is that the resistive kink mode is slowed down by toroidal effects to a weak tearing/resistive interchange mode. It is suggested that weak resistive instabilities are stabilized during the ramp phase of the sawteeth by effects not included in the linear resistive MHD model. Possible mechanisms for triggering a sawtooth crash are discussed. (author) 18 figs., 34 refs

  7. Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.

  8. Stability of multihelical tearing modes in shaped tokamaks

    International Nuclear Information System (INIS)

    Kerner, W.; Tasso, H.

    1982-03-01

    The stability of multihelical tearing modes in tokamaks with shaped cross-sections is determined numerically. The method allows inclusion of a large number of singular surfaces resolved with high accuracy. Poloidal and radial couplings are discussed and the convergence is well understood. High poloidal m number modes are found to be unstable for typical equilibria. Completely stable current distributions have been constructed for D-shaped plasmas. (orig.)

  9. Nonlinear saturation of E x B instability in a plasma slab

    International Nuclear Information System (INIS)

    Alfsen, K.H.; Holter, Oe.

    1984-09-01

    The saturation of the E bar x B bar instability is investigated in the nonlinear regime. The governing equations are studied analytically and numerically by using a spectral method with mode truncation. The nonlinear stabilization is due to modifications of the background density- and potential profiles. In the time asymptotic limit a stationary solution, which is independent of the initial conditions is obtained. The asymptotic state is characterized by a splitting of the interacting modes into two almost non-interacting groups, where the modes with even mode number sum; i.e. the modes driven by the linearly most unstable mode, is found to dominate the system. For this group fixed point calculations are performed analytically with six interacting modes. Comparison with numerical calculations indicates excellent agreement far into the unstable region. (Auth.)

  10. On fully three-dimensional resistive wall mode and feedback stabilization computations

    International Nuclear Information System (INIS)

    Strumberger, E.; Merkel, P.; Sempf, M.; Guenter, S.

    2008-01-01

    Resistive walls, located close to the plasma boundary, reduce the growth rates of external kink modes to resistive time scales. For such slowly growing resistive wall modes, the stabilization by an active feedback system becomes feasible. The fully three-dimensional stability code STARWALL, and the feedback optimization code OPTIM have been developed [P. Merkel and M. Sempf, 21st IAEA Fusion Energy Conference 2006, Chengdu, China (International Atomic Energy Agency, Vienna, 2006, paper TH/P3-8] to compute the growth rates of resistive wall modes in the presence of nonaxisymmetric, multiply connected wall structures and to model the active feedback stabilization of these modes. In order to demonstrate the capabilities of the codes and to study the effect of the toroidal mode coupling caused by multiply connected wall structures, the codes are applied to test equilibria using the resistive wall structures currently under debate for ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)] and ASDEX Upgrade [W. Koeppendoerfer et al., Proceedings of the 16th Symposium on Fusion Technology, London, 1990 (Elsevier, Amsterdam, 1991), Vol. 1, p. 208

  11. Stability Analysis of Some Nonlinear Anaerobic Digestion Models

    Directory of Open Access Journals (Sweden)

    Ivan Simeonov

    2010-04-01

    Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.

  12. The Local Stability of Solutions for a Nonlinear Equation

    Directory of Open Access Journals (Sweden)

    Haibo Yan

    2014-01-01

    Full Text Available The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R by assuming that the initial value only lies in the space L1(R∩L∞(R.

  13. Optical fibers with low nonlinearity and low polarization-mode dispersion for terabit communications

    Science.gov (United States)

    Baghdadi, J. A.; Safaai-Jazi, A.; Hattori, H. T.

    2001-07-01

    Refractive-index nonlinearities have negligible effect on the performance of short-haul fiber-optic communication links utilizing electronic repeaters. However, in long links, nonlinearities can cause severe signal degradations. To mitigate nonlinear effects, a new generation of fibers, referred to as large effective-area fibers, have been introduced in recent years. This paper reviews the latest research and development work on these fibers conducted by several research groups around the world. Attention is focused on a class of large effective-area fibers that are based on a depressed-core multiple-cladding design. Another important issue in long-haul and high capacity fiber optic systems is the polarization-mode dispersion (PMD) which has been recognized as a serious limiting factor. In this paper, an improved fiber design is proposed which, in addition to providing large effective-area and low bending loss, eliminates PMD due to elliptical deformation in the single-mode wavelength region. Furthermore, this design is allowed to provide a small chromatic dispersion about few ps/ nm km , in order to overcome four-wave mixing effects.

  14. Stability Control of Force-Reflected Nonlinear Multilateral Teleoperation System under Time-Varying Delays

    Directory of Open Access Journals (Sweden)

    Da Sun

    2016-01-01

    Full Text Available A novel control algorithm based on the modified wave-variable controllers is proposed to achieve accurate position synchronization and reasonable force tracking of the nonlinear single-master-multiple-slave teleoperation system and simultaneously guarantee overall system’s stability in the presence of large time-varying delays. The system stability in different scenarios of human and environment situations has been analyzed. The proposed method is validated through experimental work based on the 3-DOF trilateral teleoperation system consisting of three different manipulators. The experimental results clearly demonstrate the feasibility of the proposed algorithm to achieve high transparency and robust stability in nonlinear single-master-multiple-slave teleoperation system in the presence of time-varying delays.

  15. Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty

    NARCIS (Netherlands)

    van der Schaft, Arjan

    1995-01-01

    The approach to robust stabilization of linear systems using normalized left coprime factorizations with H∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust

  16. ELMs and constraints on the H-mode pedestal: A model based on peeling-ballooning modes

    International Nuclear Information System (INIS)

    Snyder, P.B.

    2002-01-01

    Maximizing the pedestal height while maintaining acceptable ELMs is a key issue for optimizing tokamak performance. We present a model for ELMs and pedestal constraints based upon theoretical analysis of edge instabilities which can limit the pedestal height and drive ELMs. Sharp pedestal pressure gradients drive large bootstrap currents which play a complex dual role in the stability physics. Consequently, the dominant modes are often intermediate-n coupled 'peeling-ballooning' modes, driven both by current and the pressure gradient. A highly efficient new MHD code, ELITE, is used to study these modes, and calculate quantitative stability constraints on the pedestal, including direct constraints on the pedestal height. A model of various ELM types is developed, and quantitatively compared to data from several tokamaks. A number of observations agree with predictions, including ELM onset times, ELM depth, and variation in pedestal height with discharge shape. Projections of pedestal stability constraints for Next Step designs, and nonlinear simulations of peeling-ballooning modes using the BOUT code are also presented. (author)

  17. Nonlinear MHD and energetic particle modes in stellarators

    International Nuclear Information System (INIS)

    Strauss, H.R.; Fu, G.Y.; Park, W.; Breslau, J.; Sugiyama, L.E.

    2003-01-01

    The M3D (Multi-level 3D) project carries out simulation studies of plasmas using multiple levels of physics, geometry and grid models. The M3D code has been applied to ideal, resistive, two fluid, and hybrid simulations of compact quasi axisymmetric stellarators. When β exceeds a threshold, moderate toroidal mode number (n ∼ 10) modes grow exponentially, clearly distinguishable from the equilibrium evolution. The β limits are significantly higher than the infinite mode number ballooning limits. In the presence of resistivity, these modes occur well below the ideal limit. Their growth rate scaling with resistivity is similar to tearing modes. At low resistivity, the modes couple to resistive interchanges, which are unstable in most stellarators. Two fluid simulations with M3D show that resistive modes can be stabilized by diamagnetic drift. The two fluid computations are done with a realistic value of the Hall parameter, the ratio of ion skin depth to major radius. Hybrid gyrokinetic simulations with energetic particles indicate that global shear Alfven TAE - like modes can be destabilized in stellarators. Computations in a two-period compact stellarator obtained a predominantly n=1 toroidal mode with the expected TAE frequency. It is found that TAE modes are more stable in the two-period compact stellarator that in a tokamak with the same q and pressure profiles. M3D combines a two dimensional unstructured mesh with finite element discretization in poloidal planes, and fourth order finite differencing in the toroidal direction. (author)

  18. The effect of partial poloidal wall sections on the wall stabilization of external kink modes

    International Nuclear Information System (INIS)

    Ward, D.J.

    1996-02-01

    An analysis of the effect on the wall stabilization of external kink modes due to toroidally continuous gaps in the resistive wall is performed. The effects with and without toroidal rotation are studied. For a high-β equilibrium, the mode structure is localized on the outboard side. Therefore, outboard gaps greatly increase the growth rate when there is no rotation. For resistive wall stabilization by toroidal rotation, the presence of gaps has the same effect as moving the wall farther away, i.e. destabilizing for the ideal plasma mode, and stabilizing for the resistive wall mode. The region of stability, in terms of wall position, is reduced in size and moved closer to the plasma. However, complete stabilization becomes possible at considerably reduced rotation frequencies. For a high-β, reverse-shear equilibrium both the resistive wall mode and the ideal plasma mode can be stabilized by close fitting discrete passive plates on the outboard side. The necessary toroidal rotation frequency to stabilize the resistive wall mode using these plates is reduced by a factor of three compared to that for a poloidally continuous and complete wall at the same plasma-wall separation. (author) 15 figs., 24 refs

  19. Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability: A Comparative Analysis with CPL Power Variation

    Directory of Open Access Journals (Sweden)

    Eklas Hossain

    2017-11-01

    Full Text Available To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC and Lyapunov Redesign Controller (LRC, two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness. CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic verification. Reasons behind inferior SMC performance and ways to mitigate that are also discussed. Finally, the effectiveness of SMC and LRC systems to attain stability in real microgrids is verified by numerical analysis.

  20. Non-parallel stability of compressible boundary layers

    Science.gov (United States)

    Chang, Chau-Lyan; Malik, Mujeeb R.

    1993-01-01

    Linear and nonlinear stability of compressible growing boundary layers is studied using parabolized stability equations (PSE). Linear PSE calculations are performed for Mach 1.6 and 4.5 plate-plate flow, and the results are compared with the predictions of the multiple-scales approach. In general, the nonparallel effect appears to be less significant for oblique waves near the lower neutral branch but it progressively becomes important at higher Reynolds numbers near the upper branch. In contrast, the nonparallel effect is more pronounced near the lower branch for two-dimensional first-mode waves. The PSE and multiple-scales results agree for the first mode waves, but in the first-second mode transition region, the latter approach tends to break down. Comparison with the first (oblique) and second mode growth rate data from Kendall's (1967) experiment shows good agreement; however, the peak second mode growth rate is over-predicted. Similar conclusions are drawn for the second mode experiment of Stetson et al. (1983) for Mach 8 flow past a sharp cone. We conjecture that the lower experimental growth rate is due to nonlinear saturation and provide supporting calculations.

  1. Stability of longitudinal modes in a bunched beam with mode coupling

    International Nuclear Information System (INIS)

    Satoh, K.

    1981-06-01

    In this paper we study a longitudinal coherent bunch instability in which the growth time is comparable to or less than the period of synchrotron oscillations. Both longitudinal and transverse bunch instabilities have been studied. In most treatments, however, the coherent force is assumed to be small and is treated as a perturbation compared with the synchrotron force. This makes the problem simpler because an individual synchrotron mode is decoupled. As bunch current increases, the coherent force is no longer small and the mode frequency shift becomes significant compared with the synchrotron frequency. Therefore in this case it is necessary to include coupling of the synchrotron modes. Recently a fast blow-up instability which comes from mode coupling was studied. Their method is to derive a dispersion relation for a bunched beam using the Vlasov equation and to analyze it as in a coasting beam. They showed that if mode coupling is included the Vlasov equation predicts a fast microwave instability with a stability condition similar to that for a coasting beam. In this paper we will partly follow their method and present a formalism which includes coupling between higher-order radial modes as well as coupling between synchrotron modes. The formalism is considered to be generalization of the Sacherer formalism without mode coupling. This theory predicts that instability is induced not only by coupling between different synchrotron modes, but also by coupling between positive and negative modes, since negative synchrotron modes are included in the theory in a natural manner. This formalism is to be used for a Gaussian bunch and a parabolic bunch, and is also useful for transverse problems

  2. Linear stability of microtearing modes in ASDEX

    International Nuclear Information System (INIS)

    Giannone, L.

    1987-12-01

    The linear stability of microtearing modes in typical ASDEX discharges have been calculated. In the case of Ohmic discharges it was found that unstable modes are predicted to be located towards the centre of the plasma. For L and H discharges the zone of instability shifts towards the plasma edge. The interpretation of an increase or decrease in the amplitude of broadband magnetic fluctuations during L and H discharges must be interpreted with caution, since the amplitude observed is strongly dependent on the radial position of the instability. (orig./GG)

  3. Active stabilization of n=0 and n=1 modes in the TCV tokamak

    International Nuclear Information System (INIS)

    Hofmann, F.; Tonetti, G.; Ward, D.J.; Gribov, Yu.

    1991-04-01

    The limits of operation of an elongated tokamak are generally defined by axisymmetric (n=0), free-boundary n=1, and ballooning modes. While it has become common practice to stabilize n=0 modes by a combination of passive and active systems, very few experiments have been done so far to investigate active stabilization of n=1 modes. In this paper, we discuss the possibilities for acitive stabilization of n=0 and n=1 in the TCV tokamak. (author) 2 figs., 2 tabs., 10 refs

  4. Nonlinear damping of drift waves by strong flow curvature

    International Nuclear Information System (INIS)

    Sidikman, K.L.; Carreras, B.A.; Garcia, L.; Diamond, P.H.

    1993-01-01

    A single-equation model has been used to study the effect of a fixed poloidal flow (V 0 ) on turbulent drift waves. The electron dynamics come from a laminar kinetic equation in the dissipative trapped-electron regime. In the past, the authors have assumed that the mode frequency is close to the drift-wave frequency. Trapped-electron density fluctuations are then related to potential fluctuations by an open-quotes iδclose quotes term. Flow shear (V 0 ') and curvature (V 0 double-prime) both have a stabilizing effect on linear modes for this open-quotes iδclose quotes model. However, in the nonlinear regime, single-helicity effects inhibit the flow damping. Neither V 0 ' nor V 0 double-prime produces a nonlinear damping effect. The above assumption on the frequency can be relaxed by including the electron time-response in the linear part of the evolution. In this time-dependent model, instability drive due to trapped electrons is reduced when mode frequency is greater than drift-wave frequency. Since V 0 double-prime produces such a frequency shift, its linear effect is enhanced. There is also nonlinear damping, since single-helicity effects do not eliminate the shift. Renormalized theory for this model predicts nonlinear stability for sufficiently large curvature. Single-helicity calculations have already shown nonlinear damping, and this strong V 0 double-prime regime is being explored. In the theory, the Gaussian shape of the nonlinear diffusivity is expanded to obtain a quadratic potential. The implications of this assumption will be tested by solving the full renormalized equation using a shooting method

  5. Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

    International Nuclear Information System (INIS)

    Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E

    2012-01-01

    Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

  6. Improving the theoretical foundations of the multi-mode transport model

    International Nuclear Information System (INIS)

    Bateman, G.; Kritz, A.H.; Redd, A.J.; Erba, M.; Rewoldt, G.; Weiland, J.; Strand, P.; Kinsey, J.E.; Scott, B.

    1999-01-01

    A new version of the Multi-Mode transport model, designated MMM98, is being developed with improved theoretical foundations, in an ongoing effort to predict the temperature and density profiles in tokamaks. For transport near the edge of the plasma, MMM98 uses a new model based on 3-D nonlinear simulations of drift Alfven mode turbulence. Flow shear stabilization effects have been added to the Weiland model for Ion Temperature Gradient and Trapped Electron Modes, which usually dominates in most of the plasma core. For transport near the magnetic axis at high beta, a new kinetic ballooning mode model has been constructed based on FULL stability code computations. (author)

  7. Improving the theoretical foundations of the multi-mode transport model

    International Nuclear Information System (INIS)

    Bateman, G.; Kritz, A.H.; Redd, A.J.; Erba, M.; Rewoldt, G.; Weiland, J.; Strand, P.; Kinsey, J.E.; Scott, B.

    2001-01-01

    A new version of the Multi-Mode transport model, designated MMM98, is being developed with improved theoretical foundations, in an ongoing effort to predict the temperature and density profiles in tokamaks. For transport near the edge of the plasma, MMM98 uses a new model based on 3-D nonlinear simulations of drift Alfven mode turbulence. Flow shear stabilization effects have been added to the Weiland model for Ion Temperature Gradient and Trapped Electron Modes, which usually dominates in most of the plasma core. For transport near the magnetic axis at high beta, a new kinetic ballooning mode model has been constructed based on FULL stability code computations. (author)

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

    Science.gov (United States)

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

    2001-05-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2001-05-04

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

  10. Neoclassical tearing mode stabilization by ECCD in ITER

    International Nuclear Information System (INIS)

    Giruzzi, G.; Zabiego, M.

    2001-01-01

    A dynamic model, based on a 3-D Fokker-Planck code coupled to the island evolution equations, is used to evaluate the feasibility of active control of Neoclassical Tearing modes by Electron Cyclotron Current Drive (ECCD) in International Thermonuclear Experimental Reactor (ITER). The parameters of the present version of ITER, i.e., RTO/RC ITER (IAM option) are used. Both m=3, n=2 and m=2, n=1 modes are considered. It is shown that an Electron Cyclotron wave system at 140 GHz, with toroidally steerable antennas, can stabilize both modes simultaneously if a power ≥30 MW is available

  11. Adaptive integral backstepping sliding mode control for opto-electronic tracking system based on modified LuGre friction model

    Science.gov (United States)

    Yue, Fengfa; Li, Xingfei; Chen, Cheng; Tan, Wenbin

    2017-12-01

    In order to improve the control accuracy and stability of opto-electronic tracking system fixed on reef or airport under friction and external disturbance conditions, adaptive integral backstepping sliding mode control approach with friction compensation is developed to achieve accurate and stable tracking for fast moving target. The nonlinear observer and slide mode controller based on modified LuGre model with friction compensation can effectively reduce the influence of nonlinear friction and disturbance of this servo system. The stability of the closed-loop system is guaranteed by Lyapunov theory. The steady-state error of the system is eliminated by integral action. The adaptive integral backstepping sliding mode controller and its performance are validated by a nonlinear modified LuGre dynamic model of the opto-electronic tracking system in simulation and practical experiments. The experiment results demonstrate that the proposed controller can effectively realise the accuracy and stability control of opto-electronic tracking system.

  12. Microgrid Stability Controller Based on Adaptive Robust Total SMC

    OpenAIRE

    Su, Xiaoling; Han, Minxiao; Guerrero, Josep M.; Sun, Hai

    2015-01-01

    This paper presents a microgrid stability controller (MSC) in order to provide existing distributed generation units (DGs) the additional functionality of working in islanding mode without changing their control strategies in grid-connected mode and to enhance the stability of the microgrid. Microgrid operating characteristics and mathematical models of the MSC indicate that the system is inherently nonlinear and time-variable. Therefore, this paper proposes an adaptive robust total sliding...

  13. Stability of limit cycles in autonomous nonlinear systems

    Czech Academy of Sciences Publication Activity Database

    Náprstek, Jiří; Fischer, Cyril

    2014-01-01

    Roč. 49, č. 8 (2014), s. 1929-1943 ISSN 0025-6455 R&D Projects: GA AV ČR(CZ) IAA200710902; GA ČR(CZ) GA103/09/0094; GA ČR(CZ) GC13-34405J Institutional support: RVO:68378297 Keywords : limit cycle * nonlinear oscillator * stability Subject RIV: JM - Building Engineering Impact factor: 1.949, year: 2014 http://link.springer.com/article/10.1007/s11012-014-9899-8

  14. Neoclassical effects on the stabilization of tearing mode by current modulation

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Xiaoqing, E-mail: inkyang@mail.ustc.edu.cn; Wang, Shaojie; Yang, Weihong [Department of Modern Physics, University of Science and Technology of China, Hefei, 230026 (China)

    2014-02-15

    The neoclassical effects on the stabilization of tearing modes by current modulation have been investigated. Neoclassical effects enhance the resistivity and reduce the resistive diffusion time of the modulation current. Therefore, the oscillating current can penetrate deeper into the plasma. With an oscillating loop voltage, the plasma oscillates radially at the Ware-pinch velocity. These neoclassical effects improve the efficiency of tearing mode stabilization by the current modulation.

  15. 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.

  16. On Reynolds stress and neutral azimuthal modes in the stability ...

    Indian Academy of Sciences (India)

    Some results of Miles on the parallel flow stability theory are extended to the .... can lie on the stability boundary these modes were studied by him in detail. ... play important roles in the linear viscous critical layer theory (see, for example,.

  17. External kink mode stability of tokamaks with finite edge current density in plasma outside separatrix

    International Nuclear Information System (INIS)

    Degtyarev, L.; Martynov, A.; Medvedev, S.; Troyon, F.; Villard, L.

    1996-01-01

    Large pressure gradients and current density at the plasma edge and accompanying edge-localized MHD instabilities are typical for H-mode discharges. Low-n external kink modes are a possible cause of the instabilities. The paper mostly deals with external kink modes driven by a finite current density at the plasma boundary (so called peeling modes). It was shown earlier that for a single axis plasma embedded into vacuum the peeling modes are stabilized when separatrix is approaching the plasma boundary. For doublet configurations a finite current density at the internal separatrix does not necessarily lead to external kink instability when the current density vanishes at the boundary. However, a finite current density at the plasma boundary outside the separatrix can drive outer peeling modes. The stability properties and structure of these modes depend on the plasma equilibrium outside the separatrix. The influence of plasma shear and pressure gradient at the boundary on the stability of the outer peeling modes in doublets is studied. The stability of kink modes in divertor configurations with plasma outside the separatrix is very sensitive to the boundary conditions set at open field lines. The choice of the boundary conditions and kink mode stability calculations for the divertor configurations are discussed. (author) 4 figs., 5 refs

  18. Nonlinear eigen-mode structures in complex astroclouds

    Science.gov (United States)

    Karmakar, P. K.; Haloi, A.

    2017-05-01

    The evolutionary dynamics of strongly nonlinear waves (of arbitrary amplitude) in an inhomogeneous complex astrophysical viscous cloud is investigated without recourse to any kind of swindle. It consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neural hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method transforms the analytic model into a conjugated pair of intermixed non-integrable energy integral laws. A natural excitation of electrostatic quasi-monotonic compressive dispersive shock-like eigen-modes is numerically demonstrated. In contrast, the self-gravitational waves grow purely as non-monotonic compressive oscillatory shock-like structures. The unique features of both the distinct classes are depicted. Their non-trivial significance in the astro-context is emphasized.

  19. Nonlinear optical beam manipulation, beam combining, and atmospheric propagation

    International Nuclear Information System (INIS)

    Fischer, R.A.

    1988-01-01

    These proceedings collect papers on optics: Topics include: diffraction properties of laser speckle, coherent beam combination by plasma modes, nonlinear responses, deformable mirrors, imaging radiometers, electron beam propagation in inhomogeneous media, and stability of laser beams in a structured environment

  20. NONLINEAR TIDES IN CLOSE BINARY SYSTEMS

    International Nuclear Information System (INIS)

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

    2012-01-01

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

  1. On a program manifold's stability of one contour automatic control systems

    Science.gov (United States)

    Zumatov, S. S.

    2017-12-01

    Methodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold's absolute stability of one contour automatic control systems are obtained. The Hurwitz's angle of absolute stability was determined. The sufficient conditions of program manifold's absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov's second method.

  2. LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno's form.

    Science.gov (United States)

    Lam, H K; Leung, Frank H F

    2007-10-01

    This correspondence presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. The idea of the nonparallel-distributed-compensation (non-PDC) control laws is extended to the continuous-time fuzzy-model-based control systems. A nonlinear controller with non-PDC control laws is proposed to stabilize the continuous-time nonlinear systems in Takagi-Sugeno's form. To produce the stability-analysis result, a parameter-dependent Lyapunov function (PDLF) is employed. However, two difficulties are usually encountered: 1) the time-derivative terms produced by the PDLF will complicate the stability analysis and 2) the stability conditions are not in the form of linear-matrix inequalities (LMIs) that aid the design of feedback gains. To tackle the first difficulty, the time-derivative terms are represented by some weighted-sum terms in some existing approaches, which will increase the number of stability conditions significantly. In view of the second difficulty, some positive-definitive terms are added in order to cast the stability conditions into LMIs. In this correspondence, the favorable properties of the membership functions and nonlinear control laws, which allow the introduction of some free matrices, are employed to alleviate the two difficulties while retaining the favorable properties of PDLF-based approach. LMI-based stability conditions are derived to ensure the system stability. Furthermore, based on a common scalar performance index, LMI-based performance conditions are derived to guarantee the system performance. Simulation examples are given to illustrate the effectiveness of the proposed approach.

  3. Tearing-mode stability in a cylindrical plasma with equilibrium flows

    International Nuclear Information System (INIS)

    Wessen, K.P.; Persson, M.; Australian National Univ., Canberra

    1991-01-01

    The effect of a sheared equilibrium mass flow on the resistive tearing mode is studied numerically by calculating Δ. Both stabilizing and destabilizing effects are found, depending on the velocity and magnetic field profiles. Specifically, when q o ''varies as'' 1, the flow is strongly stabilizing for centrally peaked current profiles, whereas the flow has a strongly destabilizing effect for flatter current profiles. While the extreme effects are more pronounced for larger flows, a smaller flow may have more influence on marginal stability. The case where the flow speed becomes comparable to the Alfven speed is also examined. It is found that this may lead to the equations being singular at points other than a rational surface, drastically changing the behaviour of the mode. (author)

  4. Robust stabilization of nonlinear systems by quantized and ternary control

    NARCIS (Netherlands)

    Persis, Claudio De

    2009-01-01

    Results on the problem of stabilizing a nonlinear continuous-time minimum-phase system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive robust practical stabilizability results by

  5. Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling

    Science.gov (United States)

    Dumeige, Yannick; Féron, Patrice

    2011-10-01

    Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processing or ternary optical logic applications.

  6. Stability and time-domain analysis of the dispersive tristability in microresonators under modal coupling

    International Nuclear Information System (INIS)

    Dumeige, Yannick; Feron, Patrice

    2011-01-01

    Coupled nonlinear resonators have potential applications for the integration of multistable photonic devices. The dynamic properties of two coupled-mode nonlinear microcavities made of Kerr material are studied by linear stability analysis. Using a suitable combination of the modal coupling rate and the frequency detuning, it is possible to obtain configurations where a hysteresis loop is included inside other bistable cycles. We show that a single resonator with two modes both linearly and nonlinearly coupled via the cross-Kerr effect can have a multistable behavior. This could be implemented in semiconductor nonlinear whispering-gallery-mode microresonators under modal coupling for all optical signal processing or ternary optical logic applications.

  7. Resistive Wall Mode Stability and Control in the Reversed Field Pinch

    International Nuclear Information System (INIS)

    Yadikin, Dmitriy

    2006-03-01

    Control of MHD instabilities using a conducting wall together with external magnetic fields is an important route to improved performance and reliability in fusion devices. Active control of MHD modes is of interest for both the Advanced Tokamak and the Reversed Field Pinch (RFP) configurations. A wide range of unstable, current driven MHD modes is present in the RFP. An ideally conducting wall facing the plasma can in principle provide stabilization to these modes. However, a real, resistive wall characterized by a wall field diffusion time, cannot stabilize the ideal MHD modes unless they rotate with Alfvenic velocity, which is usually not the case. With a resistive wall, the ideal modes are converted into resistive wall modes (RWM) with growth rates comparable to the inverse wall time. Resistive wall modes have been studied in the EXTRAP T2R thin shell RFP device. Growth rates have been measured and found in agreement with linear MHD stability calculations. An advanced system for active control has been developed and installed on the EXTRAP T2R device. The system includes an array of 128 active saddle coils, fully covering the torus surface. Experiments on EXTRAP T2R have for the first time demonstrated simultaneous active suppression of multiple independent RWMs. In experiments with a partial array, coupling of different modes due to the limited number of feedback coils has been observed, in agreement with theory. Different feedback strategies, such as the intelligent shell, the rotating shell, and mode control have been studied. Further, feedback operation with different types of magnetic field sensors, measuring either the radial or the toroidal field components have been compared

  8. Beam stability ampersand nonlinear dynamics. Formal report

    International Nuclear Information System (INIS)

    Parsa, Z.

    1996-01-01

    This report includes copies of transparencies and notes from the presentations made at the Symposium on Beam Stability and Nonlinear Dynamics, December 3-5, 1996 at the Institute for Theoretical Physics, University of California, Santa Barbara California, that was made available by the authors. Editing, reduction and changes to the authors contributions were made only to fulfill the printing and publication requirements. We would like to take this opportunity and thank the speakers for their informative presentations and for providing copies of their transparencies and notes for inclusion in this Report

  9. Numerical Study of the Formation, Ion Spin-up and Nonlinear Stability Properties of Field-reversed Configurations

    International Nuclear Information System (INIS)

    Belova, E.V.; Davidson, R.C.; Ji, H.; Yamada, M.; Cothran, C.D.; Brown, M.R.; Schaffer, M.J.

    2004-01-01

    Results of three-dimensional numerical simulations of field-reversed configurations (FRCs) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs and the new FRC formation method by the counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n = 1 tilt mode, where n is the toroidal mode number. The n = 2 and n = 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux, and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good agreement with results from the SSX-FRC experiment. Simulations show formation of an FRC in about 30 Alfven times for typical experimental parameters. The growth rate of the n = 1 tilt mode is shown to be significantly reduced compared to the MHD growth rate due to the large plasma viscosity and field-line-tying effects

  10. Global Hybrid Simulations of Energetic Particle-driven Modes in Toroidal Plasmas

    International Nuclear Information System (INIS)

    Fu, G.Y.; Breslau, J.; Fredrickson, E.; Park, W.; Strauss, H.R.

    2004-01-01

    Global hybrid simulations of energetic particle-driven MHD modes have been carried out for tokamaks and spherical tokamaks using the hybrid code M3D. The numerical results for the National Spherical Tokamak Experiments (NSTX) show that Toroidal Alfven Eigenmodes are excited by beam ions with their frequencies consistent with the experimental observations. Nonlinear simulations indicate that the n=2 mode frequency chirps down as the mode moves out radially. For ITER, it is shown that the alpha-particle effects are strongly stabilizing for internal kink mode when central safety factor q(0) is sufficiently close to unity. However, the elongation of ITER plasma shape reduces the stabilization significantly

  11. Fast particle effects on the internal kink, fishbone and Alfven modes

    International Nuclear Information System (INIS)

    Gorelenkov, N.N.; Bernabei, S.; Cheng, C.Z.; Fu, G.Y.; Hill, K.; Kaye, S.; Kramer, G.J.; Nazikian, R.; Park, W.; Kusama, Y.; Shinokhara, K.; Ozeki, T.

    2001-01-01

    The issues of linear stability of low frequency perturbative and nonperturbative modes in advanced tokamak regimes are addressed based on recent developments in theory, computational methods, and progress in experiments. Perturbative codes NOVA and ORBIT are used to calculate the effects of TAEs on fast particle population in spherical tokamak NSTX. Nonperturbative analysis of chirping frequency modes in experiments on TFTR and JT-60U is presented using the kinetic code HINST, which identified such modes as a separate branch of Alfven modes - resonance TAE (R-TAE). Internal kink mode stability in the presence of fast particles is studied using the NOVA code and hybrid kinetic-MHD nonlinear code M3D. (author)

  12. Fast Particle Effects on the Internal Kink, Fishbone and Alfven Modes

    International Nuclear Information System (INIS)

    Gorelenkov, N.N.; Bernabei, S.; Cheng, C.Z.; Fu, G.Y.; Hill, K.; Kaye, S.; Kramer, G.J.; Kusama, Y.; Shinohara, K.; Nazikian, R.; Ozeki, T.; Park, W.

    2000-01-01

    The issues of linear stability of low frequency perturbative and nonperturbative modes in advanced tokamak regimes are addressed based on recent developments in theory, computational methods, and progress in experiments. Perturbative codes NOVA and ORBIT are used to calculate the effects of TAEs on fast particle population in spherical tokamak NSTX. Nonperturbative analysis of chirping frequency modes in experiments on TFTR and JT-60U is presented using the kinetic code HINST, which identified such modes as a separate branch of Alfven modes - resonance TAE (R-TAE). Internal kink mode stability in the presence of fast particles is studied using the NOVA code and hybrid kinetic-MHD nonlinear code M3D

  13. Gravitational waves from nonlinear couplings of radial and polar nonradial modes in relativistic stars

    International Nuclear Information System (INIS)

    Passamonti, Andrea; Stergioulas, Nikolaos; Nagar, Alessandro

    2007-01-01

    The postbounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wideband resonant detectors

  14. Nonlinear δf Simulation Studies of Intense Charged Particle Beams with Large Temperature Anisotropy

    International Nuclear Information System (INIS)

    Startsev, Edward A.; Davidson, Ronald C.; Qin, Hong

    2002-01-01

    In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) [H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401] is used to systematically study the stability properties of intense nonneutral charged particle beams with large temperature anisotropy (T perpendicularb >> T parallelb ). The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined for axisymmetric perturbations with ∂/∂θ = 0

  15. Secondary Instability of Second Modes in Hypersonic Boundary Layers

    Science.gov (United States)

    Li, Fei; Choudhari, Meelan M.; Chang, Chau-Lyan; White, Jeffery A.

    2012-01-01

    Second mode disturbances dominate the primary instability stage of transition in a number of hypersonic flow configurations. The highest amplification rates of second mode disturbances are usually associated with 2D (or axisymmetric) perturbations and, therefore, a likely scenario for the onset of the three-dimensionality required for laminar-turbulent transition corresponds to the parametric amplification of 3D secondary instabilities in the presence of 2D, finite amplitude second mode disturbances. The secondary instability of second mode disturbances is studied for selected canonical flow configurations. The basic state for the secondary instability analysis is obtained by tracking the linear and nonlinear evolution of 2D, second mode disturbances using nonlinear parabolized stability equations. Unlike in previous studies, the selection of primary disturbances used for the secondary instability analysis was based on their potential relevance to transition in a low disturbance environment and the effects of nonlinearity on the evolution of primary disturbances was accounted for. Strongly nonlinear effects related to the self-interaction of second mode disturbances lead to an upstream shift in the upper branch neutral location. Secondary instability computations confirm the previously known dominance of subharmonic modes at relatively small primary amplitudes. However, for the Purdue Mach 6 compression cone configuration, it was shown that a strong fundamental secondary instability can exist for a range of initial amplitudes of the most amplified second mode disturbance, indicating that the exclusive focus on subharmonic modes in the previous applications of secondary instability theory to second mode primary instability may not have been fully justified.

  16. Power-induced evolution and increased dimensionality of nonlinear modes in reorientational soft matter.

    Science.gov (United States)

    Laudyn, Urszula A; Jung, Paweł S; Zegadło, Krzysztof B; Karpierz, Miroslaw A; Assanto, Gaetano

    2014-11-15

    We demonstrate the evolution of higher order one-dimensional guided modes into two-dimensional solitary waves in a reorientational medium. The observations, carried out at two different wavelengths in chiral nematic liquid crystals, are in good agreement with a simple nonlocal nonlinear model.

  17. Optical frequency comb generation based on the dual-mode square microlaser and a nonlinear fiber loop

    Science.gov (United States)

    Weng, Hai-Zhong; Han, Jun-Yuan; Li, Qing; Yang, Yue-De; Xiao, Jin-Long; Qin, Guan-Shi; Huang, Yong-Zhen

    2018-05-01

    A novel approach using a dual-mode square microlaser as the pump source is demonstrated to produce wideband optical frequency comb (OFC). The enhanced nonlinear frequency conversion processes are accomplished in a nonlinear fiber loop, which can reduce the stimulated Brillouin scattering threshold and then generate a dual-mode Brillouin laser with improved optical signal-to-noise ratio. An OFC with 130 nm bandwidth and 76 GHz repetition rate is successfully generated under the four-wave mixing, and the number of the comb lines is enhanced by 26 times compared with the system without fiber loop. In addition, the repetition rate of the comb can be adjusted by changing the injection current of the microlaser. The pulse width of the comb spectrum is also compressed from 3 to 1 ps with an extra amplification-nonlinear process.

  18. Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique

    Science.gov (United States)

    Zhang, Tie-Yan; Zhao, Yan; Xie, Xiang-Peng

    2012-12-01

    This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.

  19. Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique

    International Nuclear Information System (INIS)

    Zhang Tie-Yan; Zhao Yan; Xie Xiang-Peng

    2012-01-01

    This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach. (general)

  20. Nonlinear eigen-mode structures in complex astroclouds

    International Nuclear Information System (INIS)

    Karmakar, P K; Haloi, A

    2017-01-01

    The evolutionary dynamics of strongly nonlinear waves (of arbitrary amplitude) in an inhomogeneous complex astrophysical viscous cloud is investigated without recourse to any kind of swindle. It consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neural hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method transforms the analytic model into a conjugated pair of intermixed non-integrable energy integral laws. A natural excitation of electrostatic quasi-monotonic compressive dispersive shock-like eigen-modes is numerically demonstrated. In contrast, the self-gravitational waves grow purely as non-monotonic compressive oscillatory shock-like structures. The unique features of both the distinct classes are depicted. Their non-trivial significance in the astro-context is emphasized. (paper)

  1. Linear and nonlinear dynamics of electron temperature gradient mode in non-Maxwellian plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Zakir, U.; Qamar, A. [Institute of Physics and Electronics, University of Peshawar, Peshawar (Pakistan); Haque, Q. [Theoretical Plasma Physics Division, PINSTECH, Islamabad (Pakistan); National Centre for Physics, Islamabad (Pakistan)

    2013-05-15

    The effect of non-Maxwellian distributed ions on electron temperature gradient mode is investigated. The linear dispersion relation of η{sub e}−mode is obtained which shows that the behavior of this mode changes in the presence of superthermal ions. The growth rate of η{sub e}−mode driven linear instability is found and is observed to modify due to nonthermal ions. However, it is found that this leaves the electron energy transport coefficient unchanged. In the nonlinear regime, a dipolar vortex solution is derived which indicates that the dynamic behavior of the vortices changes with the inclusion of kappa distributed ions. The importance of present study with respect to space and laboratory plasmas is also pointed out.

  2. Analytical modelling of resistive wall mode stabilization by rotation in toroidal tokamak plasmas

    International Nuclear Information System (INIS)

    Ham, C J; Gimblett, C G; Hastie, R J

    2011-01-01

    Stabilization of the resitive wall mode (RWM) may allow fusion power to be doubled for a given magnetic field in advanced tokamak operation. Experimental evidence from DIII-D and other machines suggests that plasma rotation can stabilize the RWM. Several authors (Finn 1995 Phys. Plasmas 2 3782, Bondeson and Xie 1997 Phys. Plasmas 4 2081) have constructed analytical cylindrical models for the RWM, but these do not deal with toroidal effects. The framework of Connor et al (1988 Phys. Fluids 31 577) is used to develop ideal plasma analytic models with toroidicity included. Stepped pressure profiles and careful ordering of terms are used to simplify the analysis. First, a current driven kink mode model is developed and a dispersion relation for arbitrary current profile is calculated. Second, the external pressure driven kink mode is similarly investigated as the most important RWM arises from this mode. Using this latter model it is found that the RWM is stabilized by Alfven continuum damping with rotation levels similar to those seen in experiments. An expression for the stability of the external kink mode for more general current profiles and a resistive wall is derived in the appendix.

  3. Effect of weak nonlinearities on the plane waves in a plasma stream

    International Nuclear Information System (INIS)

    Seshadri, S.R.

    1976-01-01

    The effect of weak nonlinearities on the monochromatic plane waves in a cold infinite plasma stream is investigated for the case in which the waves are progressing parallel to the drift velocity. The fast and the slow space-charge waves undergo amplitude-dependent frequency and wave number shifts. There is a long time slow modulation of the amplitude of the electromagnetic mode which becomes unstable to this nonlinear wave modulation. The importance of using the relativistically correct equation of motion for predicting correctly the modulational stability of the electromagnetic mode is pointed out. (author)

  4. Eigenvalue problem and nonlinear evolution of kink modes in a toroidal plasma

    International Nuclear Information System (INIS)

    Ogino, T.; Takeda, S.; Sanuki, H.; Kamimura, T.

    1979-04-01

    The internal kink modes of a cylindrical plasma are investigated by a linear eigen value problem and their nonlinear evolution is studied by 3-dimensional MHD simulation based on the rectangular column model under the fixed boundary condition. The growth rates in two cases, namely uniform and diffused current profiles are analyzed in detail, which agree with the analytical estimation by Shafranov. The time evolution of the m = 1 mode showed that q > 1 is satisfied at the relaxation time (q safety factor), a stable configuration like a horse shoe (a new equilibrium) was formed. Also, the time evolution of the pressure p for the m = 2 mode showed that a stable configuration like a pair of anchors was formed. (author)

  5. Noise Reduction for Nonlinear Nonstationary Time Series Data using Averaging Intrinsic Mode Function

    Directory of Open Access Journals (Sweden)

    Christofer Toumazou

    2013-07-01

    Full Text Available A novel noise filtering algorithm based on averaging Intrinsic Mode Function (aIMF, which is a derivation of Empirical Mode Decomposition (EMD, is proposed to remove white-Gaussian noise of foreign currency exchange rates that are nonlinear nonstationary times series signals. Noise patterns with different amplitudes and frequencies were randomly mixed into the five exchange rates. A number of filters, namely; Extended Kalman Filter (EKF, Wavelet Transform (WT, Particle Filter (PF and the averaging Intrinsic Mode Function (aIMF algorithm were used to compare filtering and smoothing performance. The aIMF algorithm demonstrated high noise reduction among the performance of these filters.

  6. Nonlinear disturbance observer based sliding mode control of a cable-driven rehabilitation robot.

    Science.gov (United States)

    Niu, Jie; Yang, Qianqian; Chen, Guangtao; Song, Rong

    2017-07-01

    This paper introduces a cable-driven robot for upper-limb rehabilitation. Kinematic and dynamic of this rehabilitation robot is analyzed. A sliding mode controller combined with a nonlinear disturbance observer is proposed to control this robot in the presence of disturbances. Simulation is carried out to prove the effectiveness of the proposed control scheme, and the results of the proposed controller is compared with a PID controller and a traditional sliding mode controller. Results show that the proposed controller can effectively improve the tracking performance as compared with the other two controllers and cause lower chattering as compared with a traditional sliding mode controller.

  7. Two-Fluid and Resistive Nonlinear Simulations of Tokamak Equilibrium, Stability, and Reconnection

    International Nuclear Information System (INIS)

    Jardin, S.; Sovinec, C.; Breslau, J.; Ferraro, N.; Hudson, S.; King, J.; Kruger, S.; Ramos, J.; Schnack, D.

    2008-01-01

    The NIMROD and M3D/M3D-C1 codes now each have both a resistive MHD and a two-fluid (2F) capability including gyroviscosity and Hall terms. We describe: (1) a nonlinear 3D verification test in the resistive MHD regime in which the two codes are in detailed agreement, (2) new studies that illuminate the effect of two-fluid physics on spontaneous rotation in tokamaks, (3) studies of nonlinear reconnection in regimes of relevance to fusion plasmas with peak nonlinear reconnection rates that are essentially independent of the resistivity, and (4) linear two-fluid tearing mode calculations including electron mass that agree with analytic studies over a wide range of parameter regimes

  8. Linear and nonlinear stability analysis, associated to experimental fast reactors. Part 2

    International Nuclear Information System (INIS)

    Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

    1980-07-01

    The nonlinear effects in fast reactors kinetics and their stability are studied. The Lyapunov criteria and the Lurie-Letov functions for nonlinear systems were established and simulated. Small oscillations were studied by a Fourier analysis to clarify particular aspects of feedback and load functions in fast reactor at zero power, or/and in normal power level. The results were in agreement with the experimental data existing in the literature. (E.G.) [pt

  9. Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

    Science.gov (United States)

    Do, K. D.

    2018-05-01

    Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

  10. Electron thermal effect on linear and nonlinear coupled Shukla-Varma and convective cell modes in dust-contaminated magnetoplasma

    Science.gov (United States)

    Masood, W.; Mirza, Arshad M.

    2010-11-01

    Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.

  11. Electron thermal effect on linear and nonlinear coupled Shukla-Varma and convective cell modes in dust-contaminated magnetoplasma

    International Nuclear Information System (INIS)

    Masood, W.; Mirza, Arshad M.

    2010-01-01

    Linear and nonlinear properties of coupled Shukla-Varma (SV) and convective cell modes in the presence of electron thermal effects are studied in a nonuniform magnetoplasma composed of electrons, ions, and extremely massive and negatively charged immobile dust grains. In the linear case, the modified dispersion relation is given and, in the nonlinear case, stationary solutions of the nonlinear equations that govern the dynamics of coupled SV and convective cell modes are obtained. It is found that electrostatic dipolar and vortex street type solutions can appear in such a plasma. The relevance of the present investigation with regard to the Earth's mesosphere as well as in ionospheric plasmas is also pointed out.

  12. Nonlinear stability of m=1 flute mode in a nonparaxial open plasma device

    International Nuclear Information System (INIS)

    Lanskij, I.M.; Stupakov, G.V.

    1991-01-01

    Plasma flute stability as to high shifts under strong effects of ion Larmor finite radius conditions is studied. System consisting of long axisymmetric paraxial mirror device with stabilizing cells at its edges is considered. Variation of plasma energy as to its shift as a whole is calculated. It is shown, that depending on stabilizer type the force bringing plasma back in equilibrium state with shift growth may both increase and decrease

  13. Effects of a sheared toroidal rotation on the stability boundary of the MHD modes in the tokamak edge pedestal

    International Nuclear Information System (INIS)

    Aiba, N.; Tokuda, S.; Oyama, N.; Ozeki, T.; Furukawa, M.

    2009-01-01

    Effects of a sheared toroidal rotation are investigated numerically on the stability of the MHD modes in the tokamak edge pedestal, which relate to the type-I edge-localized mode. A linear MHD stability code MINERVA is newly developed for solving the Frieman-Rotenberg equation that is the linear ideal MHD equation with flow. Numerical stability analyses with this code reveal that the sheared toroidal rotation destabilizes edge localized MHD modes for rotation frequencies which are experimentally achievable, though the ballooning mode stability changes little by rotation. This rotation effect on the edge MHD stability becomes stronger as the toroidal mode number of the unstable MHD mode increases when the stability analysis was performed for MHD modes with toroidal mode numbers smaller than 40. The toroidal mode number of the unstable MHD mode depends on the stabilization of the current-driven mode and the ballooning mode by increasing the safety factor. This dependence of the toroidal mode number of the unstable mode on the safety factor is considered to be the reason that the destabilization by toroidal rotation is stronger for smaller edge safety factors.

  14. Numerical Δ' studies of the nonlinear finite-β tearing mode

    International Nuclear Information System (INIS)

    Pletzer, A.

    1996-01-01

    Tearing modes have recently attracted attention following theoretical successes in predicting the presence of magnetic island with moderate poloidal m = 3,4 and toroidal n = 2,3 mode numbers during TFTR (Tokamak Fusion Test Reactor) supershots. Classical linear resistive mode theory predicts instability when the asymptotic matching index Δ' defined as the jump of logarithmic derivative of the radial magnetic perturbation across the rational surface is positive. Recently, it was suggested that tearing modes could also persist when Δ'<0 provided bootstrap current effects are taken into account. In all the above theories, the crucial parameter which determines the stability from both the geometry and equilibrium profiles is Δ'. It is shown in the present study that the Δ' of the (m=2, n=1) mode computed with the PEST-3 code is virtually always positive. Saturation can nevertheless be achieved provided the symmetry breaking term of a current gradient is included in the resistive layer. (author) 3 figs., 11 refs

  15. Free-vibration acoustic resonance of a nonlinear elastic bar

    Science.gov (United States)

    Tarumi, Ryuichi; Oshita, Yoshihito

    2011-02-01

    Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.

  16. Adaptive Integral Sliding Mode Stabilization of Nonholonomic Drift-Free Systems

    Directory of Open Access Journals (Sweden)

    Waseem Abbasi

    2016-01-01

    Full Text Available This article presents adaptive integral sliding mode control algorithm for the stabilization of nonholonomic drift-free systems. First the system is transformed, by using input transform, into a special structure containing a nominal part and some unknown terms which are computed adaptively. The transformed system is then stabilized using adaptive integral sliding mode control. The stabilizing controller for the transformed system is constructed that consists of the nominal control plus a compensator control. The compensator control and the adaptive laws are derived on the basis of Lyapunov stability theory. The proposed control algorithm is applied to three different nonholonomic drift-free systems: the unicycle model, the front wheel car model, and the mobile robot with trailer model. The controllability Lie algebra of the unicycle model contains Lie brackets of depth one, the model of a front wheel car contains Lie brackets of depths one and two, and the model of a mobile robot with trailer contains Lie brackets of depths one, two, and three. The effectiveness of the proposed control algorithm is verified through numerical simulations.

  17. Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into into the numerical behavior of this rather complicated system of nonlinear PDEs....

  18. Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays

    Science.gov (United States)

    Nguimdo, Romain Modeste

    2018-03-01

    Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.

  19. Robust Stabilization of Nonlinear Systems with Uncertain Varying Control Coefficient

    Directory of Open Access Journals (Sweden)

    Zaiyue Yang

    2014-01-01

    Full Text Available This paper investigates the stabilization problem for a class of nonlinear systems, whose control coefficient is uncertain and varies continuously in value and sign. The study emphasizes the development of a robust control that consists of a modified Nussbaum function to tackle the uncertain varying control coefficient. By such a method, the finite-time escape phenomenon has been prevented when the control coefficient is crossing zero and varying its sign. The proposed control guarantees the asymptotic stabilization of the system and boundedness of all closed-loop signals. The control performance is illustrated by a numerical simulation.

  20. Asymptotic stability of linearly evolving non-stationary modes in a ...

    Indian Academy of Sciences (India)

    attention and it is believed to shed important light on the unresolved .... number assumption and is termed as the triple-deck theory. Having ... to analyse asymptotically the linear and weakly non-linear stability features of the station- ..... A numerical integration of equations (7–9) was implemented first to obtain the basic flow.

  1. Ballooning mode second stability region for sequences of tokamak equilibria

    International Nuclear Information System (INIS)

    Sugiyama, L.; Mark, J.W.K.

    A numerical study of several sequences of tokamak equilibria derived from two flux conserving sequences confirms the tendency of high n ideal MHD ballooning modes to stabilize for values of the plasma beta greater than a second critical beta, for sufficiently favorable equilibria. The major stabilizing effect of increasing the inverse rotational transform profile q(Psi) for equilibria with the same flux surface geometry is shown. The unstable region shifts toward larger shear d ln q/d ln γ and the width of the region measured in terms of the poloidal beta or a pressure gradient parameter, for fixed shear, decreases. The smaller aspect ratio sequences are more sensitive to changes in q and have less stringent limits on the attainable value of the plasma beta in the high beta stable region. Finally, the disconnected mode approximation is shown to provide a reasonable description of the second high beta stability boundary

  2. Quasi-stability of a vector trajectorial problem with non-linear partial criteria

    Directory of Open Access Journals (Sweden)

    Vladimir A. Emelichev

    2003-10-01

    Full Text Available Multi-objective (vector combinatorial problem of finding the Pareto set with four kinds of non-linear partial criteria is considered. Necessary and sufficient conditions of that kind of stability of the problem (quasi-stability are obtained. The problem is a discrete analogue of the lower semicontinuity by Hausdorff of the optimal mapping. Mathematics Subject Classification 2000: 90C10, 90C05, 90C29, 90C31.

  3. Finite Larmor radius stabilization of ballooning modes in tokamaks

    International Nuclear Information System (INIS)

    Tsang, K.T.

    1980-07-01

    A ballooning mode equation that includes full finite Larmor radius effects has been derived from the Vlasov equation for a circular tokamak equilibrium. Numerical solution of this equation shows that finite Larmor radius effects are stabilizing

  4. On a program manifold’s stability of one contour automatic control systems

    Directory of Open Access Journals (Sweden)

    Zumatov S. S.

    2017-12-01

    Full Text Available Methodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold’s absolute stability of one contour automatic control systems are obtained. The Hurwitz’s angle of absolute stability was determined. The sufficient conditions of program manifold’s absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov’s second method.

  5. Modulational instability and discrete breathers in a nonlinear helicoidal lattice model

    Science.gov (United States)

    Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing

    2018-06-01

    We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.

  6. Effect of plasma rotation on sawtooth stabilization by beam ion

    International Nuclear Information System (INIS)

    Gorelenkov, N. N.; Nave, M. F. F.; Budny, R.; Cheng, C. Z.; Fu, G. Y.; Hastie, J.; Manickam, J.; Park, W.

    2000-01-01

    The sawtooth period in JET ELM-free H-Mode plasmas is increasing with Neutral Beam Injection (NBI) power. For injected power PNBI 12MW no large sawtooth crash is observed during the ELM-free period. However, as the edge stability is improved and external kink modes and ELMs are delayed, a possible sawtooth crash at a high plasma beta becomes a concern. In JET DT experiments, delaying sawteeth was found to be crucial in the quest for high fusion power. Fast particles are known to provide stabilizing effect on sawteeth, however, sawtooth stabilization by NBI ions is not clearly understood, since NBI ions are usually not ''fast'' enough to stabilize the m/n = 1/1 internal kink mode which is believed to cause the crash. In order to understand the observed sawteeth stabilization in tokamak experiments with NBI heating, the internal kink m/n = 1/1 mode stability of JET plasmas was modeled using the NOVA-K code, which is also benchmarked with the nonperturbative version of NOVA and the M3D code. Comparison of m/n = 1/1 mode stabilization by NBI ions in JET and TFTR and application of the nonlinear stabilization criteria is given

  7. Numerical Study of Equilibrium, Stability, and Advanced Resistive Wall Mode Feedback Algorithms on KSTAR

    Science.gov (United States)

    Katsuro-Hopkins, Oksana; Sabbagh, S. A.; Bialek, J. M.; Park, H. K.; Kim, J. Y.; You, K.-I.; Glasser, A. H.; Lao, L. L.

    2007-11-01

    Stability to ideal MHD kink/ballooning modes and the resistive wall mode (RWM) is investigated for the KSTAR tokamak. Free-boundary equilibria that comply with magnetic field coil current constraints are computed for monotonic and reversed shear safety factor profiles and H-mode tokamak pressure profiles. Advanced tokamak operation at moderate to low plasma internal inductance shows that a factor of two improvement in the plasma beta limit over the no-wall beta limit is possible for toroidal mode number of unity. The KSTAR conducting structure, passive stabilizers, and in-vessel control coils are modeled by the VALEN-3D code and the active RWM stabilization performance of the device is evaluated using both standard and advanced feedback algorithms. Steady-state power and voltage requirements for the system are estimated based on the expected noise on the RWM sensor signals. Using NSTX experimental RWM sensors noise data as input, a reduced VALEN state-space LQG controller is designed to realistically assess KSTAR stabilization system performance.

  8. Experimental identification of nonlinear coupling between (intermediate, small)-scale microturbulence and an MHD mode in the core of a superconducting tokamak

    Science.gov (United States)

    Sun, P. J.; Li, Y. D.; Ren, Y.; Zhang, X. D.; Wu, G. J.; Xu, L. Q.; Chen, R.; Li, Q.; Zhao, H. L.; Zhang, J. Z.; Shi, T. H.; Wang, Y. M.; Lyu, B.; Hu, L. Q.; Li, J.; The EAST Team

    2018-01-01

    In this paper, we present clear experimental evidence of core region nonlinear coupling between (intermediate, small)-scale microturbulence and an magnetohydrodynamics (MHD) mode during the current ramp-down phase in a set of L-mode plasma discharges in the experimental advanced superconducting tokamak (EAST, Wan et al (2006 Plasma Sci. Technol. 8 253)). Density fluctuations of broadband microturbulence (k\\perpρi˜2{-}5.2 ) and the MHD mode (toroidal mode number m = -1 , poloidal mode number n = 1 ) are measured simultaneously, using a four-channel tangential CO2 laser collective scattering diagnostic in core plasmas. The nonlinear coupling between the broadband microturbulence and the MHD mode is directly demonstrated by showing a statistically significant bicoherence and modulation of turbulent density fluctuation amplitude by the MHD mode.

  9. Stability and square integrability of solutions of nonlinear fourth order differential equations

    Directory of Open Access Journals (Sweden)

    Moussadek Remili

    2016-05-01

    Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.

  10. Non-linear vibrational modes in biomolecules: A periodic orbits description

    International Nuclear Information System (INIS)

    Kampanarakis, Alexandros; Farantos, Stavros C.; Daskalakis, Vangelis; Varotsis, Constantinos

    2012-01-01

    Graphical abstract: Vibrational frequency shifts in Fe IV = O species of the active site of cytochrome c oxidase are attributed to changes in the surrounding Coulomb field. Periodic orbits analysis assists to find the most anharmonic modes in model biomolecules. Highlights: ► Periodic orbits are extended to multidimensional potentials of biomolecules. ► Highly anharmonic vibrational modes and center-saddle bifurcations are detected. ► Vibrational frequencies shifts in Oxoferryl species of CcO are observed. - Abstract: The vibrational harmonic normal modes of a molecule, which are valid at energies close to an equilibrium point (a minimum, maximum or saddle of the potential energy surface), are extended by periodic orbits to high energies where anharmonicity and coupling of the degrees of freedom are significant. In this way the assignment of the spectra, and thus the extraction of dynamics in highly excited molecules, can be obtained. New vibrational modes emanating from bifurcations of periodic orbits and long living localized trajectories signal the birth and localization of new quantum states. In this article we review and further study non-linear vibrational modes for model biomolecules such as alanine dipeptide and the active site in the oxoferryl oxidation state of the enzyme cytochrome c oxidase. We locate periodic orbits which exhibit high anhamonicity and lead to center-saddle bifurcations. These modes are associated to an isomerization process in alanine dipeptide and to frequency shifts in the oxoferryl observed by modifying the Coulomb field around the Imidazole–Fe IV = O species.

  11. Nonlinear tearing mode and vortex chains

    International Nuclear Information System (INIS)

    Jovanovic, D.; Vranjes, J.

    1996-01-01

    We study the nonlinear stage of a tearing mode, whose island width exceeds the tearing layer thickness, and the wavelength is of the order of collisionless skin depth. A coherent solution is found in the form of a moving vortex chain. It is the result of a self-organization process, which adjusts the profile of the sheared poloidal magnetic field and excites a localized perpendicular sheared plasma flow, consisting of three counterstreaming jets. A numerical solution shows a twin chain of plasma vortices, coupled with a single chain of magnetic islands, whose width is of the order of collisionless skin depth. Adiabatic evolution of the vortex chain in the presence of small viscosity reveals its finite lifetime. The chain destruction may occur either directly, or through a sequence of bifurcations (corresponding to abrupt changes of the vortex chain parameters) to magnetic field stochastization within a layer of the collisionless skin depth scale, which occurs before the magnetic island overlapping takes place. This provides a new mechanism for the anomalous transport. (orig.)

  12. Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-Propelled Space Vehicles

    Science.gov (United States)

    Ottander, John A.; Hall, Robert A.; Powers, J. F.

    2018-01-01

    A method is presented that allows for the prediction of the magnitude of limit cycles due to adverse control-slosh interaction in liquid propelled space vehicles using non-linear slosh damping. Such a method is an alternative to the industry practice of assuming linear damping and relying on: mechanical slosh baffles to achieve desired stability margins; accepting minimal slosh stability margins; or time domain non-linear analysis to accept time periods of poor stability. Sinusoidal input describing functional analysis is used to develop a relationship between the non-linear slosh damping and an equivalent linear damping at a given slosh amplitude. In addition, a more accurate analytical prediction of the danger zone for slosh mass locations in a vehicle under proportional and derivative attitude control is presented. This method is used in the control-slosh stability analysis of the NASA Space Launch System.

  13. Transport of super-thermal particles and their effect on the stability of global modes in fusion plasmas

    International Nuclear Information System (INIS)

    Schneller, Mirjam Simone

    2013-01-01

    In thermonuclear plasmas, a population of super-thermal particles generated by external heating methods or fusion reactions can lead to the excitation of global instabilities. The transport processes due to nonlinear wave-particle interactions and the consequential particle losses reduce the plasma heating and the efficiency of the fusion reaction rate. Furthermore, these energetic or fast particles may cause severe damages to the wall of the device. This thesis addresses the resonance mechanisms between these energetic particles and global MHD and kinetic MHD waves, employing the hybrid code HAGIS. A systematic investigation of energetic particles resonant with multiple modes (double-resonance) is presented for the first time. The double-resonant mode coupling is modeled for waves with different frequencies in various overlapping scenarios. It is found that, depending on the radial mode distance, double-resonance is able to significantly enhance, both the growth rates and the saturation amplitudes. Small radial mode distances, however can lead to strong nonlinear mode stabilization of a linear dominant mode. For the first time, simulations of experimental conditions in the ASDEX Upgrade fusion device are performed for different plasma equilibria (particularly for different q profiles). An understanding of fast particle behavior for non-monotonic q profiles is important for the development of advanced fusion scenarios. The numerical tool is the extended version of the HAGIS code, which computes the particle motion in the vacuum region between vessel wall in addition to the internal plasma volume. For this thesis, a consistent fast particle distribution function was implemented, to represent the fast particle population generated by the particular heating method (ICRH). Furthermore, HAGIS was extended to use more realistic eigenfunctions, calculated by the gyrokinetic eigenvalue solver LIGKA. One important aim of these simulations is to allow fast ion loss

  14. Transport of super-thermal particles and their effect on the stability of global modes in fusion plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Schneller, Mirjam Simone

    2013-08-02

    In thermonuclear plasmas, a population of super-thermal particles generated by external heating methods or fusion reactions can lead to the excitation of global instabilities. The transport processes due to nonlinear wave-particle interactions and the consequential particle losses reduce the plasma heating and the efficiency of the fusion reaction rate. Furthermore, these energetic or fast particles may cause severe damages to the wall of the device. This thesis addresses the resonance mechanisms between these energetic particles and global MHD and kinetic MHD waves, employing the hybrid code HAGIS. A systematic investigation of energetic particles resonant with multiple modes (double-resonance) is presented for the first time. The double-resonant mode coupling is modeled for waves with different frequencies in various overlapping scenarios. It is found that, depending on the radial mode distance, double-resonance is able to significantly enhance, both the growth rates and the saturation amplitudes. Small radial mode distances, however can lead to strong nonlinear mode stabilization of a linear dominant mode. For the first time, simulations of experimental conditions in the ASDEX Upgrade fusion device are performed for different plasma equilibria (particularly for different q profiles). An understanding of fast particle behavior for non-monotonic q profiles is important for the development of advanced fusion scenarios. The numerical tool is the extended version of the HAGIS code, which computes the particle motion in the vacuum region between vessel wall in addition to the internal plasma volume. For this thesis, a consistent fast particle distribution function was implemented, to represent the fast particle population generated by the particular heating method (ICRH). Furthermore, HAGIS was extended to use more realistic eigenfunctions, calculated by the gyrokinetic eigenvalue solver LIGKA. One important aim of these simulations is to allow fast ion loss

  15. Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

    Science.gov (United States)

    Moawad, S. M.; Moawad

    2013-10-01

    The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

  16. Dynamic stability of a vertically excited non-linear continuous system

    Czech Academy of Sciences Publication Activity Database

    Náprstek, Jiří; Fischer, Cyril

    2015-01-01

    Roč. 155, July (2015), s. 106-114 ISSN 0045-7949 R&D Projects: GA ČR(CZ) GA15-01035S Institutional support: RVO:68378297 Keywords : non-linear systems * auto-parametric systems * semi-trivial solution * dynamic stability * system recovery * post- critical response Subject RIV: JM - Building Engineering Impact factor: 2.425, year: 2015 http://www.sciencedirect.com/science/article/pii/S0045794915000024

  17. Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

    Science.gov (United States)

    Gil', M. I.

    2005-08-01

    We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

  18. Stability aspects of plasmas penetrated by neutral gas with respect to velocity driven modes

    International Nuclear Information System (INIS)

    Ohlsson, D.

    1978-08-01

    A study of the stability properties of dense partially ionized plasmas immersed in strong magnetic fields with respect to velocity driven modes are presented. First we consider modes driven by mass motion perpendicular to the lines of force and the unperturbed density and temperature gradients. The presence of a third fluid, neutral gas, gives under certain conditions rise to unstable modes. This type of instability arises independently or whether the applied electric field transverse to the lines of force, driving the mass motion, being parallel or antiparallel to the unperturbed density and temperature gradient. The presence of neutral gas also corresponds to stabilizing effects which, in certain parameter regions, result in a quenching of this instability. It is shown that modes driven by velocity shear perpendicular to the lines of force are effectively stabilized by viscous and resistive effects. These effects are in certain parameter ranges strongly enhanced on account of plasma-neutral gas interaction effects. In collisionless plasmas, modes driven by velocity shear parallel to the lines of force are stabilized by compressibility effects parallel to the magnetic field and by finite Larmor radius effects. (author)

  19. Nonlinear polarization effects in a birefringent single mode optical fiber

    International Nuclear Information System (INIS)

    Ishiekwene, G.C.; Mensah, S.Y.; Brown, C.S.

    2001-04-01

    The nonlinear polarization effects in a birefringent single mode optical fiber is studied using Jacobi elliptic functions. We find that the polarization state of the propagating beam depends on the initial polarization as well as the intensity of the input light in a complicated way. The Stokes polarization parameters are either periodic or aperiodic depending on the value of the Jacobian modulus. Our calculations suggest that the effective beat length of the fiber can become infinite at a higher critical value of the input power when polarization dependent losses are considered. (author)

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

    Directory of Open Access Journals (Sweden)

    Mingzhu Song

    2016-01-01

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

  1. Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities

    International Nuclear Information System (INIS)

    Chen, S.-F.

    2009-01-01

    The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.

  2. Finite beta and compressibility effects on stability of resistive modes in toroidal geometry

    International Nuclear Information System (INIS)

    Leboeuf, J-N.G.; Kurita, Gen-ichi.

    1998-03-01

    Linear resistive stability results obtained from the toroidal magnetohydrodynamic codes FAR developed at the Oak Ridge National Laboratory in United States of America and AEOLUS developed at the Japan Atomic Energy Research Institute are compared for carefully constructed benchmark profiles and parameters. These are unstable to a tearing mode with toroidal mode number n=1. The eigenvalues and eigenfunctions calculated with both codes are in close agreement and show that the effect of compressibility is weak for these modes. The effect of finite plasma beta is considered, and the eigenvalues calculated by the FAR and AEOLUS codes also show good agreement. It is shown that the finite beta has a stabilizing effect on the toroidal tearing mode, but that the compressibility also has little effect on finite beta tearing modes. (author)

  3. A model for roll stall and the inherent stability modes of low aspect ratio wings at low Reynolds numbers

    Science.gov (United States)

    Shields, Matt

    The development of Micro Aerial Vehicles has been hindered by the poor understanding of the aerodynamic loading and stability and control properties of the low Reynolds number regime in which the inherent low aspect ratio (LAR) wings operate. This thesis experimentally evaluates the static and damping aerodynamic stability derivatives to provide a complete aerodynamic model for canonical flat plate wings of aspect ratios near unity at Reynolds numbers under 1 x 105. This permits the complete functionality of the aerodynamic forces and moments to be expressed and the equations of motion to solved, thereby identifying the inherent stability properties of the wing. This provides a basis for characterizing the stability of full vehicles. The influence of the tip vortices during sideslip perturbations is found to induce a loading condition referred to as roll stall, a significant roll moment created by the spanwise induced velocity asymmetry related to the displacement of the vortex cores relative to the wing. Roll stall is manifested by a linearly increasing roll moment with low to moderate angles of attack and a subsequent stall event similar to a lift polar; this behavior is not experienced by conventional (high aspect ratio) wings. The resulting large magnitude of the roll stability derivative, Cl,beta and lack of roll damping, Cl ,rho, create significant modal responses of the lateral state variables; a linear model used to evaluate these modes is shown to accurately reflect the solution obtained by numerically integrating the nonlinear equations. An unstable Dutch roll mode dominates the behavior of the wing for small perturbations from equilibrium, and in the presence of angle of attack oscillations a previously unconsidered coupled mode, referred to as roll resonance, is seen develop and drive the bank angle? away from equilibrium. Roll resonance requires a linear time variant (LTV) model to capture the behavior of the bank angle, which is attributed to the

  4. Tokamak m = 1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations

    International Nuclear Information System (INIS)

    Charlton, L.A.; Carreras, B.A.; Holmes, J.A.; Lynch, V.E.

    1988-01-01

    The linear stability and nonlinear evolution of the resistive m = 1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta

  5. Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance

    International Nuclear Information System (INIS)

    Guo, Wencheng; Yang, Jiandong; Wang, Mingjiang; Lai, Xu

    2015-01-01

    Highlights: • Novel nonlinear mathematical model of hydro-turbine governing system is proposed. • Hopf bifurcation analysis on the governing system is conducted. • Stability of the system under load disturbance is studied. • Influence of four factors on stability is analyzed. • Optimization methods of improving system stability are put forward. - Abstract: In order to overcome the problem of nonlinear dynamics of hydro-turbine governing system with sloping ceiling tailrace tunnel, which is caused by the interface movement of the free surface-pressurized flow in the tailrace tunnel, and the difficulty of analyzing the stability of system, this paper uses the Hopf bifurcation theory to study the stability of hydro-turbine governing system of hydropower station with sloping ceiling tailrace tunnel. Firstly, a novel and rational nonlinear mathematical model of the hydro-turbine governing system is proposed. This model contains the dynamic equation of pipeline system which can accurately describe the motion characteristics of the interface of free surface-pressurized flow in sloping ceiling tailrace tunnel. According to the nonlinear mathematical model, the existence and direction of Hopf bifurcation of the nonlinear dynamic system are analyzed. Furthermore, the algebraic criterion of the occurrence of Hopf bifurcation is derived. Then the stability domain and bifurcation diagram of hydro-turbine governing system are drawn by the algebraic criterion, and the characteristics of stability under different state parameters are investigated. Finally, the influence of step load value, ceiling slope angle and section form of tailrace tunnel and water depth at the interface in tailrace tunnel on stability are analyzed based on stable domain. The results indicate that: The Hopf bifurcation of hydro-turbine governing system with sloping ceiling tailrace tunnel is supercritical. The phase space trajectories of characteristic variables stabilize at the equilibrium points

  6. Stability of short-axial-wavelength internal kink modes of an anisotropic plasma

    Science.gov (United States)

    Faghihi, M.; Scheffel, J.

    1987-12-01

    The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m ≥ 1) modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also, constant-current-density equilibria can be stabilized for P > P and large β

  7. Loss of Energy Concentration in Nonlinear Evolution Beam Equations

    Science.gov (United States)

    Garrione, Maurizio; Gazzola, Filippo

    2017-12-01

    Motivated by the oscillations that were seen at the Tacoma Narrows Bridge, we introduce the notion of solutions with a prevailing mode for the nonlinear evolution beam equation u_{tt} + u_{xxxx} + f(u)= g(x, t) in bounded space-time intervals. We give a new definition of instability for these particular solutions, based on the loss of energy concentration on their prevailing mode. We distinguish between two different forms of energy transfer, one physiological (unavoidable and depending on the nonlinearity) and one due to the insurgence of instability. We then prove a theoretical result allowing to reduce the study of this kind of infinite-dimensional stability to that of a finite-dimensional approximation. With this background, we study the occurrence of instability for three different kinds of nonlinearities f and for some forcing terms g, highlighting some of their structural properties and performing some numerical simulations.

  8. Finite-time output feedback stabilization of high-order uncertain nonlinear systems

    Science.gov (United States)

    Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

    2018-06-01

    This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

  9. Design Sliding Mode Controller of with Parallel Fuzzy Inference System Compensator to Control of Robot Manipulator

    Directory of Open Access Journals (Sweden)

    Farzin Piltan

    2013-06-01

    Full Text Available Sliding mode controller (SMC is a significant nonlinear controller under condition of partly uncertain dynamic parameters of system. This controller is used to control of highly nonlinear systems especially for robot manipulators, because this controller is a robust and stable. Conversely, pure sliding mode controller is used in many applications; it has two important drawbacks namely; chattering phenomenon, and nonlinear equivalent dynamic formulation in uncertain dynamic parameter. The nonlinear equivalent dynamic formulation problem and chattering phenomenon in uncertain system can be solved by using artificial intelligence theorem. However fuzzy logic controller is used to control complicated nonlinear dynamic systems, but it cannot guarantee stability and robustness.  In this research parallel fuzzy logic theory is used to compensate the system dynamic uncertainty.

  10. Nonlinear robust hierarchical control for nonlinear uncertain systems

    Directory of Open Access Journals (Sweden)

    Leonessa Alexander

    1999-01-01

    Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

  11. Magnetohydrodynamic stability of tokamak plasmas with poloidal mode coupling

    International Nuclear Information System (INIS)

    Shigueoka, H.; Sakanaka, P.H.

    1987-01-01

    The stability behavior with respect to internal modes is examined for a class of tokamak equilibria with non-circular cross sections. The surfaces of the constant poloidal magnetic flux ψ (R,Z) are obtained numerically by solving the Grad-Shafranov's equation with a specified shape for the outmost plasma surface. The equation of motion for ideal MHD stability is written in a ortogonal coordinate system (ψ, χ, φ). Th e stability analysis is performance numerically in a truncated set of coupled m (poloidal wave number) equations. The calculations involve no approximations, and so all parameters of the equilibrium solution can be arbitrarily varied. (author) [pt

  12. Stabilizing periodic orbits of chaotic systems using fuzzy adaptive sliding mode control

    Energy Technology Data Exchange (ETDEWEB)

    Layeghi, Hamed [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: layeghi@mech.sharif.edu; Arjmand, Mehdi Tabe [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: arjmand@mech.sharif.edu; Salarieh, Hassan [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Department of Mechanical Engineering, Sharif University of Technology, Center of Excellence in Design, Robotics and Automation, Azadi Avenue, Postal Code 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu

    2008-08-15

    In this paper by using a combination of fuzzy identification and the sliding mode control a fuzzy adaptive sliding mode scheme is designed to stabilize the unstable periodic orbits of chaotic systems. The chaotic system is assumed to have an affine form x{sup (n)} = f(X) + g(X)u where f and g are unknown functions. Using only the input-output data obtained from the underlying dynamical system, two fuzzy systems are constructed for identification of f and g. Two distinct methods are utilized for fuzzy modeling, the least squares and the gradient descent techniques. Based on the estimated fuzzy models, an adaptive controller, which works through the sliding mode control, is designed to make the system track the desired unstable periodic orbits. The stability analysis of the overall closed loop system is presented in the paper and the effectiveness of the proposed adaptive scheme is numerically investigated. As a case of study, modified Duffing system is selected for applying the proposed method to stabilize its 2{pi} and 4{pi} periodic orbits. Simulation results show the high performance of the method for stabilizing the unstable periodic orbits of unknown chaotic systems.

  13. Nuclear-coupled thermal-hydraulic nonlinear stability analysis using a novel BWR reduced order model. Pt. 1. The effects of using drift flux versus homogeneous equilibrium models

    International Nuclear Information System (INIS)

    Dokhane, A.; Henning, D.; Chawla, R.; Rizwan-Uddin

    2003-01-01

    BWR stability analysis at PSI, as at other research centres, is usually carried out employing complex system codes. However, these do not allow a detailed investigation of the complete manifold of all possible solutions of the associated nonlinear differential equation set. A novel analytical, reduced order model for BWR stability has been developed at PSI, in several successive steps. In the first step, the thermal-hydraulic model was used for studying the thermal-hydraulic instabilities. A study was then conducted of the one-channel nuclear-coupled thermal-hydraulic dynamics in a BWR by adding a simple point kinetic model for neutron kinetics and a model for the fuel heat conduction dynamics. In this paper, a two-channel nuclear-coupled thermal-hydraulic model is introduced to simulate the out-of phase oscillations in a BWR. This model comprises three parts: spatial mode neutron kinetics with the fundamental and fist azimuthal modes; fuel heat conduction dynamics; and thermal-hydraulics model. This present model is an extension of the Karve et al. model i.e., a drift flux model is used instead of the homogeneous equilibrium model for two-phase flow, and lambda modes are used instead of the omega modes for the neutron kinetics. This two-channel model is employed in stability and bifurcation analyses, carried out using the bifurcation code BIFDD. The stability boundary (SB) and the nature of the Poincare-Andronov-Hopf bifurcation (PAF-B) are determined and visualized in a suitable two-dimensional parameter/state space. A comparative study of the homogeneous equilibrium model (HEM) and the drift flux model (DFM) is carried out to investigate the effects of the DFM parameters the void distribution parameter C 0 and the drift velocity V gi -on the SB, the nature of PAH bifurcation, and on the type of oscillation mode (in-phase or out-of-phase). (author)

  14. Stabilization of ideal plasma resistive wall modes in cylindrical geometry: The effect of resistive layers

    International Nuclear Information System (INIS)

    Finn, J.M.

    1995-01-01

    A cylindrical model with finite beta having an external resonant ideal magnetohydrodynamic instability has been constructed. This resonant mode has a mode rational surface, where the safety factor q equals m/n, within the plasma. In this model, the perturbed radial magnetic field for the ideal mode is nonzero between the mode rational surface and the wall, even though it must vanish at the mode rational surface. This property of the mode is in common with the toroidal external kink. Results are presented showing that in the parameter range for which this ideal mode is stable with a conducting wall but unstable with the wall at infinity, a resistive wall mode persists. However, in the presence of plasma resistivity in a resistive layer about the mode rational surface, this resistive wall mode can be stabilized by a plasma rotation frequency of order a nominal resistive instability growth rate. Furthermore, the stabilization occurs in a large gap in wall position or beta. It is also shown that for the ideal resonant mode, as well as resistive plasma modes and nonresonant ideal plasma modes, there is a maximum value of plasma rotation above which there is no stability gap. Discussions are presented suggesting that these properties may hold for the toroidal external kink. copyright 1995 American Institute of Physics

  15. Effects of toroidal coupling on the stability of tearing modes

    International Nuclear Information System (INIS)

    Carreras, B.; Hicks, H.R.; Lee, D.K.

    1980-06-01

    The time evolution of tearing modes in toroidal geometry is studied in the low-β and large aspect ratio limit. An initial value three-dimensional computer code, which numerically advances the reduced set of resistive magnetohydrodynamic equations is employed. Toroidicity has, in general, a destabilizing effect on tearing modes in this limit. A generalization of the Δ' formalism can be used to study the linear regime. The results obtained in this way are in very good agreement with the results from the initial value code. The nonlinear phase of the evolution is also followed numerically. In the case of strong interaction of different helicities, a larger region of stochastic magnetic field lines results than in the cylindrical geometry case

  16. Stability of small axial wavelength internal kink modes of an anisotropic plasma

    International Nuclear Information System (INIS)

    Faghihi, M.; Scheffel, J.

    1987-03-01

    The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m>=1)modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also constant current density equilibria can be stabilized for P per >P par and large β per . (authors)

  17. Nonlinear stability of source defects in the complex Ginzburg–Landau equation

    International Nuclear Information System (INIS)

    Beck, Margaret; Nguyen, Toan T; Sandstede, Björn; Zumbrun, Kevin

    2014-01-01

    In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction–diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg–Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for Green's function, which allow one to close a nonlinear iteration scheme. (paper)

  18. Nonlinear theory of trapped electron temperature gradient driven turbulence in flat density H-mode plasmas

    International Nuclear Information System (INIS)

    Hahm, T.S.

    1990-12-01

    Ion temperature gradient turbulence based transport models have difficulties reconciling the recent DIII-D H-mode results where the density profile is flat, but χ e > χ i in the core region. In this work, a nonlinear theory is developed for recently discovered ion temperature gradient trapped electron modes propagating in the electron diamagnetic direction. This instability is predicted to be linearly unstable for L Ti /R approx-lt κ θ ρ s approx-lt (L Ti /R) 1/4 . They are also found to be strongly dispersive even at these long wavelengths, thereby suggesting the importance of the wave-particle-wave interactions in the nonlinear saturation phase. The fluctuation spectrum and anomalous fluxes are calculated. In accordance with the trends observed in DIII-D, the predicted electron thermal diffusivity can be larger than the ion thermal diffusivity. 17 refs., 3 figs

  19. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    KAUST Repository

    Gottlieb, Sigal

    2015-04-10

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

  20. Initial evolution of nonlinear magnetic islands in high temperature plasmas

    International Nuclear Information System (INIS)

    Kotschenreuther, M.

    1988-06-01

    The evolution of nonlinear magnetic islands is computed in the kinetic collisionality regime called the semicollisional regime, which is appropriate to present fusion confinement devices. Realistic effects are included, such as the presence of small external field errors, radial electric fields, and omega. When present simultaneously, these effects can greatly change the stability of small amplitude nonlinear islands. Islands with Δ' > O can sometimes be prevented from growing to macroscopic size; it is also possible to produce moderate mode-number nonlinear instabilities in the plasma edge. Furthermore, island growth can be prevented by application of external fields with suitably chosen amplitude and frequency

  1. Self-sustained turbulence and L-mode confinement in toroidal plasmas

    International Nuclear Information System (INIS)

    Itoh, K.; Itoh, S.; Fukuyama, A.; Yagi, M.; Azumi, M.

    1993-04-01

    Theory of the L-mode confinement in toroidal plasmas is developed. The quantitative effect of the anomalous transport, which is caused by microscopic fluctuations, on the pressure-gradient- driven modes is analyzed. The ExB nonlinearity is renormalized in a form of the transport coefficient such as the thermal diffusivity, the ion viscosity and the current diffusivity. The destabilization by the current-diffusivity and the stabilization by the thermal transport and ion viscosity are analyzed. By use of the mean-field approximations, the nonlinear dispersion relation is solved. Growth rate and stability condition are expressed in terms of the renormalized transport coefficients. The transport coefficients in the steady state are obtained by the marginal stability condition for the least stable mode. This method is applied to the microscopic ballooning mode for the toroidal plasma with the magnetic well (such as tokamak). The comparison with experimental observations are made. A good agreement is found in a various aspects of the L-mode plasmas; The typical wavenumber and level of the fluctuations for the self-sustained turbulence is also obtained. The analysis is also made for the plasma with magnetic hill and shear (such as torsatron/Heliotron devices). This method is applied to the interchange modes. Formula of the anomalous transport is obtained. Also investigated is the case of the magnetic well and low magnetic shear (conventional stellarator). The roles of the pressure gradient and the collisionless skin depth in determining the anomalous transport are found to be generic in toroidal plasmas. The difference in the magnetic configuration affects the transport coefficient. These formula explain major experimental observations. (J.P.N.)

  2. Non-linear numerical studies of the tearing mode

    International Nuclear Information System (INIS)

    Schnack, D.D. Jr.

    1978-01-01

    A non-linear, time dependent, hydromagnetic model is developed and applied to the tearing mode, one of a class of instabilities which can occur in a magnetically confined plasma when the constraint of infinite conductivity is relaxed. The model is based on the eight partial differential equations of resistive magnetohydrodynamics (MHD). The equations are expressed as a set of conservation laws which conserves magnetic flux, momentum, mass, and total energy. These equations are then written in general, orthogonal, curvilinear coordinates in two space dimensions, so that the model can readily be applied to a variety of geometries. No assumption about the ordering of terms is made. The resulting equations are then solved by the method of finite differences on an Eulerian mesh. The model is applied to several geometries

  3. Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.

    Science.gov (United States)

    Bai, L; Wang, F; Wadee, M A; Yang, J

    2017-11-01

    A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented and the results show good agreement with the variational model.

  4. Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

    Directory of Open Access Journals (Sweden)

    Chang Che

    2018-01-01

    Full Text Available This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

  5. Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D

    Energy Technology Data Exchange (ETDEWEB)

    Shen, Wei; Sheng, Zheng-Mao [Department of Physics, Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027 (China); Fu, G. Y.; Tobias, Benjamin [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Zeeland, Michael Van [General Atomics, San Diego, California 92186-5608 (United States); Wang, Feng [School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024 (China)

    2015-04-15

    In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.

  6. Stability of short-axial-wavelength internal kink modes of an anisotropic plasma

    International Nuclear Information System (INIS)

    Faghihi, M.; Schefffel, J.

    1987-01-01

    The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m ≥ 1) modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also, constant-current-density equilibria can be stabilized for Psub(perpendicular) > Psub(parallel) and large βsub(perpendicular). (author)

  7. Effects of ion temperature fluctuations on the stability of resistive ballooning modes

    International Nuclear Information System (INIS)

    Singh, R.; Nordman, H.; Jarmen, A.; Weiland, J.

    1996-01-01

    The influence of ion temperature fluctuations on the stability of resistive drift- and ballooning-modes is investigated using a two-fluid model. The Eigenmode equations are derived and solved analytically in a low beta model equilibrium. Parameters relevant to L-mode edge plasmas from the Texas Experimental Tokamak are used. The resistive modes are found to be destabilized by ion temperature fluctuations over a broad range of mode numbers. The scaling of the growth rate with magnetic shear and mode number is elucidated. 13 refs, 4 figs

  8. Stability analysis of explicit entropy viscosity methods for non-linear scalar conservation equations

    KAUST Repository

    Bonito, Andrea; Guermond, Jean-Luc; Popov, Bojan

    2013-01-01

    We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method

  9. Magnetohydrodynamic stability of tokamaks

    CERN Document Server

    Zohm, Hartmut

    2014-01-01

    This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong lin

  10. The nonlinear interaction of convection modes in a box of a saturated porous medium

    Science.gov (United States)

    Florio, Brendan J.; Bassom, Andrew P.; Fowkes, Neville; Judd, Kevin; Stemler, Thomas

    2015-05-01

    A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.

  11. Slope stability analysis using limit equilibrium method in nonlinear criterion.

    Science.gov (United States)

    Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu

    2014-01-01

    In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.

  12. Strong toroidal effects on tokamak tearing mode stability in the hybrid and conventional scenarios

    International Nuclear Information System (INIS)

    Ham, C J; Connor, J W; Cowley, S C; Gimblett, C G; Hastie, R J; Hender, T C; Martin, T J

    2012-01-01

    The hybrid scenario is thought to be an important mode of operation for the ITER tokamak. Analytic and numerical calculations demonstrate that toroidal effects at finite β have a strong influence on tearing mode stability of hybrid modes. Indeed, they persist in the large aspect ratio limit, R/a → ∞. A similar strong coupling effect is found between the m = 1, n = 1 harmonic and the m = 2, n = 1 harmonic if the minimum safety factor is less than unity. In both cases the tearing stability index, Δ′ increases rapidly as β approaches ideal marginal stability, providing a potential explanation for the onset of linearly unstable tearing modes. The numerical calculations have used an improved version of the T7 code (Fitzpatrick et al 1993 Nucl. Fusion 33 1533), and complete agreement is obtained with the analytic theory for this demanding test of the code. (paper)

  13. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    KAUST Repository

    Kabanov, Dmitry I.

    2017-12-08

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  14. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    KAUST Repository

    Kabanov, Dmitry; Kasimov, Aslan R.

    2018-01-01

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  15. Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

    KAUST Repository

    Kabanov, Dmitry

    2018-03-20

    We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.

  16. Nonlinear dynamics and stability of boiling water reactors: qualitative and quantitative analyses

    International Nuclear Information System (INIS)

    March-Leuba, J.; Cacuci, D.G.; Perez, R.B.

    1985-01-01

    A phenomenological model has been developed to simulate the qualitative behavior of boiling water reactors (BWRs) in the nonlinear regime under deterministic and stochastic excitations. After the linear stability threshold is crossed, limit cycle oscillations appear due to interactions between two unstable equilibrium points and the phase-space trajectories. This limit cycle becomes unstable when the feedback gain exceeds a certain critical value. Subsequent limit cycle instabilities produce a cascade of period-doubling bifurcations that leads to a periodic pulsed behavior. Under stochastic excitations, BWRs exhibit a single characteristic resonance, at approx.0.5 Hz, in the linear regime. By contrast, this work shows that harmonics of this characteristic frequency appear in the nonlinear regime. Furthermore, this work also demonstrates that amplitudes of the limit cycle oscillations do not depend on the variance of the stochastic excitation and remain bounded at all times. A physical model of nonlinear BWR dynamics has also been developed and employed to calculate the amplitude of limit cycle oscillations and their effects on fuel integrity over a wide range of operating conditions in the Vermont Yankee reactor. These calculations have confirmed that, beyond the threshold for linear stability, the reactor's state variable undergo limit cycle oscillations

  17. Transient stability improvement by nonlinear controllers based on tracking

    Energy Technology Data Exchange (ETDEWEB)

    Ramirez, Juan M. [Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015 (Mexico); Arroyave, Felipe Valencia; Correa Gutierrez, Rosa Elvira [Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica (Colombia)

    2011-02-15

    This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition's suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. (author)

  18. Multimode nonlinear optical imaging of the dermis in ex vivo human skin based on the combination of multichannel mode and Lambda mode.

    Science.gov (United States)

    Zhuo, Shuangmu; Chen, Jianxin; Luo, Tianshu; Zou, Dingsong

    2006-08-21

    A Multimode nonlinear optical imaging technique based on the combination of multichannel mode and Lambda mode is developed to investigate human dermis. Our findings show that this technique not only improves the image contrast of the structural proteins of extracellular matrix (ECM) but also provides an image-guided spectral analysis method to identify both cellular and ECM intrinsic components including collagen, elastin, NAD(P)H and flavin. By the combined use of multichannel mode and Lambda mode in tandem, the obtained in-depth two photon-excited fluorescence (TPEF) and second-harmonic generation (SHG) imaging and TPEF/SHG signals depth-dependence decay can offer a sensitive tool for obtaining quantitative tissue structural and biochemical information. These results suggest that the technique has the potential to provide more accurate information for determining tissue physiological and pathological states.

  19. Engineering non-linear resonator mode interactions in circuit QED by continuous driving: Introduction

    Science.gov (United States)

    Pfaff, Wolfgang; Reagor, Matthew; Heeres, Reinier; Ofek, Nissim; Chou, Kevin; Blumoff, Jacob; Leghtas, Zaki; Touzard, Steven; Sliwa, Katrina; Holland, Eric; Krastanov, Stefan; Frunzio, Luigi; Devoret, Michel; Jiang, Liang; Schoelkopf, Robert

    2015-03-01

    High-Q microwave resonators show great promise for storing and manipulating quantum states in circuit QED. Using resonator modes as such a resource in quantum information processing applications requires the ability to manipulate the state of a resonator efficiently. Further, one must engineer appropriate coupling channels without spoiling the coherence properties of the resonator. We present an architecture that combines millisecond lifetimes for photonic quantum states stored in a linear resonator with fast measurement provided by a low-Q readout resonator. We demonstrate experimentally how a continuous drive on a transmon can be utilized to generate highly non-classical photonic states inside the high-Q resonator via effective nonlinear resonator mode interactions. Our approach opens new avenues for using modes of long-lived linear resonators in the circuit QED platform for quantum information processing tasks.

  20. Polarization dynamics in nonlinear anisotropic fibers

    International Nuclear Information System (INIS)

    Komarov, Andrey; Komarov, Konstantin; Meshcheriakov, Dmitry; Amrani, Foued; Sanchez, Francois

    2010-01-01

    We give an extensive study of polarization dynamics in anisotropic fibers exhibiting a third-order index nonlinearity. The study is performed in the framework of the Stokes parameters with the help of the Poincare sphere. Stationary states are determined, and their stability is investigated. The number of fixed points and their stability depend on the respective magnitude of the linear and nonlinear birefringence. A conservation relation analogous to the energy conservation in mechanics allows evidencing a close analogy between the movement of the polarization in the Poincare sphere and the motion of a particle in a potential well. Two distinct potentials are found, leading to the existence of two families of solutions, according to the sign of the total energy of the equivalent mechanical system. The mechanical analogy allows us to fully characterize the solutions and also to determine analytically the associated beat lengths. General analytical solutions are given for the two families in terms of Jacobi's functions. The intensity-dependent transmission of a fiber placed between two crossed polarizers is calculated. Optimal conditions for efficient nonlinear switching compatible with mode-locking applications are determined. The general case of a nonlinear fiber ring with an intracavity polarizer placed between two polarization controllers is also considered.

  1. Contractivity and Exponential Stability of Solutions to Nonlinear Neutral Functional Differential Equations in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Wan-sheng WANG; Shou-fu LI; Run-sheng YANG

    2012-01-01

    A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.

  2. Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

    DEFF Research Database (Denmark)

    Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....

  3. Complete mode-set stability analysis of magnetically insulated ion diode equilibria

    International Nuclear Information System (INIS)

    Slutz, S.A.; Lemke, R.W.

    1993-01-01

    We present the first analysis of the stability of magnetically insulated ion diodes that is fully relativistic and includes electromagnetic perturbations both parallel and perpendicular to the applied magnetic field. Applying this formalism to a simple diode equilibrium model that neglects velocity shear and density gradients, we find a fast growing mode that has all of the important attributes of the low frequency mode observed in numerical simulations of magnetically insulated ion diodes, which may be a major cause of ion divergence. We identify this mode as a modified two-stream instability. Previous stability analyses indicate a variety of unstable modes, but none of these exhibit the same behavior as the low frequency mode observed in the simulations. In addition, we analyze a realistic diode equilibrium model that includes velocity shear and an electron density profile consistent with that observed in the numerical simulations. We find that the diocotron instability is reduced, but not fully quenched by the extension of the electron sheath to the anode. However, the inclusion of perturbations parallel to the applied magnetic field with a wavelength smaller than the diode height does eliminate growth of this instability. This may explain why the diocotron mode has been observed experimentally with proton sources, but not with LiF, since the turn on of LiF is not uniform

  4. Influence of radio frequency waves on the interchange stability in HANBIT mirror plasmas

    International Nuclear Information System (INIS)

    Hogun Jhang; Kim, S.S.; Lee, S.G.; Park, B.H.; Bak, J.G.

    2005-01-01

    Experimental and theoretical studies are made of the influence of high frequency radio frequency (rf) waves upon interchange stability in HANBIT mirror plasmas. An emphasis is put on the interchange stability near the resonance region, ω 0 ∼Ω i , where ω 0 is the angular frequency of the applied rf wave and Ω i is the ion cyclotron frequency. Recent HANBIT experiments have shown the existence of the interchange-stable operation window in favor of ω 0 /Ω i ≤1 with its sensitivity on the applied rf power. A strong nonlinear interaction between the rf wave and the interchange mode has been observed with the generation of sideband waves. A theoretical analysis including both the ponderomotive force and the nonlinear sideband wave coupling has been developed and applied to the interpretation of the experiments, resulting in a good agreement. From the study, it is concluded that the nonlinear wave-wave coupling process is responsible for the rf stabilization of the interchange modes in HANBIT mirror plasmas operating near the resonance condition. (author)

  5. Correlating non-linear properties with spectral states of RXTE data: possible observational evidences for four different accretion modes around compact objects

    Science.gov (United States)

    Adegoke, Oluwashina; Dhang, Prasun; Mukhopadhyay, Banibrata; Ramadevi, M. C.; Bhattacharya, Debbijoy

    2018-05-01

    By analysing the time series of RXTE/PCA data, the non-linear variabilities of compact sources have been repeatedly established. Depending on the variation in temporal classes, compact sources exhibit different non-linear features. Sometimes they show low correlation/fractal dimension, but in other classes or intervals of time they exhibit stochastic nature. This could be because the accretion flow around a compact object is a non-linear general relativistic system involving magnetohydrodynamics. However, the more conventional way of addressing a compact source is the analysis of its spectral state. Therefore, the question arises: What is the connection of non-linearity to the underlying spectral properties of the flow when the non-linear properties are related to the associated transport mechanisms describing the geometry of the flow? This work is aimed at addressing this question. Based on the connection between observed spectral and non-linear (time series) properties of two X-ray binaries: GRS 1915+105 and Sco X-1, we attempt to diagnose the underlying accretion modes of the sources in terms of known accretion classes, namely, Keplerian disc, slim disc, advection dominated accretion flow and general advective accretion flow. We explore the possible transition of the sources from one accretion mode to others with time. We further argue that the accretion rate must play an important role in transition between these modes.

  6. Stabilization of business cycles of finance agents using nonlinear optimal control

    Science.gov (United States)

    Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

    2017-11-01

    Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

  7. Instability threshold of neoclassical tearing mode, double tearing mode and off-axis sawteeth crash in tokamaks

    International Nuclear Information System (INIS)

    Li, D.

    2001-01-01

    The neoclassical and double tearing modes have been analyzed with related new phenomena in the reversed magnetic shear tokamak plasmas. The instability threshold, and the linear and nonlinear evolution are derived for the neoclassical tearing modes. It is found that the perturbed bootstrap current in the resistive layer has a stabilizing effect while the equilibrium bootstrap current in the outer region can destabilize the modes. The dispersion relation is derived for the double tearing mode. It is found that the onset of ''annular crash'' is due to the fast reconnection of the hot and cold islands, triggered by the interaction of both branches. The onset of ''core crash'' is mainly due to the coalescence between the hot islands, triggered by the explosive growth of the inner branch. (author)

  8. Instability threshold of neoclassical tearing mode, double tearing mode and off-axis sawteeth crash in tokamaks

    International Nuclear Information System (INIS)

    Li Ding

    1999-01-01

    The neoclassical and double tearing modes have been analyzed with related new phenomena in the reversed magnetic shear tokamak plasmas. The instability threshold, and the linear and nonlinear evolution are derived for the neoclassical tearing modes. It is found that the perturbed bootstrap current in the resistive layer has a stabilizing effect while the equilibrium bootstrap current in the outer region can destabilize the modes. The dispersion relation is derived for the double tearing mode. It is found that the onset of 'annular crash' is due to the fast reconnection of the hot and cold islands, triggered by the interaction of both branches. The onset of 'core crash' is mainly due to the coalescence between the hot islands, triggered by the explosive growth of the inner branch. (author)

  9. Stability of short-axial-wavelength internal kink modes of an anisotropic plasma

    Energy Technology Data Exchange (ETDEWEB)

    Faghihi, M.; Schefffel, J.

    1987-12-01

    The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m greater than or equal to 1) modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also, constant-current-density equilibria can be stabilized for Psub(perpendicular) > Psub(parallel) and large ..beta..sub(perpendicular).

  10. Optimal model of PDIG based microgrid and design of complementary stabilizer using ICA.

    Science.gov (United States)

    Amini, R Mohammad; Safari, A; Ravadanegh, S Najafi

    2016-09-01

    The generalized Heffron-Phillips model (GHPM) for a microgrid containing a photovoltaic (PV)-diesel machine (DM)-induction motor (IM)-governor (GV) (PDIG) has been developed at the low voltage level. A GHPM is calculated by linearization method about a loading condition. An effective Maximum Power Point Tracking (MPPT) approach for PV network has been done using sliding mode control (SMC) to maximize output power. Additionally, to improve stability of microgrid for more penetration of renewable energy resources with nonlinear load, a complementary stabilizer has been presented. Imperialist competitive algorithm (ICA) is utilized to design of gains for the complementary stabilizer with the multiobjective function. The stability analysis of the PDIG system has been completed with eigenvalues analysis and nonlinear simulations. Robustness and validity of the proposed controllers on damping of electromechanical modes examine through time domain simulation under input mechanical torque disturbances. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Integrability and Linear Stability of Nonlinear Waves

    Science.gov (United States)

    Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo

    2018-03-01

    It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.

  12. Adaptive fuzzy observer-based stabilization of a class of uncertain time-delayed chaotic systems with actuator nonlinearities

    International Nuclear Information System (INIS)

    Shahnazi, Reza; Haghani, Adel; Jeinsch, Torsten

    2015-01-01

    An observer-based output feedback adaptive fuzzy controller is proposed to stabilize a class of uncertain chaotic systems with unknown time-varying time delays, unknown actuator nonlinearities and unknown external disturbances. The actuator nonlinearity can be backlash-like hysteresis or dead-zone. Based on universal approximation property of fuzzy systems the unknown nonlinear functions are approximated by fuzzy systems, where the consequent parts of fuzzy rules are tuned with adaptive schemes. The proposed method does not need the availability of the states and an observer based output feedback approach is proposed to estimate the states. To have more robustness and at the same time to alleviate chattering an adaptive discontinuous structure is suggested. Semi-global asymptotic stability of the overall system is ensured by proposing a suitable Lyapunov–Krasovskii functional candidate. The approach is applied to stabilize the time-delayed Lorenz chaotic system with uncertain dynamics amid significant disturbances. Analysis of simulations reveals the effectiveness of the proposed method in terms of coping well with the modeling uncertainties, nonlinearities in actuators, unknown time-varying time-delays and unknown external disturbances while maintaining asymptotic convergence

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

    Directory of Open Access Journals (Sweden)

    Wen-Jer Chang

    2014-01-01

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

  14. Stabilization of external kink modes in a tokamak with rotating plasma

    International Nuclear Information System (INIS)

    Mikhailovskii, A.B.; Kuvshinov, B.N.

    1995-01-01

    An analytical theory of stabilization of external kink modes in a tokamak with rotating plasma is developed, which is of interest in connection with experiments on the DIII-D tokamak demonstrating such a stabilization. It is assumed that, in addition to the main poloidal harmonic, the mode includes one or more side-band poloidal harmonics with singular points lying inside the plasma. Near these singular points, plasma inertia and related toroidal effects, the compressible part of plasma pressure and longitudinal viscosity, are allowed for. These effects are described kinetically taking into account the toroidal trapping of the resonant ions, which is essential if the toroidal velocity is small compared to the ion thermal velocity. Thereby, the theory presented includes both ion Landau damping and its weakening due to toroidal trapping. Near the singular points high-beta effects, which result in the finiteness of the Mercier index s, are allowed for. It is shown that the influence of plasma rotation on the external kink modes is most significant in the case of s<0, i.e., when the development of the instability in a non-rotating plasma is most highly favored. In this case, the plasma rotation plays a stabilizing role, even when the ion Landau damping is neglected. The analysis presented also confirms the hypothesis of Bondeson and Ward on the stabilizing effect of ion Landau damping if this damping is not too small

  15. Controlled generation of nonlinear resonances through sinusoidal lattice modes in Bose–Einstein condensate

    International Nuclear Information System (INIS)

    Das, Priyam; Panigrahi, Prasanta K

    2015-01-01

    We study Bose–Einstein condensate in the combined presence of time modulated optical lattice and harmonic trap in the mean-field approach. Through the self-similar method, we show the existence of sinusoidal lattice modes in this inhomogeneous system, commensurate with the lattice potential. A significant advantage of this system is wide tunability of the parameters through chirp management. The combined effect of the interaction, harmonic trap and lattice potential leads to the generation of nonlinear resonances, exactly where the matter wave changes its direction. When the harmonic trap is switched off, the BEC undergoes a nonlinear compression for the static optical lattice potential. For better understanding of chirp management and the nature of the sinusoidal excitation, we investigate the energy spectrum of the condensate, which clearly reveals the generation of nonlinear resonances in the appropriate regime. We have also identified a classical dynamical phase transition occurring in the system, where loss of superfluidity takes the superfluid phase to an insulating state. (paper)

  16. A net normal dispersion all-fiber laser using a hybrid mode-locking mechanism

    International Nuclear Information System (INIS)

    Xu, Bo; Martinez, Amos; Yamashita, Shinji; Set, Sze Yun; Goh, Chee Seong

    2014-01-01

    We propose and demonstrate an all-fiber, dispersion-mapped, erbium-doped fiber laser with net normal dispersion generating dissipative solitons. The laser is mode-locked by a hybrid mode-locking mechanism consisting of a nonlinear amplifying loop mirror and a carbon nanotube saturable absorber. We achieve self-starting, mode-locked operation generating 2.75 nJ pulses at a fundamental repetition rate of 10.22 MHz with remarkable long term stability. (letter)

  17. Internal Kink Mode Dynamics in High-β NSTX Plasmas

    International Nuclear Information System (INIS)

    Menard, J.E.; Bell, R.E.; Fredrickson, E.D.; Gates, D.A.; Kaye, S.M.; LeBlanc, B.P.; Medley, S.S.; Park, W.; Sabbagh, S.A.; Sontag, A.; Stutman, D.; Tritz, K.; Zhu, W.

    2004-01-01

    Saturated internal kink modes have been observed in many of the highest toroidal beta discharges of the National Spherical Torus Experiment (NSTX). These modes often cause rotation flattening in the plasma core, can degrade energy confinement, and in some cases contribute to the complete loss of plasma angular momentum and stored energy. Characteristics of the modes are measured using soft X-ray, kinetic profile, and magnetic diagnostics. Toroidal flows approaching Alfvenic speeds, island pressure peaking, and enhanced viscous and diamagnetic effects associated with high-beta may contribute to mode nonlinear stabilization. These saturation mechanisms are investigated for NSTX parameters and compared to experimental data

  18. Internal kink mode dynamics in high-β NSTX plasmas

    International Nuclear Information System (INIS)

    Menard, J.E.; Bell, R.E.; Fredrickson, E.D.; Gates, D.A.; Kaye, S.M.; LeBlanc, B.P.; Medley, S.S.; Park, W.; Sabbagh, S.A.; Sontag, A.; Zhu, W.; Stutman, D.; Tritz, K.

    2005-01-01

    Saturated internal kink modes have been observed in many of the highest toroidal beta discharges of the National Spherical Torus Experiment (NSTX). These modes often cause rotation flattening in the plasma core, can degrade energy confinement, and in some cases contribute to the complete loss of plasma angular momentum and stored energy. Characteristics of the modes are measured using soft X-ray, kinetic profile, and magnetic diagnostics. Toroidal flows approaching Alfvenic speeds, island pressure peaking, and enhanced viscous and diamagnetic effects associated with high-beta may contribute to mode non-linear stabilization. These saturation mechanisms are investigated for NSTX parameters and compared to experiment. (author)

  19. Anchor stabilization of trapped particle modes in mirror machines

    International Nuclear Information System (INIS)

    Berk, H.L.; Roslyakov, G.V.

    1986-07-01

    It is shown that for trapped particle modes in tandem mirrors, the pressure of the passing particles in the anchor region introduces a stabilizing term proportional to the sum of the anchor's field line curvature and total diamagnetic pressure. The theory is applied to the proposed gas dynamic trap experiment

  20. Anchor stabilization of trapped particle modes in mirror machines

    International Nuclear Information System (INIS)

    Berk, H.L.; Roslyakov, G.V.

    1986-04-01

    It is shown that for trapped particle modes in tandem mirrors, the pressure of the passing particles in the anchor region introduces a stabilizing term proportional to the sum of the anchor's field line curvature and total diamagnetic pressure. The theory is applied to the proposed gas dynamic trap experiment

  1. The quiescent H-mode regime for high performance edge localized mode-stable operation in future burning plasmas

    Energy Technology Data Exchange (ETDEWEB)

    Garofalo, A. M., E-mail: garofalo@fusion.gat.com; Burrell, K. H.; Meneghini, O.; Osborne, T. H.; Paz-Soldan, C.; Smith, S. P.; Snyder, P. B.; Turnbull, A. D. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Eldon, D.; Grierson, B. A.; Solomon, W. M. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Hanson, J. M. [Columbia University, 2960 Broadway, New York, New York 10027-6900 (United States); Holland, C. [University of California San Diego, 9500 Gilman Dr., La Jolla, California 92093-0417 (United States); Huijsmans, G. T. A.; Liu, F.; Loarte, A. [ITER Organization, Route de Vinon sur Verdon, 13067 St Paul Lez Durance (France); Zeng, L. [University of California Los Angeles, P.O. Box 957099, Los Angeles, California 90095-7099 (United States)

    2015-05-15

    For the first time, DIII-D experiments have achieved stationary quiescent H-mode (QH-mode) operation for many energy confinement times at simultaneous ITER-relevant values of beta, confinement, and safety factor, in an ITER-like shape. QH-mode provides excellent energy confinement, even at very low plasma rotation, while operating without edge localized modes (ELMs) and with strong impurity transport via the benign edge harmonic oscillation (EHO). By tailoring the plasma shape to improve the edge stability, the QH-mode operating space has also been extended to densities exceeding 80% of the Greenwald limit, overcoming the long-standing low-density limit of QH-mode operation. In the theory, the density range over which the plasma encounters the kink-peeling boundary widens as the plasma cross-section shaping is increased, thus increasing the QH-mode density threshold. The DIII-D results are in excellent agreement with these predictions, and nonlinear magnetohydrodynamic analysis of reconstructed QH-mode equilibria shows unstable low n kink-peeling modes growing to a saturated level, consistent with the theoretical picture of the EHO. Furthermore, high density operation in the QH-mode regime has opened a path to a new, previously predicted region of parameter space, named “Super H-mode” because it is characterized by very high pedestals that can be more than a factor of two above the peeling-ballooning stability limit for similar ELMing H-mode discharges at the same density.

  2. Linear local stability of electrostatic drift modes in helical systems

    International Nuclear Information System (INIS)

    Yamagishi, O.; Nakajima, N.; Sugama, H.; Nakamura, Y.

    2003-01-01

    We investigate the stability of the drift wave in helical systems. For this purpose, we solve the linear local gyrokinetic-Poisson equation, in the electrostatic regime. As a model of helical plasmas, Large helical Device (LHD) is considered. The equation we apply is rather exact in the framework of linear gyrokinetic theory, where only the approximation is the ballooning representation. In this paper, we consider only collisionless cases. All the frequency regime can be naturally reated without any assumptions, and in such cases, ion temperature gradient modes (ITG), trapped electron modes (TEM), and electron temperature gradient modes (ETG) are expected to become unstable linearly independently. (orig.)

  3. Measurement of Resistive Wall Mode stability in rotating high beta plasmas

    International Nuclear Information System (INIS)

    Reimerdes, H.; Bialek, J.; Garofalo, A.M.; Navratil, G.A.; Chance, M.S.; Menard, J.E.; Okabayashi, M.; Takahashi, H.; Chu, M.S.; Gohil, P.; Jackson, G.L.; Jensen, T.H.; La Haye, R.J.; Scoville, J.T.; Strait, E.J.; Jayakumar, R.J.; Liu, Y.Q.

    2005-01-01

    Toroidal plasma rotation in the order of a few percent of the Alfven velocity can stabilize the resistive wall mode and extend the operating regime of tokamaks from the conventional, ideal MHD no-wall limit up to the ideal MHD ideal wall limit. The stabilizing effect has been measured passively by measuring the critical plasma rotation required for stability and actively by probing the plasma with externally applied resonant magnetic fields. These measurements are compared to predictions of rotational stabilization of the sound wave damping and of the kinetic damping model using the MARS code. (author)

  4. Geodesic acoustic modes excited by finite beta drift waves

    DEFF Research Database (Denmark)

    Chakrabarti, Nikhil Kumar; Guzdar, P.N.; Kleva, R.G.

    2008-01-01

    Presented in this paper is a mode-coupling analysis for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by finite beta drift waves. The finite beta effects give rise to a strong stabilizing influence on the parametric excitation process. The dominant finite beta...... effect is the combination of the Maxwell stress, which has a tendency to cancel the primary drive from the Reynolds stress, and the finite beta modification of the drift waves. The zonal magnetic field is also excited at the GAM frequency. However, it does not contribute to the overall stability...... of the three-wave process for parameters of relevance to the edge region of tokamaks....

  5. Stabilization of kinetic internal kink mode by ion diamagnetic effects

    International Nuclear Information System (INIS)

    Naitou, H.; Kuramoto, T.; Kobayashi, T.; Yagi, M.; Tokuda, S.; Matsumoto, T.

    2000-04-01

    Ion diamagnetic effects on the m=1 (poloidal mode number) and n=1 (toroidal mode number) kinetic internal kink mode are studied numerically by the three-field gyro-reduced-MHD code in the cylindrical coordinates, GRM3F-CY. In the derivation of the gryo-reduced-MHD model including the ion diamagnetic effects, finite gyroradius effects of ions are added to the gyrokinetic Poisson equation (quasi-neutral condition) and the convection term of the conservation law of the ion density. It is found that the long wavelength approximation, ksub(perpendicular) ρ ti ti is the thermal ion gyroradius, fails to reproduce the correct dispersion relation; the formulation valid even for ksub(perpendicular) ρ ti >> 1 is necessary. The results of numerical calculation coincide with the theory for |ω *e |+|ω *i | 0 , where the growth rate reduces as the density gradient increases. Here ω *e and ω *i are electron and ion diamagnetic angular frequencies estimated at the rational surface of q=1 (q is a safety factor), respectively, and γ 0 is the growth rate for the uniform density. Very weak instability, however, is observed for |ω *e |+|ω *i | 0 , where the theory predicts the complete stabilization. This residual instability appears since the region with the density gradient is limited in the radial direction and the stabilization by the outgoing drift-wave like mode becomes incomplete. (author)

  6. Synchronization of a modified Chua's circuit system via adaptive sliding mode control

    International Nuclear Information System (INIS)

    Yan, J.-J.; Lin, J.-S.; Liao, T.-L.

    2008-01-01

    This study addresses the adaptive synchronization of a modified Chua's circuit system with both unknown system parameters and the nonlinearity in the control input. An adaptive switching surface is newly adopted such that it becomes easy to ensure the stability of the error dynamics in the sliding mode. Based on this adaptive switching surface, an adaptive sliding mode controller (ASMC) is derived to guarantee the occurrence of the sliding motion, even when the system is undergoing input nonlinearity. This method can also be easily extended to a general class of Chua's circuits. An illustrative example is given to show the applicability of the proposed ASMC design

  7. Nonlinear modelling and dynamic stability analysis of a flexible Cartesian robotic manipulator with base disturbance and terminal load

    Directory of Open Access Journals (Sweden)

    J. Ju

    2017-07-01

    Full Text Available The flexible Cartesian robotic manipulator (FCRM is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.

  8. On the role of resonances in double-mode pulsation

    International Nuclear Information System (INIS)

    Dziembowski, W.; Kovacs, G.

    1984-01-01

    Simultaneous effects of resonant coupling and non-linear saturation of linear driving mechanism on the finite amplitude solution of multi-modal pulsation problem and on its stability are investigated. Both effects are calculated in the lowest order of approximation in terms of amplitudes. It is shown that the 2:1 resonance between one of the two linearly unstable modes and a higher frequency mode causes double-mode (fundamental and first overtone) pulsation. In a certain range of parameters, such as the frequency mismatch, the linear growth and damping rates, it is the only stable solution of the problem. (author)

  9. Bifurcation and stability analysis of a nonlinear milling process

    Science.gov (United States)

    Weremczuk, Andrzej; Rusinek, Rafal; Warminski, Jerzy

    2018-01-01

    Numerical investigations of milling operations dynamics are presented in this paper. A two degree of freedom nonlinear model is used to study workpiece-tool vibrations. The analyzed model takes into account both flexibility of the tool and the workpiece. The dynamics of the milling process is described by the discontinuous ordinary differential equation with time delay, which can cause process instability. First, stability lobes diagrams are created on the basis of the parameters determined in impact test of an end mill and workpiece. Next, the bifurcations diagrams are performed for different values of rotational speeds.

  10. Nonlinear two-stream interaction between a cold, relativistic electron beam and a collisional plasma-Astron experiment

    International Nuclear Information System (INIS)

    Newberger, B.S.; Thode, L.E.

    1979-05-01

    Experiments on the two-stream instability of a relativistic electron beam propagating through a neutral gas, carried out with the Lawrence Livermore Laboratory Astron beam, have been analyzed using a nonlinear saturation model for a cold beam. The behavior of the observed microwave emission due to the instability is in good agreement with that of the beam energy loss. Collisions on the plasma electrons weaken the nonlinear state of the instability but do not stabilize the mode. The beam essentially acts as if it were cold, a result substantiated by linear theory for waves propagating along the beam. In order to predict the effect of both beam momentum scatter and plasma electron collisions on the stability of the mode in future experiments a full two-dimensional linear theory must be developed

  11. Review of tearing mode stabilization by RF power in tokamaks

    International Nuclear Information System (INIS)

    Giruzzi, G.; Zabiego, M.; Zohm, H.

    1999-01-01

    Control of tearing modes by means of heating and current drive inside the magnetic islands is one of the most important applications of RF power in tokamak reactors. The theoretical basis of this concept is reviewed, focusing on aspects related to RF-plasma interaction. Applications to the stabilization of neoclassical tearing modes in ITER by Electron Cyclotron Current Drive are presented to illustrate the basic physical dependences. The most significant experimental results and prospects for future applications are also discussed

  12. Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management

    Science.gov (United States)

    Cuevas-Maraver, J.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.

    2018-04-01

    We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.

  13. Nonlinear traveling waves in rotating Rayleigh-Bacute enard convection: Stability boundaries and phase diffusion

    International Nuclear Information System (INIS)

    Liu, Y.; Ecke, R.E.

    1999-01-01

    We present experimental measurements of a sidewall traveling wave in rotating Rayleigh-Bacute enard convection. The fluid, water with Prandtl number about 6.3, was confined in a 1-cm-high cylindrical cell with radius-to-height ratio Γ=5. We used simultaneous optical-shadowgraph, heat-transport, and local temperature measurements to determine the stability and characteristics of the traveling-wave state for dimensionless rotation rates 60<Ω<420. The state is well described by the one-dimensional complex Ginzburg-Landau (CGL) equation for which the linear and nonlinear coefficients were determined for Ω=274. The Eckhaus-Benjamin-Feir-stability boundary was established and the phase-diffusion coefficient and nonlinear group velocity were determined in the stable regime. Higher-order corrections to the CGL equation were also investigated. copyright 1999 The American Physical Society

  14. Breatherlike impurity modes in discrete nonlinear lattices

    DEFF Research Database (Denmark)

    Hennig, D.; Rasmussen, Kim; Tsironis, G. P.

    1995-01-01

    We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...

  15. Nonlinear Simulations of Trapped Electron Mode Turbulence in Low Magnetic Shear Stellarators

    Science.gov (United States)

    Faber, B. J.; Pueschel, M. J.; Terry, P. W.; Hegna, C. C.

    2017-10-01

    Optimized stellarators, like the Helically Symmetric eXperiment (HSX), often operate with small global magnetic shear to avoid low-order rational surfaces and magnetic islands. Nonlinear, flux-tube gyrokinetic simulations of density-gradient-driven Trapped Electron Mode (TEM) turbulence in HSX shows two distinct spectral fluctuation regions: long-wavelength slab-like TEMs localized by global magnetic shear that extend along field lines and short-wavelength TEMs localized by local magnetic shear to a single helical bad curvature region. The slab-like TEMs require computational domains significantly larger than one poloidal turn and are computationally expensive, making turbulent optimization studies challenging. A computationally more efficient, zero-average-magnetic-shear approximation is shown to sufficiently describe the relevant nonlinear physics and replicate finite-shear computations, and can be exploited in quasilinear models based on linear gyrokinetics as a feasible optimization tool. TEM quasilinear heat fluxes are computed with the zero-shear approximation and compared to experimentally-relevant nonlinear gyrokinetic TEM heat fluxes for HSX. Research supported by U.S. DoE Grants DE-FG02-99ER54546, DE-FG02-93ER54222 and DE-FG02-89ER53291.

  16. PWL approximation of nonlinear dynamical systems, part I: structural stability

    International Nuclear Information System (INIS)

    Storace, M; De Feo, O

    2005-01-01

    This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes the approximation method and applies it to some particularly significant dynamical systems (topological normal forms). The structural stability of the PWL approximations of such systems is investigated through a bifurcation analysis (via continuation methods)

  17. Stabilization of neoclassical tearing modes by electron cyclotron current drive in JT-60U

    International Nuclear Information System (INIS)

    Isayama, A.; Oyama, N.; Urano, H.; Suzuki, T.; Takechi, M.; Hayashi, N.; Nagasaki, K.; Kamada, Y.; Ide, S.; Ozeki, T.

    2007-01-01

    Results of active control of neoclassical tearing modes (NTMs) by electron cyclotron current drive (ECCD) in JT-60U are described. Growth of an NTM with poloidal mode number m = 3 and toroidal mode number n = 2 has been suppressed by ECCD inside the sawtooth inversion radius in the co-direction, showing the possibility of the coexistence of sawtooth oscillations and a small-amplitude m/n = 3/2 NTM without large confinement degradation. Stabilization of an m/n = 2/1 NTM by ECCD at the mode rational surface has been demonstrated with a small ratio of the current density driven by the electron cyclotron (EC) wave to the local bootstrap current density (∼ 0.5). In addition, dependence of the stabilization effect on ECCD location has been investigated in detail. It has been found that an m/n = 2/1 NTM can be completely stabilized with the misalignment of the ECCD location less than about half of the full island width, and that the m/n = 2/1 NTM is destabilized with the misalignment comparable to the full island width. Time-dependent, self-consistent simulation of magnetic island evolution using the TOPICS code has shown that the stabilization and destabilization of an m/n = 2/1 NTM are well reproduced with the same set of coefficients of the modified Rutherford equation. The TOPICS simulation has also clarified that EC wave power required for complete stabilization can be significantly reduced by narrowing the ECCD deposition width

  18. Core Power Control of the fast nuclear reactors with estimation of the delayed neutron precursor density using Sliding Mode method

    International Nuclear Information System (INIS)

    Ansarifar, G.R.; Nasrabadi, M.N.; Hassanvand, R.

    2016-01-01

    Highlights: • We present a S.M.C. system based on the S.M.O for control of a fast reactor power. • A S.M.O has been developed to estimate the density of delayed neutron precursor. • The stability analysis has been given by means Lyapunov approach. • The control system is guaranteed to be stable within a large range. • The comparison between S.M.C. and the conventional PID controller has been done. - Abstract: In this paper, a nonlinear controller using sliding mode method which is a robust nonlinear controller is designed to control a fast nuclear reactor. The reactor core is simulated based on the point kinetics equations and one delayed neutron group. Considering the limitations of the delayed neutron precursor density measurement, a sliding mode observer is designed to estimate it and finally a sliding mode control based on the sliding mode observer is presented. The stability analysis is given by means Lyapunov approach, thus the control system is guaranteed to be stable within a large range. Sliding Mode Control (SMC) is one of the robust and nonlinear methods which have several advantages such as robustness against matched external disturbances and parameter uncertainties. The employed method is easy to implement in practical applications and moreover, the sliding mode control exhibits the desired dynamic properties during the entire output-tracking process independent of perturbations. Simulation results are presented to demonstrate the effectiveness of the proposed controller in terms of performance, robustness and stability.

  19. Problems in nonlinear resistive MHD

    International Nuclear Information System (INIS)

    Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.

    1998-01-01

    Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1

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

    Science.gov (United States)

    Michiels, Wim; Nijmeijer, Henk

    2009-09-01

    We consider the synchronization problem of an arbitrary number of coupled nonlinear oscillators with delays in the interconnections. The network topology is described by a directed graph. Unlike the conventional approach of deriving directly sufficient synchronization conditions, the approach of the paper starts from an exact stability analysis in a (gain, delay) parameter space of a synchronized equilibrium and extracts insights from an analysis of its bifurcations and from the corresponding emerging behavior. Instrumental to this analysis a factorization of the characteristic equation is employed that not only facilitates the analysis and reduces computational cost but also allows to determine the precise role of the individual agents and the topology of the network in the (in)stability mechanisms. The study provides an algorithm to perform a stability and bifurcation analysis of synchronized equilibria. Furthermore, it reveals fundamental limitations to synchronization and it explains under which conditions on the topology of the network and on the characteristics of the coupling the systems are expected to synchronize. In the second part of the paper the results are applied to coupled Lorenz systems. The main results show that for sufficiently large coupling gains, delay-coupled Lorenz systems exhibit a generic behavior that does not depend on the number of systems and the topology of the network, as long as some basic assumptions are satisfied, including the strong connectivity of the graph. Here the linearized stability analysis is strengthened by a nonlinear stability analysis which confirms the predictions based on the linearized stability and bifurcation analysis. This illustrates the usefulness of the exact linearized analysis in a situation where a direct nonlinear stability analysis is not possible or where it yields conservative conditions from which it is hard to get qualitative insights in the synchronization mechanisms and their scaling properties

  1. Nonlinear stability control and λ-bifurcation

    International Nuclear Information System (INIS)

    Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.

    1987-01-01

    Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed

  2. 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$.

  3. Stability of the mode-locking regime in tapered quantum-dot lasers

    Science.gov (United States)

    Bardella, P.; Drzewietzki, L.; Rossetti, M.; Weber, C.; Breuer, S.

    2018-02-01

    We study numerically and experimentally the role of the injection current and reverse bias voltage on the pulse stability of tapered, passively mode-locked, Quantum Dot (QD) lasers. By using a multi-section delayed differential equation and introducing in the model the QD inhomogenous broadening, we are able to predict the onset of leading and trailing edge instabilities in the emitted pulse trains and to identify specific trends of stability in dependence on the laser biasing conditions. The numerical results are confirmed experimentally trough amplitude and timing stability analysis of the pulses.

  4. ELM triggering by energetic particle driven mode in wall-stabilized high-β plasmas

    International Nuclear Information System (INIS)

    Matsunaga, G.; Aiba, N.; Shinohara, K.; Asakura, N.; Isayama, A.; Oyama, N.

    2013-01-01

    In the JT-60U high-β plasmas above the no-wall β limit, a triggering of an edge localized mode (ELM) by an energetic particle (EP)-driven mode has been observed. This EP-driven mode is thought to be driven by trapped EPs and it has been named EP-driven wall mode (EWM) on JT-60U (Matsunaga et al 2009 Phys. Rev. Lett. 103 045001). When the EWM appears in an ELMy H-mode phase, ELM crashes are reproducibly synchronized with the EWM bursts. The EWM-triggered ELM has a higher repetition frequency and less energy loss than those of the natural ELM. In order to trigger an ELM by the EP-driven mode, some conditions are thought to be needed, thus an EWM with large amplitude and growth rate, and marginal edge stability. In the scrape-off layer region, several measurements indicate an ion loss induced by the EWM. The ion transport is considered as the EP transport through the edge region. From these observations, the EP contributions to edge stability are discussed as one of the ELM triggering mechanisms. (paper)

  5. Kelvin-Helmholtz instability as a possible cause of edge localized modes

    International Nuclear Information System (INIS)

    Strauss, H.R.

    1992-01-01

    Edge localized modes may be a Kelvin-Helmholtz instability caused by the sheared rotation of H-mode plasmas. The Kelvin-Helmholtz instability is stabilized by coupling to Alfven waves. There is a critical velocity gradient, of the order of the Alfven velocity divided by the magnetic shear length. This is verified in a numerical simulation. The critical velocity shear is consistent with experiment. A non-linear simulation shows how the Kelvin-Helmholtz mode can cause oscillations of the velocity profile. (author). Letter-to-the-editor. 13 refs, 6 figs

  6. Stability diagram of colliding beams

    CERN Document Server

    Buffat, X; Mounet, N; Pieloni, T

    2014-01-01

    The effect of the beam-beam interactions on the stability of impedance mode is discussed. The detuning is evaluated by the means of single particle tracking in arbitrarily complex collision configurations, including lattice non-linearities, and used to numerically evaluate the dispersion integral. This approach also allows the effect of non-Gaussian distributions to be considered. Distributions modified by the action of external noise are discussed.

  7. Stability of the static solitons in a pure spinor theory with fractional power nonlinearities

    International Nuclear Information System (INIS)

    Akdeniz, K.G.; Tezgor, G.; Barut, A.O.; Kalayci, J.; Okan, S.E.

    1988-08-01

    Soliton solutions are obtained in a pure fermionic model with fractional power nonlinear self-interactions. The stability properties of the minimum solutions have also been investigated within the framework of the Shatah-Strauss formalism. (author). 10 refs

  8. Immiscible three-dimensional fingering in porous media: A weakly nonlinear analysis

    Science.gov (United States)

    Brandão, Rodolfo; Dias, Eduardo O.; Miranda, José A.

    2018-03-01

    We present a weakly nonlinear theory for the development of fingering instabilities that arise at the interface between two immiscible viscous fluids flowing radially outward in a uniform three-dimensional (3D) porous medium. By employing a perturbative second-order mode-coupling scheme, we investigate the linear stability of the system as well as the emergence of intrinsically nonlinear finger branching events in this 3D environment. At the linear stage, we find several differences between the 3D radial fingering and its 2D counterpart (usual Saffman-Taylor flow in radial Hele-Shaw cells). These include the algebraic growth of disturbances and the existence of regions of absolute stability for finite values of viscosity contrast and capillary number in the 3D system. On the nonlinear level, our main focus is to get analytical insight into the physical mechanism resulting in the occurrence of finger tip-splitting phenomena. In this context, we show that the underlying mechanism leading to 3D tip splitting relies on the coupling between the fundamental interface modes and their first harmonics. However, we find that in three dimensions, in contrast to the usual 2D fingering structures normally encountered in radial Hele-Shaw flows, tip splitting into three branches can also be observed.

  9. Ballooning mode stability for self-consistent pressure and current profiles at the H-mode edge

    International Nuclear Information System (INIS)

    Miller, R.L.; Lin-Liu, Y.R.; Osborne, T.H.; Taylor, T.S.

    1997-11-01

    The edge pressure gradient (H-mode pedestal) for computed equilibria in which the current density profile is consistent with the bootstrap current may not be limited by the first regime ballooning limit. The transition to second stability is easier for: higher elongation, intermediate triangularity, larger ratio, pedestal at larger radius, narrower pedestal width, higher q 95 , and lower collisionality

  10. Adaptive Sliding Mode Control Method Based on Nonlinear Integral Sliding Surface for Agricultural Vehicle Steering Control

    Directory of Open Access Journals (Sweden)

    Taochang Li

    2014-01-01

    Full Text Available Automatic steering control is the key factor and essential condition in the realization of the automatic navigation control of agricultural vehicles. In order to get satisfactory steering control performance, an adaptive sliding mode control method based on a nonlinear integral sliding surface is proposed in this paper for agricultural vehicle steering control. First, the vehicle steering system is modeled as a second-order mathematic model; the system uncertainties and unmodeled dynamics as well as the external disturbances are regarded as the equivalent disturbances satisfying a certain boundary. Second, a transient process of the desired system response is constructed in each navigation control period. Based on the transient process, a nonlinear integral sliding surface is designed. Then the corresponding sliding mode control law is proposed to guarantee the fast response characteristics with no overshoot in the closed-loop steering control system. Meanwhile, the switching gain of sliding mode control is adaptively adjusted to alleviate the control input chattering by using the fuzzy control method. Finally, the effectiveness and the superiority of the proposed method are verified by a series of simulation and actual steering control experiments.

  11. Ideal MHD stability properties of pressure-driven modes in low shear tokamaks

    International Nuclear Information System (INIS)

    Manickam, J.; Pomphrey, N.; Todd, A.M.M.

    1987-03-01

    The role of shear in determining the ideal MHD stability properties of tokamaks is discussed. In particular, we assess the effects of low shear within the plasma upon pressure-driven modes. The standard ballooning theory is shown to break down, as the shear is reduced and the growth rate is shown to be an oscillatory function of n, the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure and safety-factor profiles. When the shear is sufficiently weak, the oscillations can result in bands of unstable n values which are present even when the standard ballooning theory predicts complete stability. These instabilities are named ''infernal modes.'' The occurrence of these instabilities at integer n is shown to be a sensitive function of q-axis, raising the possibility of a sharp onset as plasma parameters evolve. 20 refs., 31 figs

  12. Simulation of non-resonant internal kink mode with toroidal rotation in the National Spherical Torus Experiment

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Feng; Liu, J. Y. [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Fu, G. Y.; Breslau, J. A. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Tritz, Kevin [Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218 (United States)

    2013-07-15

    Plasmas in spherical and conventional tokamaks, with weakly reversed shear q profile and minimum q above but close to unity, are susceptible to an non-resonant (m,n) = (1,1) internal kink mode. This mode can saturate and persist and can induce a (2,1) seed island for Neoclassical Tearing Mode. [Breslau et al. Nucl. Fusion 51, 063027 (2011)]. The mode can also lead to large energetic particle transport and significant broadening of beam-driven current. Motivated by these important effects, we have carried out extensive nonlinear simulations of the mode with finite toroidal rotation using parameters and profiles of an NTSX plasma with a weakly reversed shear profile. The numerical results show that, at the experimental level, plasma rotation has little effect on either equilibrium or linear stability. However, rotation can significantly influence the nonlinear dynamics of the (1,1) mode and the induced (2,1) magnetic island. The simulation results show that a rotating helical equilibrium is formed and maintained in the nonlinear phase at finite plasma rotation. In contrast, for non-rotating cases, the nonlinear evolution exhibits dynamic oscillations between a quasi-2D state and a helical state. Furthermore, the effects of rotation are found to greatly suppress the (2,1) magnetic island even at a low level.

  13. Analytical and numerical studies of approximate phase velocity matching based nonlinear S0 mode Lamb waves for the detection of evenly distributed microstructural changes

    International Nuclear Information System (INIS)

    Wan, X; Xu, G H; Tao, T F; Zhang, Q; Tse, P W

    2016-01-01

    Most previous studies on nonlinear Lamb waves are conducted using mode pairs that satisfying strict phase velocity matching and non-zero power flux criteria. However, there are some limitations in existence. First, strict phase velocity matching is not existed in the whole frequency bandwidth; Second, excited center frequency is not always exactly equal to the true phase-velocity-matching frequency; Third, mode pairs are isolated and quite limited in number; Fourth, exciting a single desired primary mode is extremely difficult in practice and the received signal is quite difficult to process and interpret. And few attention has been paid to solving these shortcomings. In this paper, nonlinear S0 mode Lamb waves at low-frequency range satisfying approximate phase velocity matching is proposed for the purpose of overcoming these limitations. In analytical studies, the secondary amplitudes with the propagation distance considering the fundamental frequency, the maximum cumulative propagation distance (MCPD) with the fundamental frequency and the maximum linear cumulative propagation distance (MLCPD) using linear regression analysis are investigated. Based on analytical results, approximate phase velocity matching is quantitatively characterized as the relative phase velocity deviation less than a threshold value of 1%. Numerical studies are also conducted using tone burst as the excitation signal. The influences of center frequency and frequency bandwidth on the secondary amplitudes and MCPD are investigated. S1–S2 mode with the fundamental frequency at 1.8 MHz, the primary S0 mode at the center frequencies of 100 and 200 kHz are used respectively to calculate the ratios of nonlinear parameter of Al 6061-T6 to Al 7075-T651. The close agreement of the computed ratios to the actual value verifies the effectiveness of nonlinear S0 mode Lamb waves satisfying approximate phase velocity matching for characterizing the material nonlinearity. Moreover, the ratios derived

  14. Burn Control in Fusion Reactors via Nonlinear Stabilization Techniques

    International Nuclear Information System (INIS)

    Schuster, Eugenio; Krstic, Miroslav; Tynan, George

    2003-01-01

    Control of plasma density and temperature magnitudes, as well as their profiles, are among the most fundamental problems in fusion reactors. Existing efforts on model-based control use control techniques for linear models. In this work, a zero-dimensional nonlinear model involving approximate conservation equations for the energy and the densities of the species was used to synthesize a nonlinear feedback controller for stabilizing the burn condition of a fusion reactor. The subignition case, where the modulation of auxiliary power and fueling rate are considered as control forces, and the ignition case, where the controlled injection of impurities is considered as an additional actuator, are treated separately.The model addresses the issue of the lag due to the finite time for the fresh fuel to diffuse into the plasma center. In this way we make our control system independent of the fueling system and the reactor can be fed either by pellet injection or by puffing. This imposed lag is treated using nonlinear backstepping.The nonlinear controller proposed guarantees a much larger region of attraction than the previous linear controllers. In addition, it is capable of rejecting perturbations in initial conditions leading to both thermal excursion and quenching, and its effectiveness does not depend on whether the operating point is an ignition or a subignition point.The controller designed ensures setpoint regulation for the energy and plasma parameter β with robustness against uncertainties in the confinement times for different species. Hence, the controller can increase or decrease β, modify the power, the temperature or the density, and go from a subignition to an ignition point and vice versa

  15. ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.

  16. Adaptive Sliding Mode Control of Chaos in Permanent Magnet Synchronous Motor via Fuzzy Neural Networks

    Directory of Open Access Journals (Sweden)

    Tat-Bao-Thien Nguyen

    2014-01-01

    Full Text Available In this paper, based on fuzzy neural networks, we develop an adaptive sliding mode controller for chaos suppression and tracking control in a chaotic permanent magnet synchronous motor (PMSM drive system. The proposed controller consists of two parts. The first is an adaptive sliding mode controller which employs a fuzzy neural network to estimate the unknown nonlinear models for constructing the sliding mode controller. The second is a compensational controller which adaptively compensates estimation errors. For stability analysis, the Lyapunov synthesis approach is used to ensure the stability of controlled systems. Finally, simulation results are provided to verify the validity and superiority of the proposed method.

  17. Nonlinear vibrations of an inclined beam subjected to a moving load

    International Nuclear Information System (INIS)

    Mamandi, A; Kargarnovin, M H; Younesian, D

    2009-01-01

    In this paper, the nonlinear dynamic responses of an inclined pinned-pinned Euler-Bernoulli beam with a constant cross section and finite length subjected to a concentrated vertical force traveling with constant velocity is investigated by using the mode summation method. Frequency analysis of the PDE's governing equations of motion for steady-state response is studied by applying multiple scales method. The nonlinear dynamic deflections of the beam are obtained by solving two coupled nonlinear PDE's governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the numerical results are compared with those obtained from traditional linear solution. It is found that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also stability analysis of the steady-state response for the modes equations having quadratic nonlinearity is carried out and it is observed from the amplitude response curves that for the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon are predicted for the longitudinal excitation.

  18. On the roles of direct feedback and error field correction in stabilizing resistive-wall modes

    International Nuclear Information System (INIS)

    In, Y.; Bogatu, I.N.; Kim, J.S.; Garofalo, A.M.; Jackson, G.L.; La Haye, R.J.; Schaffer, M.J.; Strait, E.J.; Lanctot, M.J.; Reimerdes, H.; Marrelli, L.; Martin, P.; Okabayashi, M.

    2010-01-01

    Active feedback control in the DIII-D tokamak has fully stabilized the current-driven ideal kink resistive-wall mode (RWM). While complete stabilization is known to require both low frequency error field correction (EFC) and high frequency feedback, unambiguous identification has been made about the distinctive role of each in a fully feedback-stabilized discharge. Specifically, the role of direct RWM feedback, which nullifies the RWM perturbation in a time scale faster than the mode growth time, cannot be replaced by low frequency EFC, which minimizes the lack of axisymmetry of external magnetic fields. (letter)

  19. Nonlinear dynamics in micromechanical and nanomechanical resonators and oscillators

    Science.gov (United States)

    Dunn, Tyler

    In recent years, the study of nonlinear dynamics in microelectromechanical and nanoelectromechanical systems (MEMS and NEMS) has attracted considerable attention, motivated by both fundamental and practical interests. One example is the phenomenon of stochastic resonance. Previous measurements have established the presence of this counterintuitive effect in NEMS, showing that certain amounts of white noise can effectively amplify weak switching signals in nanomechanical memory elements and switches. However, other types of noise, particularly noises with 1/falpha spectra, also bear relevance in these and many other systems. At a more fundamental level, the role which noise color plays in stochastic resonance remains an open question in the field. To these ends, this work presents systematic measurements of stochastic resonance in a nanomechanical resonator using 1/f alpha and Ornstein-Uhlenbeck noise types. All of the studied noise spectra induce stochastic resonance, proving that colored noise can also be beneficial; however, stronger noise correlations suppress the effect, decreasing the maximum signal-to-noise ratio and increasing the optimal noise intensity. Evidence suggests that 1/falpha noise spectra with increasing noise color lead to increasingly asymmetric switching, reducing the achievable amplification. Another manifestly nonlinear effect anticipated in these systems is modal coupling. Measurements presented here demonstrate interactions between various mode types on a wide scale, providing the first reported observations of coupling in bulk longitudinal modes of MEMS. As a result of anharmonic elastic effects, each mode shifts in frequency by an amount proportional to the squared displacement (or energy) of a coupled mode. Since all resonator modes couple in this manner, these effects enable nonlinear measurement of energy and mechanical nonlinear signal processing across a wide range of frequencies. Finally, while these experiments address nonlinear

  20. On nonlinear stability in various random normed spaces

    Directory of Open Access Journals (Sweden)

    Saadati Reza

    2011-01-01

    Full Text Available Abstract In this article, we prove the nonlinear stability of the quartic functional equation 1 6 f ( x + 4 y + f ( 4 x - y = 3 0 6 9 f x + y 3 + f ( x + 2 y (1 + 1 3 6 f ( x - y - 1 3 9 4 f ( x + y + 4 2 5 f ( y - 1 5 3 0 f ( x (2 (3  in the setting of random normed spaces Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the theory of fixed point theory, the theory of intuitionistic spaces and the theory of functional equations are also presented in the article.

  1. Stabilization of the hypersonic boundary layer by finite-amplitude streaks

    Science.gov (United States)

    Ren, Jie; Fu, Song; Hanifi, Ardeshir

    2016-02-01

    Stabilization of two-dimensional disturbances in hypersonic boundary layer flows by finite-amplitude streaks is investigated using nonlinear parabolized stability equations. The boundary-layer flows at Mach numbers 4.5 and 6.0 are studied in which both first and second modes are supported. The streaks considered here are driven either by the so-called optimal perturbations (Klebanoff-type) or the centrifugal instability (Görtler-type). When the streak amplitude is in an appropriate range, i.e., large enough to modulate the laminar boundary layer but low enough to not trigger secondary instability, both first and second modes can effectively be suppressed.

  2. Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary

    International Nuclear Information System (INIS)

    Chattopadhyay, S.; Audy, P.; Courant, E.D.

    1988-07-01

    A summary and commentary of the available theoretical and analytical tools and recent advances in the nonlinear dynamics, stability and aperture issues in storage rings are presented. 11 refs., 4 figs

  3. Unconditional nonlinear exponential stability in the Benard problem; Stabilita' nonlineare esponenziale incondizionata nel problema di Be'nard per ina miscela: condizioni necessarie e sufficienti.

    Energy Technology Data Exchange (ETDEWEB)

    Mulione, G. [Catania, Univ. (Italy). Dip. di Matematica; Rionero, S. [Napoli, Univ. (Italy). Dip. di Matematica e applicazioni

    1998-07-01

    The Lyapunov direct method is applied to study nonlinear stability of a basic motionless state to imposed linear temperature and concentration fields of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme. Stress-free and rigid surfaces are considered and absence of Hopf bifurcation is assumed. We prove the coincidence of the linear and (unconditional) nonlinear critical stability limits, when the ratio between the Schmidt and the Prandtl numbers is less or equal to 1. Precisely, we obtain necessary and sufficient conditions of unconditional nonlinear exponential stability of the basic motionless state. [Italian] Si applica il metodo diretto di Lyapunov allo studio della stabilita' non lineare esponenziale della soluzione di conduzione-diffusione di una miscela fluida binaria riscaldata e salata da sotto, nello schema di Oberbeck-Boussinesq. Si considerano superfici rigide e 'stress-free'; si supponeche non ci sia biforcazione di Hpf. Supposto che il rapporto fra i numeri di Schmidt e di Prandtl e' minore o uguale a 1, si prova la coincidenza tra i paramentri critici della stabilita' lineare e non lineare. Si ottengono condizioni necessarie e sufficienti di stabilita' non lineare esponenziale del moto base.

  4. Harnessing mode-selective nonlinear optics for on-chip multi-channel all-optical signal processing

    Directory of Open Access Journals (Sweden)

    Ming Ma

    2016-11-01

    Full Text Available All-optical signal processing based on nonlinear optical effects allows for the realization of important functions in telecommunications including wavelength conversion, optical multiplexing/demultiplexing, Fourier transformation, and regeneration, amongst others, on ultrafast time scales to support high data rate transmission. In integrated photonic subsystems, the majority of all-optical signal processing systems demonstrated to date typically process only a single channel at a time or perform a single processing function, which imposes a serious limitation on the functionality of integrated solutions. Here, we demonstrate how nonlinear optical effects can be harnessed in a mode-selective manner to perform simultaneous multi-channel (two and multi-functional optical signal processing (i.e., regenerative wavelength conversion in an integrated silicon photonic device. This approach, which can be scaled to a higher number of channels, opens up a new degree of freedom for performing a broad range of multi-channel nonlinear optical signal processing functions using a single integrated photonic device.

  5. Assessment of Slope Stability and Interference of Structures Considering Seismity in Complex Engineering-Geological Conditions Using the Method of Finite Elements

    International Nuclear Information System (INIS)

    Menabdishvili, Papuna; Eremadze, Nelly

    2008-01-01

    There is elaborated the calculation model of slope deformation mode stability and the methodic of calculation considering the interference of structures to be built on it using the method of finite elements. There is examined the task of slope stability using the soil physically nonlinear finite element considering the seismicity 8. The deformation mode and field of coefficients of stability are obtained and slope supposed sliding curve is determined. The elaborated calculation methodic allows to determine the slope deformation mode, stability and select the optimum version of structure foundation at any slant and composition of slope layers

  6. Airfoil stall interpreted through linear stability analysis

    Science.gov (United States)

    Busquet, Denis; Juniper, Matthew; Richez, Francois; Marquet, Olivier; Sipp, Denis

    2017-11-01

    Although airfoil stall has been widely investigated, the origin of this phenomenon, which manifests as a sudden drop of lift, is still not clearly understood. In the specific case of static stall, multiple steady solutions have been identified experimentally and numerically around the stall angle. We are interested here in investigating the stability of these steady solutions so as to first model and then control the dynamics. The study is performed on a 2D helicopter blade airfoil OA209 at low Mach number, M 0.2 and high Reynolds number, Re 1.8 ×106 . Steady RANS computation using a Spalart-Allmaras model is coupled with continuation methods (pseudo-arclength and Newton's method) to obtain steady states for several angles of incidence. The results show one upper branch (high lift), one lower branch (low lift) connected by a middle branch, characterizing an hysteresis phenomenon. A linear stability analysis performed around these equilibrium states highlights a mode responsible for stall, which starts with a low frequency oscillation. A bifurcation scenario is deduced from the behaviour of this mode. To shed light on the nonlinear behavior, a low order nonlinear model is created with the same linear stability behavior as that observed for that airfoil.

  7. Microgrid Stability Controller Based on Adaptive Robust Total SMC

    DEFF Research Database (Denmark)

    Su, Xiaoling; Han, Minxiao; Guerrero, Josep M.

    2015-01-01

    This paper presents a microgrid stability controller (MSC) in order to provide existing DGs the additional functionality of working in islanding mode without changing their control strategies in grid-connected mode and to enhance the stability of the microgrid. Microgrid operating characteristics....... The MSC provides fast dynamic response and robustness to the microgrid. When the system is operating in grid-connected mode, it is able to improve the controllability of the exchanged power between the microgrid and the utility grid, while smoothing DG’s output power. When the microgrid is operating...... and mathematical models of the MSC indicate that the system is inherently nonlinear and time-variable. Therefore, this paper proposes an adaptive robust total sliding-mode control (ARTSMC) system for the MSC. It is proved that the ARTSMC system is insensitive to parametric uncertainties and external disturbances...

  8. Nonlinear control of voltage source converters in AC-DC power system.

    Science.gov (United States)

    Dash, P K; Nayak, N

    2014-07-01

    This paper presents the design of a robust nonlinear controller for a parallel AC-DC power system using a Lyapunov function-based sliding mode control (LYPSMC) strategy. The inputs for the proposed control scheme are the DC voltage and reactive power errors at the converter station and the active and reactive power errors at the inverter station of the voltage-source converter-based high voltage direct current transmission (VSC-HVDC) link. The stability and robust tracking of the system parameters are ensured by applying the Lyapunov direct method. Also the gains of the sliding mode control (SMC) are made adaptive using the stability conditions of the Lyapunov function. The proposed control strategy offers invariant stability to a class of systems having modeling uncertainties due to parameter changes and exogenous inputs. Comprehensive computer simulations are carried out to verify the proposed control scheme under several system disturbances like changes in short-circuit ratio, converter parametric changes, and faults on the converter and inverter buses for single generating system connected to the power grid in a single machine infinite-bus AC-DC network and also for a 3-machine two-area power system. Furthermore, a second order super twisting sliding mode control scheme has been presented in this paper that provides a higher degree of nonlinearity than the LYPSMC and damps faster the converter and inverter voltage and power oscillations. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  9. Rotational and magnetic shear stabilization of magnetohydrodynamic modes and turbulence in DIII-D high performance discharges

    International Nuclear Information System (INIS)

    Lao, L.L.; Burrell, K.H.; Casper, T.S.

    1996-08-01

    The confinement and the stability properties of the DIII-D tokamak high performance discharges are evaluated in terms of rotational and magnetic shear with emphasis on the recent experimental results obtained from the negative central magnetic shear (NCS) experiments. In NCS discharges, a core transport barrier is often observed to form inside the NCS region accompanied by a reduction in core fluctuation amplitudes. Increasing negative magnetic shear contributes to the formation of this core transport barrier, but by itself is not sufficient to fully stabilize the toroidal drift mode (trapped- electron-η i mode) to explain this formation. Comparison of the Doppler shift shear rate to the growth rate of the η i mode suggests that the large core E x B flow shear can stabilize this mode and broaden the region of reduced core transport . Ideal and resistive stability analysis indicates the performance of NCS discharges with strongly peaked pressure profiles is limited by the resistive interchange mode to low Β N < 2.3. This mode is insensitive to the details of the rotational and the magnetic shear profiles. A new class of discharges which has a broad region of weak or slightly negative magnetic shear (WNS) is described. The WNS discharges have broader pressure profiles and higher values than the NCS discharges together with high confinement and high fusion reactivity

  10. Homogeneous Stabilizer by State Feedback for Switched Nonlinear Systems Using Multiple Lyapunov Functions’ Approach

    Directory of Open Access Journals (Sweden)

    Hui Ye

    2017-01-01

    Full Text Available This paper investigates the problem of global stabilization for a class of switched nonlinear systems using multiple Lyapunov functions (MLFs. The restrictions on nonlinearities are neither linear growth condition nor Lipschitz condition with respect to system states. Based on adding a power integrator technique, we design homogeneous state feedback controllers of all subsystems and a switching law to guarantee that the closed-loop system is globally asymptotically stable. Finally, an example is given to illustrate the validity of the proposed control scheme.

  11. Univariate and Bivariate Empirical Mode Decomposition for Postural Stability Analysis

    Directory of Open Access Journals (Sweden)

    Jacques Duchêne

    2008-05-01

    Full Text Available The aim of this paper was to compare empirical mode decomposition (EMD and two new extended methods of  EMD named complex empirical mode decomposition (complex-EMD and bivariate empirical mode decomposition (bivariate-EMD. All methods were used to analyze stabilogram center of pressure (COP time series. The two new methods are suitable to be applied to complex time series to extract complex intrinsic mode functions (IMFs before the Hilbert transform is subsequently applied on the IMFs. The trace of the analytic IMF in the complex plane has a circular form, with each IMF having its own rotation frequency. The area of the circle and the average rotation frequency of IMFs represent efficient indicators of the postural stability status of subjects. Experimental results show the effectiveness of these indicators to identify differences in standing posture between groups.

  12. Mode-locking peculiarities in an all-fiber erbium-doped ring ultrashort pulse laser with a highly-nonlinear resonator

    Science.gov (United States)

    Dvoretskiy, Dmitriy A.; Sazonkin, Stanislav G.; Kudelin, Igor S.; Orekhov, Ilya O.; Pnev, Alexey B.; Karasik, Valeriy E.; Denisov, Lev K.

    2017-12-01

    Today ultrashort pulse (USP) fiber lasers are in great demand in a frequency metrology field, THz pulse spectroscopy, optical communication, quantum optics application, etc. Therefore mode-locked (ML) fiber lasers have been extensively investigated over the last decade due the number of scientific, medical and industrial applications. It should be noted, that USP fiber lasers can be treated as an ideal platform to expand future applications due to the complex ML nonlinear dynamics in a laser resonator. Up to now a series of novel ML regimes have been investigated e.g. self-similar pulses, noise-like pulses, multi-bound solitons and soliton rain generation. Recently, we have used a highly nonlinear germanosilicate fiber (with germanium oxides concentration in the core 50 mol. %) inside the resonator for more reliable and robust launching of passive mode-locking based on the nonlinear polarization evolution effect in fibers. In this work we have measured promising and stable ML regimes such as stretched pulses, soliton rain and multi-bound solitons formed in a highly-nonlinear ring laser and obtained by intracavity group velocity dispersion (GVD) variation in slightly negative region. As a result, we have obtained the low noise ultrashort pulse generation with duration 59 dB) and relative intensity noise <-101 dBc / Hz.

  13. Feedback and rotational stabilization of resistive wall modes in ITER

    International Nuclear Information System (INIS)

    Liu Yueqiang; Bondeson, A.; Chu, M.S.; La Haye, R.J.; Favez, J.-Y.; Lister, J.B.; Gribov, Y.; Gryaznevich, M.; Hender, T.C.; Howell, D.F.

    2005-01-01

    Different models have been introduced in the stability code MARS-F in order to study the damping effect of resistive wall modes (RWM) in rotating plasmas. Benchmark of MARS-F calculations with RWM experiments on JET and D3D indicates that the semi-kinetic damping model is a good candidate for explaining the damping mechanisms. Based on these results, the critical rotation speeds required for RWM stabilization in an advanced ITER scenario are predicted. Active feedback control of the n = 1 RWM in ITER is also studied using the MARS-F code. (author)

  14. Stability of tearing modes in tokamak plasmas

    International Nuclear Information System (INIS)

    Hegna, C.C.; Callen, J.D.

    1994-02-01

    The stability properties of m ≥ 2 tearing instabilities in tokamak plasmas are analyzed. A boundary layer theory is used to find asymptotic solutions to the ideal external kink equation which are used to obtain a simple analytic expression for the tearing instability parameter Δ'. This calculation generalizes previous work on this topic by considering more general toroidal equilibria (however, toroidal coupling effects are ignored). Constructions of Δ' are obtained for plasmas with finite beta and for islands that have nonzero width. A simple heuristic estimate is given for the value of the saturated island width when the instability criterion is violated. A connection is made between the calculation of the asymptotic matching parameter in the finite beta and island width case to the nonlinear analog of the Glasser effect

  15. Two-Dimensional Fuzzy Sliding Mode Control of a Field-Sensed Magnetic Suspension System

    Directory of Open Access Journals (Sweden)

    Jen-Hsing Li

    2014-01-01

    Full Text Available This paper presents the two-dimensional fuzzy sliding mode control of a field-sensed magnetic suspension system. The fuzzy rules include both the sliding manifold and its derivative. The fuzzy sliding mode control has advantages of the sliding mode control and the fuzzy control rules are minimized. Magnetic suspension systems are nonlinear and inherently unstable systems. The two-dimensional fuzzy sliding mode control can stabilize the nonlinear systems globally and attenuate chatter effectively. It is adequate to be applied to magnetic suspension systems. New design circuits of magnetic suspension systems are proposed in this paper. ARM Cortex-M3 microcontroller is utilized as a digital controller. The implemented driver, sensor, and control circuits are simpler, more inexpensive, and effective. This apparatus is satisfactory for engineering education. In the hands-on experiments, the proposed control scheme markedly improves performances of the field-sensed magnetic suspension system.

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

    Science.gov (United States)

    Peter, Simon; Leine, Remco I.

    2017-11-01

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

  17. Passive impedance-based second-order sliding mode control for non-linear teleoperators

    Directory of Open Access Journals (Sweden)

    Luis G García-Valdovinos

    2017-02-01

    Full Text Available Bilateral teleoperation systems have attracted significant attention in the last decade mainly because of technological advancements in both the communication channel and computers performance. In addition, non-linear multi-degree-of-freedom bilateral teleoperators along with state observers have become an open research area. In this article, a model-free exact differentiator is used to estimate the full state along with a chattering-free second-order sliding mode controller to guarantee a robust impedance tracking under both constant and an unknown time delay of non-linear multi-degree-of-freedom robots. The robustness of the proposed controller is improved by introducing a change of coordinates in terms of a new nominal reference similar to that used in adaptive control theory. Experimental results that validate the predicted behaviour are presented and discussed using a Phantom Premium 1.0 as the master robot and a Catalyst-5 virtual model as the slave robot. The dynamics of the Catalyst-5 system is solved online.

  18. Stability of ideal and resistive modes in cylindrical plasmas with resistive walls and plasma rotation

    International Nuclear Information System (INIS)

    Bondeson, A.; Xie, H.X.

    1996-01-01

    The stabilization of cylindrical plasmas by resistive walls combined with plasma rotation is analyzed. Perturbations with a single mode rational surface q=m/n in a finitely conducting plasma are treated by the resistive kink dispersion relation of Coppi. The possibilities for stabilization of ideal and resistive instabilities are explored systematically in different regions of parameter space. The study confirms that an ideal instability can be stabilized by a close-fitting wall and a rotation velocity of the order of resistive growth rate. However, the region in parameter space where such stabilization occurs is very small and appears to be difficult to exploit in experiments. The overall conclusion from the cylindrical plasma model is that resistive modes can readily be wall stabilized, whereas complete wall stabilization is hard to achieve for plasmas that are ideally unstable with the wall at infinity. 26 refs, 5 figs

  19. Effect of the X-point on the stability of the edge-current-driven MHD mode in Tokamaks

    International Nuclear Information System (INIS)

    Kwon, Ohjin

    2010-01-01

    Quasi-periodic bursts of edge magnetohydrodynamic (MHD) activities, called edge localized modes (ELMs), have been observed in many tokamaks during the H-mode. The high level of heat and particle transport associated with ELMs may cause serious damage to divertors or plasma facing components. It is therefore important to understand the underlying physics of ELMs. We have numerically investigated the effect of the X-point on the stability of the peeling mode, which is thought to be one of the MHD instabilities responsible for small ELMs. Equilibria with pressure and current profiles, which are unstable to the pure peeling mode for moderately elongated plasma, have been used. The X-point in a diverted plasma has been simulated by introducing of a hump in the plasma boundary. The position, depth and width of the X-point have been varied, and their effect on the stability of the peeling mode has been investigated. We have shown that the peeling mode growth rate decreases as the depth increases. This effect is greater for smaller widths for all positions of the X-point considered. Therefore, a sharper X-point is more efficient in stabilizing the peeling mode. Increasing the depth acts to increase the magnetic shear, the stabilizing effect of which has been shown to have very little dependence on the position or the width of the X-point.

  20. Quantitative comparison of electron temperature fluctuations to nonlinear gyrokinetic simulations in C-Mod Ohmic L-mode discharges

    Energy Technology Data Exchange (ETDEWEB)

    Sung, C., E-mail: csung@physics.ucla.edu [University of California, Los Angeles, Los Angeles, California 90095 (United States); White, A. E.; Greenwald, M.; Howard, N. T. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Mikkelsen, D. R.; Churchill, R. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Holland, C. [University of California, San Diego, La Jolla, California 92093 (United States); Theiler, C. [Ecole Polytechnique Fédérale de Lausanne, SPC, Lausanne 1015 (Switzerland)

    2016-04-15

    Long wavelength turbulent electron temperature fluctuations (k{sub y}ρ{sub s} < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (k{sub y}ρ{sub s} ≲ 1.7) performed at r/a ∼ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the “Transport Shortfall” [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].