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...
Stabilization of switched nonlinear systems with unstable modes
Yang, Hao; Cocquempot, Vincent
2014-01-01
This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant systems in space- and aircraft; traffic control; and heat propagation control of semiconductor power chips. The practical background is emphasized throughout the book; interesting practical examples frequently illustrate the theoretical results with aircraft and spacecraft given particular prominence. Stabilization of Switched Nonlinear Systems with Unstable Modes treats several different subclasses of SNS according to the characteristics of the individual system (time-varying and distributed parameters, for example), the state composition of individual modes and the degree and distribution of instability in its various modes. Achievement and maintenance of stability across the system as a whole is bolstered by trading off between individual modes which may be either stable or unstable, or by exploiting areas of part...
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
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
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
Nonlinear MHD simulations of the gravitational ballooning mode close to marginal stability
International Nuclear Information System (INIS)
Myers, S A; Dudson, B D; Wilson, H R
2013-01-01
The ballooning mode is thought to play a key role in the mechanism which drives the problematic edge localized modes in tokamak plasmas, and possibly in other plasma eruptions, such as in the magnetosphere. We investigate the essential nonlinear physics of this mode by simulating an instability driven by gravity in a slab of magnetized plasma; magnetic field curvature plays a similar role in toroidal confinement systems. Full ideal magnetohydrodynamics (MHD) simulations are performed, which exhibit three distinct phases of the mode's evolution: (I) a linear phase that agrees well with the predictions of linear ideal MHD; (II) a non-linear regime where the instantaneous growth rate evolves, and is somewhat lower than the linear value and (III) an explosive plasma eruption. These regimes are characterized and compared with the predictions of analytic nonlinear theory, considering cases that are close to and far from marginal stability. Evidence of a subcritical instability is demonstrated in phase II where, provided the mode's amplitude is large enough, it can develop into an eruption even for values of gravity that give linear stability. The drop in growth rate during phase II depends on the strength of the linear drive, demonstrating that the initial phases of the nonlinear evolution are also dependent on the strength of the linear drive. To extend the calculations deeper into the nonlinear regime a four-field reduced MHD model is developed, which reproduces the same features as the full ideal MHD system. (paper)
Controlling the stability of nonlinear optical modes via electromagnetically induced transparency
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.
Existence, Stability and Dynamics of Nonlinear Modes in a 2D PartiallyPT Symmetric Potential
Directory of Open Access Journals (Sweden)
Jennie D’Ambroise
2017-02-01
Full Text Available It is known that multidimensional complex potentials obeying parity-time(PTsymmetry may possess all real spectra and continuous families of solitons. Recently, it was shown that for multi-dimensional systems, these features can persist when the parity symmetry condition is relaxed so that the potential is invariant under reﬂection in only a single spatial direction. We examine the existence, stability and dynamical properties of localized modes within the cubic nonlinear Schrödinger equation in such a scenario of partiallyPT-symmetric potential.
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.
International Nuclear Information System (INIS)
Ayten, B.; Westerhof, E.
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 previously by Harvey et al (1989 Phys. Rev. Lett. 62 426). We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker–Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a typical NTM stabilization experiment on ASDEX Upgrade. A particular feature of these experiments is that the rays of the EC wave beam propagate tangential to the flux surfaces in the power deposition region. The calculations show significant non-linear effects on the ECCD efficiency, when the ECCD power is increased from its experimental value of 1 MW to a larger value of 4 MW. The nonlinear effects are largest in the case of locked islands or when the magnetic island rotation period is longer than the collisional time scale. The non-linear effects result in an overall reduction of the current drive efficiency for this case with absorption of the EC power on the low-field side of the electron cyclotron resonance layer. As a consequence of the non-linear effects, also the stabilizing effect of the ECCD on the island is reduced from linear expectations. (paper)
Effect of nonlinear energy transport on neoclassical tearing mode stability in tokamak plasmas
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.
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
Nonlinear Interchange Modes in 3D
Bagaipo, Jupiter; Hassam, Adil
2012-10-01
We have shown previously that, in 2D, the ideal magnetohydrodynamic interchange mode stabilized by a constant transverse magnetic field is nonlinearly unstable if near marginal conditions. This study is extended to a 3D system where the mode is marginally stabilized by allowing for wavenumbers weakly transverse to an axial field. Two different boundary conditions are studied: periodic and line-tied in the axial direction. Periodic boundary conditions have applications in toroidal fusion devices while line-tied systems are common in the solar corona. We use reduced equations for a strong axial field to find an analytic solution as a function of the deviation from marginality. Using a systematic perturbation analysis we show that, to lowest order, there exists a secondary, quasistatic equilibrium with a critical field strength. Allowing for deviations from criticality yield a nonlinear time-evolution equation for the perturbation amplitude. The periodic case allows for two types of modes, and it is shown that the mode isomorphic to the earlier 2D problem is nonlinearly unstable, while the ``sausage''-type mode is nonlinearly stable. These modes are modes along a rational surface and ballooning type modes, respectively. The line-tied case is shown to always be nonlinearly stable.
Dissipative double-well potential: Nonlinear stationary and pulsating modes
International Nuclear Information System (INIS)
Zezyulin, Dmitry A.; Konotop, Vladimir V.; Alfimov, Georgy L.
2010-01-01
The analysis of nonlinear modes in a complex absorbing double-well potential supported by linear gain is presented. Families of the nonlinear modes and their bifurcations are found numerically by means of the properly modified 'shooting' method. Linear stability and dynamics of the modes are studied. It is shown that no stable modes exist in the case of attractive nonlinearity, while stable modes, including nonsymmetric ones, are found when the nonlinearity is repulsive. Varying a control parameter (e.g., the height of barrier between the wells) results in switching from one mode to another. Apart from stationary modes we have found pulsating solutions emergent from unstable modes.
Nonlinear saturation of the trapped-ion mode
International Nuclear Information System (INIS)
LaQuey, R.E.; Mahajan, S.M.; Rutherford, P.H.; Tang, W.M.
1974-11-01
A nonlinear model of the collisional trapped-ion mode in tokamak geometry is presented, in which the energy in long wavelength instabilities is transferred to short wavelength modes which are then damped by ion bounce resonances. Near marginal stability, the saturation of a single unstable Fourier mode is computed. Far from marginal stability, steady state nonlinear solitary waves containing many Fourier modes are found. Particle transport is computed in both cases. (auth)
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.
Nonlinear stability of supersonic jets
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.
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
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)
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
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
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
Nonlinear modes of clarinet-like musical instruments
Noreland, Daniel; Bellizzi, Sergio; Vergez, Christophe; Bouc, Robert
2009-07-01
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second-order ordinary differential equations is obtained. The equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed. The system is treated using an amplitude-phase formulation for nonlinear modes, where the frequency and damping functions, as well as the invariant manifolds in the phase space, are unknowns to be determined. The formulation gives, without explicit integration of the underlying ordinary differential equation, access to the transient, the limit cycle, its period and stability. The process is illustrated for a model reduced to three normal modes of the air column.
Control design of a nonlinear controller to stabilize the nonlinear ...
African Journals Online (AJOL)
This article presents the design of a highly efficient nonlinear0 controller which is a kind of an Active Queue Management (AQM) scheme to stabilize the nonlinear TCP model dynamics. Specific boundary conditions have been considered for stability occurrences and have been compared with other existing Active Queue ...
Mode control and mode conversion in nonlinear aluminum nitride waveguides.
Stegmaier, Matthias; Pernice, Wolfram H P
2013-11-04
While single-mode waveguides are commonly used in integrated photonic circuits, emerging applications in nonlinear and quantum optics rely fundamentally on interactions between modes of different order. Here we propose several methods to evaluate the modal composition of both externally and device-internally excited guided waves and discuss a technique for efficient excitation of arbitrary modes. The applicability of these methods is verified in photonic circuits based on aluminum nitride. We control modal excitation through suitably engineered grating couplers and are able to perform a detailed study of waveguide-internal second harmonic generation. Efficient and broadband power conversion between orthogonal polarizations is realized within an asymmetric directional coupler to demonstrate selective excitation of arbitrary higher-order modes. Our approach holds promise for applications in nonlinear optics and frequency up/down-mixing in a chipscale framework.
GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems
Directory of Open Access Journals (Sweden)
P. C. Chen
2008-01-01
Full Text Available Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC or an adaptive fuzzy sliding mode controller (AFSMC capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
desired trajectory. In Bandhyopadhyay and Deepak (2009), nonlinear sliding surface is created for varying the damping factor for improving the performance of the multi-input and multi-output linear systems with matched conditions. Some of the concepts and theoretical advances of continuous time sliding mode control are ...
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
On the nonlinear stability of dissipative fluids
International Nuclear Information System (INIS)
Tasso, H.; Camargo, S.J.
1991-02-01
A general sufficient condition for nonlinear stability of steady and unsteady flows in hydrodynamics and magnetohydrodynamics is derived. It leads to strong limitations in the Reynolds and magnetic Reynolds numbers. It is applied to the stability of generalized time-dependent planar Couette flows in magnetohydrodynamics. Reynolds and magnetic Reynolds numbers have to be typically less than 2π 2 for stability. (orig.)
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
Nonlinear and Non-ideal Effects on FRC Stability
International Nuclear Information System (INIS)
Belova, E.V.; Davidson, R.C.; Ji, H.; Yamada, M.
2002-01-01
New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). We present results of hybrid and two-fluid (Hall-MHD) simulations of prolate FRCs in strongly kinetic and small-gyroradius, MHD-like regimes. The n = 1 tilt instability mechanism and stabilizing factors are investigated in detail including nonlinear and resonant particle effects, particle losses along the open field lines, and Hall stabilization. It is shown that the Hall effect determines the mode rotation and change in the linear mode structure in the kinetic regime; however, the reduction in the growth rate is mostly due to the finite Larmor radius effects. Resonant particle effects are important in the large gyroradius regime regardless of the separatrix shape, and even in cases when a large fraction of the particle orbits are stochastic. Particle loss along the open field lines has a destabilizing effect on the tilt mode and contributes to the ion spin up in toroidal direction. The nonlinear evolution of unstable modes in both kinetic and small-gyroradius FRCs is shown to be considerably slower than that in MHD simulations. Our simulation results demonstrate that a combination of kinetic and nonlinear effects is a key for understanding the experimentally observed FRC stability properties
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.
Terminal Sliding Modes In Nonlinear Control Systems
Venkataraman, Subramanian T.; Gulati, Sandeep
1993-01-01
Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.
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
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.
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...
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
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
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
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.)
Nonlinear Stability and Structure of Compressible Reacting Mixing Layers
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.
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.)
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.
A robust nonlinear stabilizer as a controller for improving transient stability in micro-grids.
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.
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
This method is termed as Feshbach resonance management or nonlinearity management. The other method is called dispersion management as it involves periodic modulation of the dispersion term of the nonlinear evolution equa- tion which can stabilize soliton solutions. An experimental investigation of nonlinearity.
Structural stability of nonlinear population dynamics
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.
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)
Sliding mode control for a two-joint coupling nonlinear system based on extended state observer.
Zhao, Ling; Cheng, Haiyan; Wang, Tao
2018-02-01
A two-joint coupling nonlinear system driven by pneumatic artificial muscles is introduced in this paper. A sliding mode controller with extended state observer is proposed to cope with nonlinearities and disturbances for the two-joint coupling nonlinear system. In addition, convergence of the extended state observer is presented and stability analysis of the closed-loop system is also demonstrated with the sliding mode controller. Lastly, some experiments are carried out to show the reality effectiveness of the proposed method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
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)
Improved algorithm for solving nonlinear parabolized stability equations
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).
Stability of magnetic modes in tokamaks
International Nuclear Information System (INIS)
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
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
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali, E-mail: bikash.midya@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Advanced Center for Nonlinear and Complex Phenomena, Kolkata 700075 (India)
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Intrinsic localized modes and nonlinear impurity modes in curved ...
Indian Academy of Sciences (India)
structure of the localized modes induced by an isotopic light-mass impurity in this chain. We further demonstrate that a ... direct physical meaning and can describe polymers and biomolecular systems. The motion of the chain is confined to .... mode center (n = 0) the local mode must obey the expression (10). Equation (8).
Rafiq, T.; Kritz, A. H.; Weiland, J.; Luo, L.; Schuster, E.
2018-01-01
A reduced transport model for microtearing modes is developed for use in integrated predictive modeling studies, employing a unified fluid/kinetic approach to derive the nonlinear dispersion relation. This approach advances the kinetic description and allows the inclusion of nonlinear effects due to magnetic fluctuations. In this numerical study, the dependence of the microtearing mode real frequency and growth rate on plasma parameters and on DIII-D like L-mode and H-mode plasma profiles is examined. The magnetic fluctuation strength as well as electron thermal diffusivity due to microtearing modes is computed. The saturated amplitude of the magnetic fluctuations is calculated utilizing numerically determined microtearing mode eigenvalues in the nonlinear microtearing modes envelope equation. It is found that the electron temperature gradient in the presence of moderate collision frequency is required for the microtearing mode to become unstable. The effects of small and large collisionality and small and large wavenumbers on microtearing modes are found to be stabilizing, while the effects of density gradient, plasma beta, low current density, and large magnetic shear are found to be destabilizing. The microtearing mode growth rate, magnetic fluctuation strength, as well as electron thermal diffusivity is found to be larger in the H-mode plasma than in the L-mode plasma.
Influence of the linear mode coupling on the nonlinear impairments in few-mode fibers
DEFF Research Database (Denmark)
Kutluyarov, R.V.; Lyubopytov, V.S.; Bagmanov, V.Kh
2017-01-01
This paper is focused on the influence of the linear mode coupling caused by the fiber bending on the nonlinear distortions in a mode-division multiplexed system. The system under test utilizes the fundamental Gaussian mode and the conjugated first-order vortex modes propagating in the step-index...
Nonlinear evolution of drift cyclotron modes
International Nuclear Information System (INIS)
Aamodt, R.E.; Cohen, B.I.; Lee, Y.C.; Liu, C.S.; Nicholson, D.R.; Rosenbluth, M.N.
1981-01-01
The space-time evolution of the drift-cyclotron instability as influenced by the nonlinear shift in the ion-cyclotron frequency is studied analytically, numerically, and by computer simulation. The analysis is specialized to the case of a single coherent wave with frequency near both a cyclotron harmonic and the ion diamagnetic frequency. Such an analysis is motivated by observations of large-amplitude ion-cyclotron waves in the 2XIIB mirror experiment, which were highly monochromatic and often exhibited these frequency characteristics. A nonlinear dispersion relation describing saturation of the instability is derived by means of a self-consistent analytical solution of the Vlasov--Poisson equations to third order in the wave amplitude. Solitary wave and self-similar solutions are obtained that describe nonlinear wave propagation. Numerical solution of a nonlinear evolution equation and particle simulation confirm the analysis
Stochastic modeling of mode interactions via linear parabolized stability equations
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.
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.
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.
Nonlinear stability of a brane wormhole
Akai, Yumi; Nakao, Ken-ichi
2017-07-01
We analytically study the nonlinear stability of a spherically symmetric wormhole supported by an infinitesimally thin brane of negative tension, which has been devised by Barcelo and Visser. We consider a situation in which a thin spherical shell composed of dust falls into an initially static wormhole; the dust shell plays the role of the nonlinear disturbance. The self-gravity of the falling dust shell is completely taken into account through Israel's formalism of the metric junction. When the dust shell goes through the wormhole, it necessarily collides with the brane supporting the wormhole. We assume the interaction between these shells is only gravity and show the condition under which the wormhole stably persists after the dust shell goes through it.
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.
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
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.
Multi-bi- and tri-stability using nonlinear plasmonic Fano resonators
Amin, Muhammad
2013-09-01
A plasmonic Fano resonator embedding Kerr nonlinearity is used to achieve multi-bi- and tri-stability. Fano resonance is obtained by inducing higher-order plasmon modes on metallic surfaces via geometrical symmetry breaking. The presence of the multiple higher order plasmon modes provides the means for producing multi-bi- or tri-stability in the response of the resonator when it is loaded with a material with Kerr nonlinearity. The multi-stability in the response of the proposed resonator enables its use in three-state all optical memory and switching applications. © 2013 IEEE.
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.
Nonlinear mirror mode dynamics: Simulations and modeling
Czech Academy of Sciences Publication Activity Database
Califano, F.; Hellinger, Petr; Kuznetsov, E.; Passot, T.; Sulem, P. L.; Trávníček, Pavel
2008-01-01
Roč. 113, - (2008), A08219/1-A08219/20 ISSN 0148-0227 R&D Projects: GA AV ČR IAA300420702; GA AV ČR IAA300420602 Grant - others:PECS(CZ) 98024 Institutional research plan: CEZ:AV0Z30420517 Keywords : mirror instability * nonlinear evolution * numerical simulations * magnetic holes * mirror structures * kinetic plasma instabilities Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.147, year: 2008
Chattering-Free Sliding-Mode Control for Electromechanical Actuator with Backlash Nonlinearity
Directory of Open Access Journals (Sweden)
Dongqi Ma
2017-01-01
Full Text Available Considering the backlash nonlinearity and parameter time-varying characteristics in electromechanical actuators, a chattering-free sliding-mode control strategy is proposed in this paper to regulate the rudder angle and suppress unknown external disturbances. Different from most existing backlash compensation methods, a special continuous function is addressed to approximate the backlash nonlinear dead-zone model. Regarding the approximation error, unmodeled dynamics, and unknown external disturbances as a disturbance-like term, a strict feedback nonlinear model is established. Based on this nonlinear model, a chattering-free nonsingular terminal sliding-mode controller is proposed to achieve the rudder angle tracking with a chattering elimination and tracking dynamic performance improvement. A Lyapunov-based proof ensures the asymptotic stability and finite-time convergence of the closed-loop system. Experimental results have verified the effectiveness of the proposed method.
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications
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.
Nonlinear electron cloud modification of satellite modes
International Nuclear Information System (INIS)
Stettner, R.; Sveum, M.D.
1984-01-01
A one-dimensional circuit analog of the modes of a triaxial satellite is derived. Self consistent one-dimensional particle calculations utilizing this model are presented. The results suggest that electrons arriving at the satellite from tank walls and damper in an SGEMP experiment, can under some circumstances, materially affect the response of the satellite
Nonlinear plastic modes in disordered solids
Gartner, L.; Lerner, E.
We propose a theoretical framework within which a robust micromechanical definition of precursors to plastic instabilities, often termed soft spots, naturally emerges. They are shown to be collective displacements (modes) ˆz that correspond to local minima of a barrier function b(ˆz), which depends
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
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...
Integrability and Linear Stability of Nonlinear Waves
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.
Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes
2016-04-20
of the LVLH frame with respect to an inertial frame, expressed in LVLH coordinates, is given by ω = [0, 0, n]T ∈ R3, where n = √ µ/r3c is the mean ...AFRL-RV-PS- AFRL-RV-PS- TR-2015-0182 TR-2015-0182 CHARACTERIZATION OF NON-LINEARIZED SPACECRAFT RELATIVE MOTION USING NONLINEAR NORMAL MODES Eric...Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F
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
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.
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
Fuzzy Sliding Mode Controller Design Using Takagi-Sugeno Modelled Nonlinear Systems
Directory of Open Access Journals (Sweden)
S. Bououden
2013-01-01
Full Text Available Adaptive fuzzy sliding mode controller for a class of uncertain nonlinear systems is proposed in this paper. The unknown system dynamics and upper bounds of the minimum approximation errors are adaptively updated with stabilizing adaptive laws. The closed-loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded. The performance and stability of the proposed control system are achieved analytically using the Lyapunov stability theory. Simulations show that the proposed controller performs well and exhibits good performance.
Robust discrete-time nonlinear sliding mode controller with plant ...
African Journals Online (AJOL)
This paper addresses the new control algorithm, by designing the asymptotically stable nonlinear sliding surface with investigation of the states. This proposed algorithm leads to solve the problem of unstable systems, by proving the asymptotic stability of a class of uncertain discrete-time systems. A particular linear ...
Martin, Roberta I; Sakamoto, João M S; Teixeira, Marcelo C M; Martinez, Guilherme A; Pereira, Fernando C; Kitano, Cláudio
2017-03-20
This work presents a novel nonlinear control system designed for interferometry based on variable structure control and sliding modes. This approach can fully compensate the nonlinear behavior of the interferometer and lead to high accuracy control for large disturbances, featuring low cost, ease of implementation and high robustness, without a reset circuit (when compared with a linear control system). A deep stability analysis was accomplished and the global asymptotic stability of the system was proved. The results showed that the nonlinear control is able to keep the interferometer in the quadrature point and suppress signal fading for arbitrary signals, sinusoidal signals, or zero input signal, even under strong external disturbances. The system showed itself suitable to characterize a multi-axis piezoelectric flextentional actuator, which displacements that are much smaller than half wavelength. The high robustness allows the system to be embedded and to operate in harsh environments as factories, bringing the interferometry outside the laboratory.
Control Design of a Nonlinear Controller to Stabilize the Nonlinear ...
African Journals Online (AJOL)
inyangs
AQM) scheme employing .... A nonlinear control design is considered for application in this case, so that when there is any change in network .... shows that the system is asymptotically stable with a negative definite solution in equation (14).
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
Stability of tearing modes in tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Hegna, C.C.; Callen, J.D.
1994-02-01
The stability properties of m {ge} 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 {Delta}{prime}. This calculation generalizes previous work on this topic by considering more general toroidal equilibria (however, toroidal coupling effects are ignored). Constructions of {Delta}{prime} 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.
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
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.
Olazabal-Loumé, M.; Breil, J.; Hallo, L.; Ribeyre, X.; Sanz, J.
2011-01-01
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.
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.
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
Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations
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.
Nonlinear terahertz coherent excitation of vibrational modes of liquids.
Allodi, Marco A; Finneran, Ian A; Blake, Geoffrey A
2015-12-21
We report the first coherent excitation of intramolecular vibrational modes via the nonlinear interaction of a TeraHertz (THz) light field with molecular liquids. A terahertz-terahertz-Raman pulse sequence prepares the coherences with a broadband, high-energy, (sub)picosecond terahertz pulse, that are then measured in a terahertz Kerr effect spectrometer via phase-sensitive, heterodyne detection with an optical pulse. The spectrometer reported here has broader terahertz frequency coverage, and an increased sensitivity relative to previously reported terahertz Kerr effect experiments. Vibrational coherences are observed in liquid diiodomethane at 3.66 THz (122 cm(-1)), and in carbon tetrachloride at 6.50 THz (217 cm(-1)), in exact agreement with literature values of those intramolecular modes. This work opens the door to 2D spectroscopies, nonlinear in terahertz field, that can study the dynamics of condensed-phase molecular systems, as well as coherent control at terahertz frequencies.
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)
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...
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
Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System
Directory of Open Access Journals (Sweden)
Zhanshan Zhao
2015-01-01
Full Text Available A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme.
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)
Sausage mode stability boundaries: enumeration and verification
International Nuclear Information System (INIS)
Chambers, F.W.
1980-01-01
An axially symmetric sausage mode instability has been observed using particle simulation codes to propagate beams with a high degree of current neutralization. In this report the stability boundaries in terms of the magnitude and location of the return current are delineated for beams with square, Gaussian, and Bennett radial current profiles using the theoretical analysis of others. For the case in which the return current is held fixed as the beam propagates, a detailed comparison is made between the theoretical predictions and the results of the RINGFAST single disk particle simulation code. Agreement between theory and code results is good although the code results do show a slightly larger than predicted unstable region
Uniform stability of damped nonlinear vibrations of an elastic string
Indian Academy of Sciences (India)
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is ...
New stability conditions for nonlinear time varying delay systems
Elmadssia, S.; Saadaoui, K.; Benrejeb, M.
2016-07-01
In this paper, new practical stability conditions for a class of nonlinear time varying delay systems are proposed. The study is based on the use of a specific state space description, known as the Benrejeb characteristic arrow form matrix, and aggregation techniques to obtain delay-dependent stability conditions. Application of this method to delayed Lurie-Postnikov nonlinear systems is given. Illustrative examples are presented to show the effectiveness of the proposed approach.
Some Thoughts on Stability in Nonlinear Periodic Focusing Systems [Addendum
McMillan, Edwin M.
1968-03-29
Addendum to September 5, 1967 report with the same title and with the abstract: A brief discussion is given of the long-term stability of particle motions through periodic focusing structures containing lumped nonlinear elements. A method is presented whereby one can specify the nonlinear elements in such a way as to generate a variety of structures in which the motion has long-term stability.
Advanced nonlinear stability analysis of boiling water nuclear reactors
Lange, Carsten
2009-01-01
This thesis is concerned with nonlinear analyses of BWR stability behaviour, contributing to a deeper understanding in this field. Despite negative feedback-coefficients of a BWR, there are operational points (OP) at which oscillatory instabilities occur. So far, a comprehensive and an in-depth understanding of the nonlinear BWR stability behaviour are missing, even though the impact of the significant physical parameters is well known. In particular, this concerns parameter regions in whi...
Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control
Nguyen, Nhan T.; Boskovic, Jovan D.
2008-01-01
This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.
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
Nonlinear dynamo mode dynamics in reversed field pinches
International Nuclear Information System (INIS)
Fitzpatrick, Richard; Yu, Edmund P.
2000-01-01
The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the so-called ''slinky mode'' locks in some reversed field pinch devices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research. (c) 2000 American Institute of Physics
Nonlinear dynamo mode dynamics in reversed field pinches
Fitzpatrick, Richard; Yu, Edmund P.
2000-09-01
The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the so-called "slinky mode" locks in some reversed field pinch devices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research.
Nonlinear dynamo mode dynamics in reversed field pinches
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, Richard [Institute for Fusion Studies, Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States); Yu, Edmund P. [Institute for Fusion Studies, Department of Physics, University of Texas at Austin, Austin, Texas 78712 (United States)
2000-09-01
The nonlinear dynamics of a typical dynamo mode in a reversed field pinch, under the action of the braking torque due to eddy currents excited in a resistive vacuum vessel and the locking torque due to a resonant error-field, is investigated. A simple set of phase evolution equations for the mode is derived: these equations represent an important extension of the well-known equations of Zohm et al. [Europhys. Lett. 11, 745 (1990)] which incorporate a self-consistent calculation of the radial extent of the region of the plasma which corotates with the mode; the width of this region being determined by plasma viscosity. Using these newly developed equations, a comprehensive theory of the influence of a resistive vacuum vessel on error-field locking and unlocking thresholds is developed. Under certain circumstances, a resistive vacuum vessel is found to strongly catalyze locked mode formation. Hopefully, the results obtained in this paper will allow experimentalists to achieve a full understanding of why the so-called ''slinky mode'' locks in some reversed field pinch devices, but not in others. The locking of the slinky mode is currently an issue of outstanding importance in reversed field pinch research. (c) 2000 American Institute of Physics.
Low-cost sliding mode control of WECS based on DFIG with stability analysis
DJOUDI, ABDELHAK; CHEKIREB, HACHEMI; BERKOUK, EL MADJID; BACHA, SEDDIK
2015-01-01
The aim of this work is to developing sliding mode control of active and reactive stator powers produced by a wind energy conversion system (WECS), based on doubly fed induction generator (DFIG). A flux estimation model and rotor current sensor are no longer required. The controller is developed from the DFIG nonlinear-coupled model. Moreover, the global stability and the DFIG states' boundedness when our low-cost sliding mode control is applied are established analytically. It is re...
Sharp nonlinear stability for centrifugal filtration convection in magnetizable media.
Saravanan, S; Brindha, D
2011-11-01
A nonlinear stability theory is adopted to study centrifugal thermal convection in a magnetic-fluid-saturated and differentially heated porous layer placed in a zero-gravity environment. The axis of rotation of the layer is placed within its boundaries that leads to an alternating direction of the centrifugal body force. An analysis through the variational principles is made to find the unconditional and sharp nonlinear limits. The compound matrix method is employed to solve the eigenvalue problems of the nonlinear and corresponding linear theories. The importance of nonlinear theory is established by demonstrating the failure of the linear theory in capturing the physics of the onset of convection.
Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.
Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong
2014-12-01
In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.
Control Design of a Nonlinear Controller to Stabilize the Nonlinear ...
African Journals Online (AJOL)
inyangs
is used to formularize the delay differential equation in equation. (13), which accounts for the delayed terms in the system. By applying the Leibniz integration rule, the derivative. •. V shows that the system is asymptotically stable with a negative definite solution in equation (14). The conditions for the stability are: •. The delay ...
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
Verifying of reciprocal relations for nonlinear quadripole in unsteady mode
Bardin, Alexey; Ignatjev, Vyacheslav; Orlov, Andrey; Perchenko, Sergey
This paper deals with experimental verification of reciprocal relations of nonlinear quadripole for unsteady mode in external magnetic field. We find out transients of measured voltages in the quadripole after current switch. These transients are caused by changing of current-voltage characteristics (CVC) of quadripole. We propose the reciprocal relations for linear part of full resistance matrix and its experimental verification method based on algorithm of separation of resistance matrix linear part. It is shown that the proposed reciprocal relations are valid with 10-3 relatively accuracy even for non-stationary case in external magnetic field.
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
Robust stabilization of nonlinear systems: The LMI approach
Directory of Open Access Journals (Sweden)
iljak 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.
Analysis of vibrating structures with localized nonlinearities using nonlinear normal modes
International Nuclear Information System (INIS)
Moussi, E.H.
2013-01-01
This work is a collaboration between EDF R and D and the Laboratory of Mechanics and Acoustics. The objective is to develop theoretical and numerical tools to compute nonlinear normal modes (NNMs) of structures with localized nonlinearities. We use an approach combining the harmonic balance and the asymptotic numerical methods, known for its robustness principally for smooth systems. Regularization techniques are used to apply this approach for the study of non-smooth problems. Moreover, several aspects of the method are improved to allow the computation of NNMs for systems with a high number of degrees of freedom (DOF). Finally, the method is implemented in Code-Aster, an open-source finite element solver developed by EDF R and D. The nonlinear normal modes of a two degrees-of-freedom system are studied and some original characteristics are observed. These observations are then used to develop a methodology for the study of systems with a high number of DOFs. The developed method is finally used to compute the NNMs for a model U-tube of a nuclear plant steam generator. The analysis of the NNMs reveals the presence of an interaction between an out-of-plane (low frequency) and an in-plane (high frequency) modes, a result also confirmed by the experiment. This modal interaction is not possible using linear modal analysis and confirms the interest of NNMs as a diagnostic tool in structural dynamics. (author) [fr
Fault-tolerant nonlinear adaptive flight control using sliding mode online learning.
Krüger, Thomas; Schnetter, Philipp; Placzek, Robin; Vörsmann, Peter
2012-08-01
An expanded nonlinear model inversion flight control strategy using sliding mode online learning for neural networks is presented. The proposed control strategy is implemented for a small unmanned aircraft system (UAS). This class of aircraft is very susceptible towards nonlinearities like atmospheric turbulence, model uncertainties and of course system failures. Therefore, these systems mark a sensible testbed to evaluate fault-tolerant, adaptive flight control strategies. Within this work the concept of feedback linearization is combined with feed forward neural networks to compensate for inversion errors and other nonlinear effects. Backpropagation-based adaption laws of the network weights are used for online training. Within these adaption laws the standard gradient descent backpropagation algorithm is augmented with the concept of sliding mode control (SMC). Implemented as a learning algorithm, this nonlinear control strategy treats the neural network as a controlled system and allows a stable, dynamic calculation of the learning rates. While considering the system's stability, this robust online learning method therefore offers a higher speed of convergence, especially in the presence of external disturbances. The SMC-based flight controller is tested and compared with the standard gradient descent backpropagation algorithm in the presence of system failures. Copyright © 2012 Elsevier Ltd. All rights reserved.
Disturbance observer based sliding mode control of nonlinear mismatched uncertain systems
Ginoya, Divyesh; Shendge, P. D.; Phadke, S. B.
2015-09-01
This paper presents a new design of multiple-surface sliding mode control for a class of nonlinear uncertain systems with mismatched uncertainties and disturbances. In the method of multiple-surface sliding mode control, it is required to compensate for the derivatives of the virtual inputs which gives rise to the so-called problem of 'explosion of terms'. In this paper a disturbance observer based multiple-surface sliding mode control is proposed to estimate the uncertainties as well as the derivative of the virtual inputs to overcome this problem. The practical stability of the overall system is proved. The effectiveness of the proposed control strategy is illustrated via simulation of a benchmark problem and comparison with other control strategies. The proposed scheme is validated by implementing it on a serial flexible joint manipulator in the laboratory.
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
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-nonlineari......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...... to a significant increase of the nonlinear distortions. It is necessary to take this phenomenon into account in SDM systems with linear compensation of mode coupling, because the nonlinear distortions may sufficiently decrease the effectiveness of the compensation....
On the non-linear stability of scalar field cosmologies
Energy Technology Data Exchange (ETDEWEB)
Alho, Artur; Mena, Filipe C [Centro de Matematica, Universidade do Minho, 4710-057 Braga (Portugal); Kroon, Juan A Valiente, E-mail: aalho@math.uminho.pt, E-mail: fmena@math.uminho.pt, E-mail: jav@maths.qmul.ac.uk [School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
2011-09-22
We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.
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
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.
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.
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
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.
Nonlinear Stability of MKdV Breathers
DEFF Research Database (Denmark)
Alejo Plana, Miguel Angel; Muñoz, Claudio
2013-01-01
Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H 2 topology. Our proof introduces a new Lyapunov functional, at the H 2 level, which allows to describe the dynamics of small perturbations, including oscillations induced by the periodicit...... of the solution, as well as a direct control of the corresponding instability modes. In particular, degenerate directions are controlled using low-regularity conservation laws....
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
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
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.
High-mode-number ballooning modes in a heliotron/torsatron system: 2, Stability
Energy Technology Data Exchange (ETDEWEB)
Nakajima, N.
1996-05-01
In heliotron/torsantron 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 standaxd stability calculations or observed in experiments on the Compact Helical System, 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 {omega} {sup 2} to have a strong field line dependence through the strong dependence of the local magnetic curvature, such that the level surfaces of {omega} {sup 2} ({psi}, {theta} {sub k}, {alpha}), (<0) become spheroids in ({theta} {sub k}, {alpha}) space, where {psi} labels flux surfaces and {theta} {sub k} is the radial wavenumber. Because the spheroidal level surfaces for unstable eigenvalues are surrounded by level surfaces for stable eigenvalues of high-mode-number toroidal Alfven 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.
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...
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...
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)
Nonlinear eigen-mode structures in complex astroclouds
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.
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)
Stability of non-linear constitutive formulations for viscoelastic fluids
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.
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.
Robust stabilization of nonlinear systems by quantized and ternary control
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
Robust Stability Analysis of Nonlinear Switched Systems with Filippov Solutions
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
This paper addresses the stability problem of a class of nonlinear switched systems with partitioned state-space and state-dependent switching. In lieu of the Caratheodory solutions, the general Filippov solutions are considered. This encapsulates solutions with infinite switching in finite time....... which provides sufficient means to construct the corresponding Lyapunov functions via available semi-definite programming techniques....
Nonlinear stability analysis of the frame structures
Directory of Open Access Journals (Sweden)
Ćorić Stanko
2016-01-01
Full Text Available In this paper the phenomenon of instability of frames in elasto-plastic domain was investigated. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to exact solution of the differential equation of bending according to the second order theory. When the buckling of structure occurs in plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et. Tangent modulus is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. For the purposes of numerical investigation in this analysis, part of the computer program ALIN was created in a way that this program now can be used for elastic and elasto-plastic stability analysis of frame structures. This program is developed in the C++ programming language. Using this program, it is possible to calculate the critical load of frames in the elastic and inelastic domain. In this analysis, the algorithm for the calculation of buckling lengths of compressed columns of the frames was also established. The algorithm is based on the calculation of the global stability analysis of frame structures. Results obtained using this algorithm were compared with the approximate solutions from the European (EC3 and national (JUS standards for the steel structures. By the given procedure in this paper it is possible to follow the behavior of the plane frames in plastic domain and to calculate the real critical load in that domain.
Stabilization Approaches for Linear and Nonlinear Reduced Order Models
Rezaian, Elnaz; Wei, Mingjun
2017-11-01
It has been a major concern to establish reduced order models (ROMs) as reliable representatives of the dynamics inherent in high fidelity simulations, while fast computation is achieved. In practice it comes to stability and accuracy of ROMs. Given the inviscid nature of Euler equations it becomes more challenging to achieve stability, especially where moving discontinuities exist. Originally unstable linear and nonlinear ROMs are stabilized here by two approaches. First, a hybrid method is developed by integrating two different stabilization algorithms. At the same time, symmetry inner product is introduced in the generation of ROMs for its known robust behavior for compressible flows. Results have shown a notable improvement in computational efficiency and robustness compared to similar approaches. Second, a new stabilization algorithm is developed specifically for nonlinear ROMs. This method adopts Particle Swarm Optimization to enforce a bounded ROM response for minimum discrepancy between the high fidelity simulation and the ROM outputs. Promising results are obtained in its application on the nonlinear ROM of an inviscid fluid flow with discontinuities. Supported by ARL.
Nonlinear stability and time step selection for the MPM method
Berzins, Martin
2018-01-01
The Material Point Method (MPM) has been developed from the Particle in Cell (PIC) method over the last 25 years and has proved its worth in solving many challenging problems involving large deformations. Nevertheless there are many open questions regarding the theoretical properties of MPM. For example in while Fourier methods, as applied to PIC may provide useful insight, the non-linear nature of MPM makes it necessary to use a full non-linear stability analysis to determine a stable time step for MPM. In order to begin to address this the stability analysis of Spigler and Vianello is adapted to MPM and used to derive a stable time step bound for a model problem. This bound is contrasted against traditional Speed of sound and CFL bounds and shown to be a realistic stability bound for a model problem.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Stability of nonlinear ion sound waves and solitons in plasmas
International Nuclear Information System (INIS)
Infeld, E.; Rowlands, G.
1979-01-01
Large amplitude ion acoustic waves and solitons in two component plasmas are investigated for stability. The soliton solutions are found to be stable, while the nonlinear waves are always unstable, though for a significant range of parameters they are only unstable to fully three-dimensional perturbations. The results in one dimension are compared with those obtained from the Korteweg-de Vries equation, which gives stability for non linear waves and solitons. Agreement is surprisingly good for Mach numbers less than about 1.5 A three-dimensional generalization of the Korteweg-de Vries equation is considered but this leads to stability for all non linear solutions and hence is not a good model for nonlinear waves. It is, however, reasonable in the soliton limit. (author)
Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator.
Nguyen, Sy Dzung; Vo, Hoang Duy; Seo, Tae-Il
2017-09-01
It is difficult to efficiently control nonlinear systems in the presence of uncertainty and disturbance (UAD). One of the main reasons derives from the negative impact of the unknown features of UAD as well as the response delay of the control system on the accuracy rate in the real time of the control signal. In order to deal with this, we propose a new controller named CO-FSMC for a class of nonlinear control systems subjected to UAD, which is constituted of a fuzzy sliding mode controller (FSMC) and a fuzzy-based compensator (CO). Firstly, the FSMC and CO are designed independently, and then an adaptive fuzzy structure is discovered to combine them. Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed. Based on the solutions, fuzzy sliding mode technique, lumped disturbance observer and Lyapunov stability analysis, a closed-loop adaptive control law is formulated. Simulations along with a real application based on a semi-active train-car suspension are performed to fully evaluate the method. The obtained results reflected that vibration of the chassis mass is insensitive to UAD. Compared with the other fuzzy sliding mode control strategies, the CO-FSMC can provide the best control ability to reduce unwanted vibrations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Simplified laser frequency stabilization using spatial-mode interference
National Aeronautics and Space Administration — We will demonstrate a laser frequency stabilization technique based on spatial-mode interference that promises reductions in complexity, mass and power consumption...
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
On the Stability of Three-Dimensional Boundary Layers. Part 1; Linear and Nonlinear Stability
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.
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)
Nonlinear analysis of dynamic stability for the thin cylindrical shells of supercavitating vehicles
Directory of Open Access Journals (Sweden)
Hai An
2016-12-01
Full Text Available The dynamic stability of supercavitating vehicles under periodic axial loading is investigated in this article. The supercavitating vehicle is simulated as a long and thin cylindrical shell subjected to periodic axial loading and simply supported boundary conditions. The nonlinear transverse vibration differential equation is obtained in terms of nonlinear geometric equations, physical equations, and balance equations of cylindrical shells. Mathieu equation with periodic coefficients and nonlinear term is derived by employing Galerkin variational method and Bolotin method. The analytical expressions of the steady-state amplitudes of vibrations in the first- and second-order instable regions are obtained by solving nonlinear Mathieu equation derived in this article. Numerical results are presented to analyze the influence of the sailing speed, ratio of loads, the frequency of axial loads, and the mode of vibration on parametric resonance curves and to show the nonlinear parametric resonance curves incline toward the side where it is greater than the excitation frequency, which significantly extends the range of the exciting region. The presented results indicate the enlargement of the exciting region will cause shrinkage of the safe frequency range of external loads and decrease in dynamic stability of supercavitating vehicle.
On Reynolds stress and neutral azimuthal modes in the stability ...
Indian Academy of Sciences (India)
geneous flow result of Maslowe & Nigam. It is also proved that singular neutral modes do not exist whenever the value of the Richardson number at the critical layer exceeds one quarter. Keywords. Hydrodynamic stability; swirling flows; inviscid flows; variable density;. Reynolds stress. 1. Introduction. The stability of swirling ...
International Nuclear Information System (INIS)
Jammazi, Chaker
2009-01-01
The paper gives Lyapunov type sufficient conditions for partial finite-time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.
A single mode method for the analysis and identification of nonlinear MDOF systems
Huang, Liping; Iwan, W. D.
In order to apply mode approach to describe a nonlinear system, the concept of modal response of nonlinear systems is examined, and an amplitude-dependent modal model is presented based on an analysis of a single mode of response. The effectiveness of this model is examined under different types and various levels of excitation. A corresponding identification procedure for cubic systems is proposed and applied to the analysis of a 3DOF soltening nonlinear system.
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)
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
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
2015-09-23
Sep 23, 2015 ... We discuss about the theory of nonlinear localized excitations, such as soliton and compactons in the gap of the linear spectrum of the nonlinear systems. We show how the gap originates in the linear spectrum using examples of a few systems, such as nonlinear lattices, Bose–Einstein condensates in ...
Directory of Open Access Journals (Sweden)
You Zheng
2015-01-01
Full Text Available An adaptive second-order sliding mode controller is proposed for a class of nonlinear systems with unknown input. The proposed controller continuously drives the sliding variable and its time derivative to zero in the presence of disturbances with unknown boundaries. A Lyapunov approach is used to show finite time stability for the system in the presence of a class of uncertainty. An illustrative simulation example is presented to demonstrate the performance and robustness of the proposed controller.
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.
pth Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations
Directory of Open Access Journals (Sweden)
Xuetao Yang
2014-01-01
Full Text Available We are concerned with the exponential stability problem of a class of nonlinear hybrid stochastic heat equations (known as stochastic heat equations with Markovian switching in an infinite state space. The fixed point theory is utilized to discuss the existence, uniqueness, and pth moment exponential stability of the mild solution. Moreover, we also acquire the Lyapunov exponents by combining the fixed point theory and the Gronwall inequality. At last, two examples are provided to verify the effectiveness of our obtained results.
Directory of Open Access Journals (Sweden)
Ghazanfar Shahgholian
2010-01-01
Full Text Available This paper presents a new method for designing of power system stabilizer (PSS based on sliding mode control (SMC technique. The control objective is to enhance stability and improve the dynamic response of the multi-machine power system. The mathematical model of the synchronous generator is first transformed into a form that facilitates the design of nonlinear control schemes. Then, a sliding mode controller is proposed. In order to test effectiveness of the proposed scheme, simulation will be carried out to analyze the small signal stability characteristics of the system about the steady state operating condition following the change in the parameters of the system and to the disturbances. For comparison, simulation of a conventional control PSS (lead-lag compensation type will be carried out. The main approach is to focus on the control performance which later is proven to have the degree of shorter reaching time and lower spike.
International Nuclear Information System (INIS)
Cheng, Po-Jen; Chen, Cha'o-Kuang; Lai, Hsin-Yi
2001-01-01
This article investigates the weakly nonlinear stability theory of a thin pseudoplastic liquid film flowing down on a vertical wall. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equation with free film interface. The normal mode approach is used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg - Landau equation. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a pseudoplastic film flow system. The results also reveal that the pseudoplastic liquid film flows are less stable than Newtonian's as traveling down along the vertical wall. The degree of instability in the film flow is further intensified by decreasing the flow index n. [copyright] 2001 American Institute of Physics
Dynamics of Nonlinear Excitation of the High-Order Mode in a Single-Mode Step-Index Optical Fiber
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.
Helical vortices: linear stability analysis and nonlinear dynamics
Selçuk, C.; Delbende, I.; Rossi, M.
2018-02-01
We numerically investigate, within the context of helical symmetry, the dynamics of a regular array of two or three helical vortices with or without a straight central hub vortex. The Navier–Stokes equations are linearised to study the instabilities of such basic states. For vortices with low pitches, an unstable mode is extracted which corresponds to a displacement mode and growth rates are found to compare well with results valid for an infinite row of point vortices or an infinite alley of vortex rings. For larger pitches, the system is stable with respect to helically symmetric perturbations. In the nonlinear regime, we follow the time-evolution of the above basic states when initially perturbed by the dominant instability mode. For two vortices, sequences of overtaking events, leapfrogging and eventually merging are observed. The transition between such behaviours occurs at a critical ratio involving the core size and the vortex-separation distance. Cases with three helical vortices are also presented.
Geometrical Nonlinear Aeroelastic Stability Analysis of a Composite High-Aspect-Ratio Wing
Directory of Open Access Journals (Sweden)
Chang Chuan Xie
2008-01-01
Full Text Available A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN, and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.
Study of nonlinear system stability using eigenvalue analysis: Gyroscopic motion
Shabana, Ahmed A.; Zaher, Mohamed H.; Recuero, Antonio M.; Rathod, Cheta
2011-11-01
General computational multibody system (MBS) algorithms allow for the linearization of the highly nonlinear equations of motion at different points in time in order to obtain the eigenvalue solution. This eigenvalue solution of the linearized equations is often used to shed light on the system stability at different configurations that correspond to different time points. Different MBS algorithms, however, employ different sets of orientation coordinates, such as Euler angles and Euler parameters, which lead to different forms of the dynamic equations of motion. As a consequence, the forms of the linearized equations and the eigenvalue solution obtained strongly depend on the set of orientation coordinates used. This paper addresses this fundamental issue by examining the effect of the use of different orientation parameters on the linearized equations of a gyroscope. The nonlinear equations of motion of the gyroscope are formulated using two different sets of orientation parameters: Euler angles and Euler parameters. In order to obtain a set of linearized equations that can be used to define the eigenvalue solution, the algebraic equations that describe the MBS constraints are systematically eliminated leading to a nonlinear form of the equations of motion expressed in terms of the system degrees of freedom. Because in MBS applications the generalized forces can be highly nonlinear and can depend on the velocities, a state space formulation is used to solve the eigenvalue problem. It is shown in this paper that the independent state equations formulated using Euler angles and Euler parameters lead to different eigenvalue solutions. This solution is also different from the solution obtained using a form of the Newton-Euler matrix equation expressed in terms of the angular accelerations and angular velocities. A time-domain solution of the linearized equations is also presented in order to compare between the solutions obtained using two different sets of
Stability of nonlinear repetitive processes with possible failures
Directory of Open Access Journals (Sweden)
J. P. Emelianova
2014-01-01
Full Text Available Nonlinear discrete-time repetitive processes with Markovian jumps are considered. For such processes stability analysis is developed and this result is then applied to iterative learning control design.Stability of nonlinear repetitive processes has not been developed previously in the current literature. This paper proposes and characterizes a stability theory for nonlinear repetitive processes that includes stability along the pass of linear examples as a special case.For considered systems the second Lyapunov method cannot be used. Because repetitive processes belong to a class of 2D systems in which state variables are depend on two independent variables and cannot be solved using all first differences of state variables. It is not allow us to find a first difference of Lyapunov function along the trajectory of the system without finding solution of a system of equations that fully excludes a main advantage of second Lyapunov method. At the same time the use of vector Lyapunov functions and discrete-time counterpart of the divergence operator of this function along the trajectories of system instead of first difference allow us to obtain constructive results.In this paper based on vector Lyapunov function approach sufficient conditions for pass profile exponential stability are obtained which in the linear case are obtained in terms of linear matrix inequalities and in the linear case without failures these conditions are reduced to known conditions of stability along the passA major application area where repetitive process stability theory can be used is Iterative Learning Control (ILC. The idea of ILC is following.If the system repeats the same finite duration operation over and over again, it is reasonable to use the input and output variables on the current pass for improving accuracy of performance of operations on the next pass.The new theoretical stability results are applied to ILC design under possible information failures. The ILC
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
A Nonlinear Coupled-Mode System for Water Waves over a General Bathymetry
Athanassoulis, G. A.; Belibassakis, K. A.
2003-04-01
in the local-mode series References Athanassoulis, G. A. Belibassakis, K. A.: A Consistent Coupled-Mode Theory for the Propagation of Small-Amplitude Water Waves over Variable Bathymetry Regions. J. Fluid Mech. 389, 275--301, 1999. Athanassoulis, G. A. Belibassakis, K. A.: A Complete Modal Expansion of the Wave Potential and Its Application to Linear and Nonlinear Water-Wave Problems, Proc. "Rogue Waves 2000", Brest, France, 29--30 November 2000. Belibassakis, K. A. Athanassoulis, G. A. Extension of second-order Stokes theory to variable bathymetry, J. Fluid Mech. 464, 35--80, 2002. Luke, J. C.: A Variational Principle for a Fluid with a Free Surface. J. Fluid Mech. 27, 395--397, 1967. Petrov, A. A.: Variational Statement of the Problem of Liquid Motion in a Container of Finite Dimensions. PMM, 28 (4), 917--922, 1964. Zakharov, V. E.: Stability of Periodic Waves of Finite Amplitude on the Surface of a Deep Fluid. J. Appl. Math. Tech. Phys., 2 190, 1968.
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.
Transverse stability in multibunch mode for CLIC
International Nuclear Information System (INIS)
Guignard, G.
1993-01-01
In order to reach the desired luminosity with 250 GeV per beam, multibunch operation (limited to 4 bunches, say) might have to be considered in the CERN linear collider (CLIC). One limitation comes from the coupling of the bunch motion with the long-range transverse wake fields that may induce beam breakup. These wake fields have therefore to be controlled, and means of reducing their effects on the beam are discussed in a companion paper. One possibility consists in detuning the dipole modes in the cells to obtain decoherent contributions and hence reduce the field amplitude at the downstream bunch location. The important question is to know below which value this amplitude must be limited to prevent intolerable beam breakup. In a first attempt at estimating this threshold for CLIC two approaches are considered, i.e. the criterion developed at SLAC and based on the convergence of the multibunch-motion solution, and numerical simulations of two-bunch motion in a focusing lattice
Surpassing the energy method for nonlinear fluid stability
Goluskin, David; Fuentes, Federico
2017-11-01
A basic question in fluid stability is whether a laminar flow is nonlinearly stable to all perturbations. The typical way to verify stability, called the energy method, is to show that the energy of a perturbation must decay monotonically. The energy method is known to be overly conservative in many systems, particularly when turbulence arises subcritically, such as in parallel shear flows. The energy method is a special case of a Lyapunov function method in which the Lyapunov function is the perturbation energy. This talk will present a more general approach in which the Lyapunov functions (1) are not restricted to being quadratic but instead are higher-degree polynomials, and (2) can depend explicitly on the spectrum of the velocity field in the eigenbasis of the energy stability operator. The optimal construction of such Lyapunov functions is complicated but can be done with computer assistance by formulating a polynomial optimization problem, which in turn is formulated as a semidefinite program. This talk will describe the general framework of the method. A companion talk by Federico Fuentes will illustrate its application to planar Couette flow, where we have verified nonlinear stability at larger Reynolds numbers than is possible using the energy method.
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.
Third-order resonance effects and the nonlinear stability of drop oscillations
Natarajan, Ramesh; Brown, Robert A.
1987-01-01
The three-dimensional nonlinear oscillations of an isolated, inviscid drop with surface tension are studied by a multiple timescale analysis and pre-averaging applied to the variational principle for the appropriate Lagrangian. Amplitude equations are derived which describe the generic cubic resonance caused by the spatial degeneracy of the eigenfrequencies of the linear normal modes. This resonant coupling leads to the instability of the finite amplitude axisymmetric oscillations to small nonaxisymmetric perturbations, as is demonstrated here for the three- and four-lobed normal modes. Solutions to the interaction equations that describe finite amplitude, nonaxisymmetric traveling-wave solutions are also obtained and their stability is investigated. A nongeneric cubic resonance between the two-lobed and four-lobed oscillatory modes leads to quasi-periodic motions.
Diode array pumped, non-linear mirror Q-switched and mode-locked ...
Indian Academy of Sciences (India)
Abstract. 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 ...
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 ...
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 ...
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.
Nonlinear growth of a single neoclassical MHD tearing mode in a tokamak
International Nuclear Information System (INIS)
Qu, W.X.; Callen, J.D.
1985-10-01
The nonlinear evolution equation for the growth of a single neoclassical MHD tearing mode is derived from the usual resistive MHD equations with neoclassical effects included. For the case Δ' > 0 where the usual resistive MHD modes are unstable, in nonlinear neoclassical MHD there is an intermediate time regime in which the island width w grows only as t/sup 1/2/. However, eventually the neoclassical MHD tearing modes are found to enter the usual resistive MHD Rutherford regime where w infinity t. Physically, the neoclassical MHD bootstrap current effects modify the linear and early nonlinear growth of tearing modes. However, eventually the magnetic islands flatten the pressure gradient within the island to remove these effects and return, at long times, to the usual quasilinear picture for the nonlinear evolution of a single resistive MHD tearing mode
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....../softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples...
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)
Coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers.
Zhang, Junshi; Chen, Hualing; Li, Bo; McCoul, David; Pei, Qibing
2015-10-14
This article describes the development of an analytical model to study the coupled nonlinear oscillation and stability evolution of viscoelastic dielectric elastomers (DEs) under non-equibiaxial tensile forces by utilizing the method of virtual work. Numerically calculated results are employed to predict this nonlinear dynamic behavior. The resonant frequency (where the amplitude-frequency response curve peaks) and the amplitude-frequency response of the deformation in both in-plane directions are tuned by varying the values of tensile force. The oscillation response in the two in-plane directions exhibits strong nonlinearity and coupling with each other, and is tuned by the changing tensile forces under a specific excitation frequency. By varying the values of tensile forces, the dynamic viscoelastic creep in a certain in-plane direction can be eliminated. Phase diagrams and Poincaré maps under several values of tensile forces are utilized to study the stability evolution of the DE system under non-equibiaxial tensile forces.
Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.
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.
Studies of impact of plasma shaping on edge localized modes with a nonlinear code BOUT + +
Li, G. Q.; Xu, X. Q.; Snyder, P. B.; Turnbull, A. D.; Xia, T. Y.
2014-10-01
The plasma shaping has important effects on the edge localized modes (ELMs). In this work, with the 3-field BOUT + + code, we study the impact of the plasma shaping on the ELMs. Three kinds of typical plasma shapes are studied: circular (cbm), elongated (dbm) and shaped with X-point (meudas). Our calculations show that the shaped plasma and the X-point geometry have stabilizing effect on the ELMs. For linear ideal MHD calculation we benchmark BOUT + + results with ELITE and GATO codes. Then we study the role of non-ideal effects such as resistivity on the ELMs for the X-point geometry. Also the nonlinear calculations are carried out to study the impact of plasma shape on the ELM size. Work supported by China National Magnetic Confinement Fusion Science Program under Grant Nos. 2014GB106001 and 2013GB111000. Also performed for USDOE by LLNL under DE-AC52-07NA27344. LLNL-ABS-656997.
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
2015-09-23
Sep 23, 2015 ... Home; Journals; Pramana – Journal of Physics; Volume 85; Issue 5 ... We discuss about the theory of nonlinear localized excitations, such as soliton and compactons in the gap of the linear spectrum of the nonlinear systems. ... Department of Physics, Savitribai Phule Pune University, Pune 411 007, India ...
Transient stability improvement by nonlinear controllers based on tracking
Energy Technology Data Exchange (ETDEWEB)
Ramirez, Juan M. [Centro de Investigacion y Estudios Avanzados, Guadalajara, Mexico. Av. Cientifica 1145. Col. El Bajio. Zapopan, Jal. 45015 (Mexico); Arroyave, Felipe Valencia; Correa Gutierrez, Rosa Elvira [Universidad Nacional de Colombia, Sede Medellin. Facultad de Minas, Escuela de Mecatronica (Colombia)
2011-02-15
This paper deals with the control problem in multi-machine electric power systems, which represent complex great scale nonlinear systems. Thus, the controller design is a challenging problem. These systems are subjected to different perturbations, such as short circuits, connection and/or disconnection of loads, lines, or generators. Then, the utilization of controllers which guarantee good performance under those perturbations is required in order to provide electrical energy to the loads with admissible stability margins. The proposed controllers are based on a systematic strategy, which calculate nonlinear controllers for generating units in a power plant, both for voltage and velocity regulation. The formulation allows designing controllers in a multi-machine power system without intricate calculations. Results on a power system of the open research indicate the proposition's suitability. The problem is formulated as a tracking problem. The designed controllers may be implemented in any electric power system. (author)
Linear 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.)
Nonlinear MHD and energetic particle modes in stellarators
International Nuclear Information System (INIS)
Strauss, H.R.
2002-01-01
The M3D code has been applied to ideal, resistive, two fluid, and hybrid simulations of compact quasi axisymmetric stellarators. When beta exceeds a threshold, low poloidal mode number (m=6∼18) modes grow exponentially, clearly distinguishable from the equilibrium evolution. Simulations of NCSX have beta 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. With sufficient viscosity, the growth rate becomes slow enough to allow calculations of magnetic island evolution. 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 about the expected TAE frequency. Work is in progress to study fast ion-driven Alfven modes in NCSX. (author)
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
Bifurcation and stability analysis of a nonlinear milling process
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.
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
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
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)
Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonlinear Sliding Surface
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 ...
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
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
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT-symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT-symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT-symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT-symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT-symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT-symmetric phase.
Nonlinear optics in the LP(02) higher-order mode of a fiber.
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.
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.
Nonlinear mixing of collective modes in harmonically trapped Bose-Einstein condensates
Mizoguchi, Takahiro; Watabe, Shohei; Nikuni, Tetsuro
2017-03-01
We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function for the Gross-Pitaevskii equation, we find that mode mixing occurs selectively. Our perturbative approach is useful in gaining a qualitative understanding of the recent experiment [M. Yamazaki et al., J. Phys. Soc. Jpn. 84, 44001 (2015), 10.7566/JPSJ.84.044001], exhibiting a beating phenomenon of the scissors mode as well as a modulation phenomenon of the low-lying quadrupole mode by the high-lying quadrupole mode frequency. Within the second-order treatment of the nonlinear mode coupling terms, our approach predicts all the spectral peaks obtained by the numerical simulation of the Gross-Pitaevskii equation.
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
Ideal MHD stability and characteristics of edge localized modes on CFETR
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.
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 Ã¢Â€Â‰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.
Resistive Wall Mode Stabilization Studies at DIII-D
International Nuclear Information System (INIS)
Garofalo, A.M.
2005-01-01
The effort to understand the physics of the resistive wall mode (RWM) and develop methods to control this magnetohydrodynamic mode to allow achievement of higher pressure in advanced tokamak plasmas has been an example of successful multi-institutional collaboration at the DIII-D National Fusion Facility in San Diego, California. DIII-D research in this area has produced several advances and breakthroughs following a coordinated research plan involving a sequence of measurements, development of new analysis tools, and the installation of new diagnostic and feedback stabilization hardware: Suppression of the RWM by active magnetic feedback has been demonstrated using the DIII-D six-element error field correction coil, rotational stabilization of the RWM has been demonstrated and sustained for all values of the plasma pressure from the no-wall to the ideal-wall stability limits, improved RWM feedback stabilization has been shown using a new set of 12 internal control coils, and newly developed models of feedback have shown good agreement with the measurements. By so doing, the DIII-D work on RWM stabilization has become a cornerstone of the long-term advanced tokamak program and is having impact on the world fusion program. Presently both ITER and FIRE are including plans for RWM stabilization in their programs
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
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.
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)
Mode coupling in the nonlinear response of black holes
International Nuclear Information System (INIS)
Zlochower, Yosef; Gomez, Roberto; Husa, Sascha; Lehner, Luis; Winicour, Jeffrey
2003-01-01
We study the properties of the outgoing gravitational wave produced when a nonspinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes
Nonlinear modes of the tensor Dirac equation and CPT violation
Reifler, Frank J.; Morris, Randall D.
1993-01-01
Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.
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.
Stabilization effect of Weibel modes in relativistic laser fusion plasma
Energy Technology Data Exchange (ETDEWEB)
Belghit, Slimen, E-mail: Belghit.slimen@gmail.com; Sid, Abdelaziz, E-mail: Sid-abdelaziz@hotmail.com [Laboratoire de Physique des rayonnements et de leurs interactions avec la matière (PRIMALAB), département de Physique, faculté des Sciences de la Matière, Université de Batna 1, 05000DZ, Batna (Algeria)
2016-06-15
In this work, the Weibel instability (WI) due to inverse bremsstrahlung (IB) absorption in a laser fusion plasma has been investigated. The stabilization effect due to the coupling of the self-generated magnetic field by WI with the laser wave field is explicitly shown. In this study, the relativistic effects are taken into account. Here, the basic equation is the relativistic Fokker-Planck (F-P) equation. The main obtained result is that the coupling of self-generated magnetic field with the laser wave causes a stabilizing effect of excited Weibel modes. We found a decrease in the spectral range of Weibel unstable modes. This decreasing is accompanied by a reduction of two orders in the growth rate of instable Weibel modes or even stabilization of these modes. It has been shown that the previous analysis of the Weibel instability due to IB has overestimated the values of the generated magnetic fields. Therefore, the generation of magnetic fields by the WI due to IB should not affect the experiences of an inertial confinement fusion.
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.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole
2001-01-01
interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...
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.
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.
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
Directory of Open Access Journals (Sweden)
Diamandescu Aurel
2016-07-01
Full Text Available It is proved (necessary and sufficient conditions for Ψ– conditional exponential asymptotic stability of the trivial solution of nonlinear Lyapunov matrix differential equations
On the Ψ-Conditional Asymptotic Stability of Nonlinear Lyapunov Matrix Differential Equations
Directory of Open Access Journals (Sweden)
Diamandescu Aurel
2015-12-01
Full Text Available It is proved (necessary and sufficient conditions for Ψ − conditional asymptotic stability of the trivial solution of linear or nonlinear Lyapunov matrix differential equations.
Nonlinear analysis of rotor-bearing systems using component mode synthesis
Nelson, H. D.; Meacham, W. L.; Fleming, D. P.; Kascak, A. F.
1982-01-01
The method of component mode synthesis is developed to determine the forced response of nonlinear, multishaft, rotor-bearing systems. The formulation allows for simulation of system response due to blade loss, distributed unbalance, base shock, maneuver loads, and specified fixed frame forces. The motion of each rotating component of the system is described by superposing constraint modes associated with boundary coordinates and constrained precessional modes associated with internal coordinates. The precessional modes are truncated for each component and the reduced component equations are assembled with the nonlinear supports and interconnections to form a set of nonlinear system equations of reduced order. These equations are then numerically integrated to obtain the system response. A computer program, which is presently restricted to single shaft systems, has been written and results are presented for transient system response associated with blade loss dynamics with squeeze film dampers, and with interference rubs.
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
Asymptotic stability boundaries of ballooning modes in circular tokamaks
International Nuclear Information System (INIS)
Chen, L.; Bondeson, A.; Chance, M.S.
1987-06-01
The model ballooning mode equation of Connor, Hastie, and Taylor for large-aspect-ratio circular tokamaks is analyzed in the limit of large pressure gradient, and corresponding expressions for stability boundaries are derived. In particular, it is found that for a fixed radial wave number, there exists an infinite sequence of unstable bands, and that minimizing over the radial wave numbers leads to asymptotic merging between the neighboring bands
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
Linear stability analysis of collective neutrino oscillations without spurious modes
Morinaga, Taiki; Yamada, Shoichi
2018-01-01
Collective neutrino oscillations are induced by the presence of neutrinos themselves. As such, they are intrinsically nonlinear phenomena and are much more complex than linear counterparts such as the vacuum or Mikheyev-Smirnov-Wolfenstein oscillations. They obey integro-differential equations, for which it is also very challenging to obtain numerical solutions. If one focuses on the onset of collective oscillations, on the other hand, the equations can be linearized and the technique of linear analysis can be employed. Unfortunately, however, it is well known that such an analysis, when applied with discretizations of continuous angular distributions, suffers from the appearance of so-called spurious modes: unphysical eigenmodes of the discretized linear equations. In this paper, we analyze in detail the origin of these unphysical modes and present a simple solution to this annoying problem. We find that the spurious modes originate from the artificial production of pole singularities instead of a branch cut on the Riemann surface by the discretizations. The branching point singularities on the Riemann surface for the original nondiscretized equations can be recovered by approximating the angular distributions with polynomials and then performing the integrals analytically. We demonstrate for some examples that this simple prescription does remove the spurious modes. We also propose an even simpler method: a piecewise linear approximation to the angular distribution. It is shown that the same methodology is applicable to the multienergy case as well as to the dispersion relation approach that was proposed very recently.
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
Nonlinear stability of pulsational mode of gravitational collapse in ...
Indian Academy of Sciences (India)
- efied, allowing the system to reach a mass neutral point outside equilibrium in a gas-dynamic description. This may, in addition, be of astrophysical importance to electrostatic solitonic structures too, as observed by Freja satellite and Viking.
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.
Nonlinear flight dynamics and stability of hovering model insects
Liang, Bin; Sun, Mao
2013-01-01
Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect. PMID:23697714
Large Signal Stabilization of Hybrid AC/DC Micro-Grids Using Nonlinear Robust Controller
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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.
Stability of Finite-n Global Magnetohydrodynamic Modes Using the GATO Stability Code
Chu, M. S.; Wong, S. K.; Lao, L. L.; Turnbull, A. D.; Chance, M. S.
1999-11-01
This work extends the capability of the GATO stability code(L.C.Bernard et al.), Comput. Phys. Commun. 24, 377 (1981). to analyze realistic numerical tokamak equilibria for their stability to higher n ( ~5--10) MHD modes. This is motivated by the experimental evidence of these modes being relevant for both plasma termination and the behavior of ELMs. The ballooning angle transformation(R. Gruber et al.), Comput. Phys. Commun. 24, 363 (1981). is applied to the displacement variables in the GATO representation. The potential energy matrix is constructed with the inclusion of extra mapping quantities. The vacuum energy computed from the Green's function is also modified to couple to the transformed displacement at the plasma boundary. The resultant eigenvalue problem is solved with the modified boundary condition in the poloidal direction suitable for these transformed variables. The dependence of the plasma stability as a function of toroidal mode number and plasma equilibrium properties will be presented.
Measuring Resistive Wall Mode Stability in Real-time
Hanson, J. M.; Lanctot, M. J.; Navratil, G. A.; Reimerdes, H.; Strait, E. J.
2009-11-01
Measurements of the plasma response to externally applied, low-n magnetic fields can be used to determine the resistive wall mode (RWM) stability of the plasma equilibrium. Such a method, if implemented as a real-time algorithm, can be used to gate error field correction, profile control, and RWM feedback control algorithms, enabling operation close to the no-wall stability limit. In addition, the stability estimate can be used to directly update parameters in an advanced RWM controller as the plasma evolves. We have developed an efficient scheme that uses an external field rotating at a single fixed frequency. Because only one frequency is applied, the plasma response can be calculated from measurements by Fourier-analyzing the measurements at only the applied frequency and subtracting the known vacuum pickup due to the control coils. This single-frequency, Fourier-domain analysis uses a small number of arithmetical operations, which is a requisite for real-time implementation.
Profile stabilization of tilt mode in a Field Reversed Configuration
Energy Technology Data Exchange (ETDEWEB)
Cobb, J.W.; Tajima, T. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies; Barnes, D.C. [Los Alamos National Lab., NM (United States)
1993-06-01
The possibility of stabilizing the tilt mode in Field Reversed Configurations without resorting to explicit kinetic effects such as large ion orbits is investigated. Various pressure profiles, P({Psi}), are chosen, including ``hollow`` profiles where current is strongly peaked near the separatrix. Numerical equilibria are used as input for an initial value simulation which uses an extended Magnetohydrodynamic (MHD) model that includes viscous and Hall terms. Tilt stability is found for specific hollow profiles when accompanied by high values of separatrix beta, {beta}{sub sep}. The stable profiles also have moderate to large elongation, racetrack separatrix shape, and lower values of 3, average ratio of Larmor radius to device radius. The stability is unaffected by changes in viscosity, but the neglect of the Hall term does cause stable results to become marginal or unstable. Implications for interpretation of recent experiments are discussed.
Study of static and dynamic stability of flexible rods in a geometrically nonlinear statement
Annin, B. D.; Vlasov, A. Yu.; Zakharov, Yu. V.; Okhotkin, K. G.
2017-07-01
We study static and dynamic stability problems for a thin flexible rod subjected to axial compression with the geometric nonlinearity explicitly taken into account. In the case of static action of a force, the critical load and the bending shapes of the rod were determined by Euler. Lavrent'ev and Ishlinsky discovered that, in the case of rod dynamic loading significantly greater than the Euler static critical load, there arise buckling modes with a large number of waves in the longitudinal direction. Lavrent'ev and Ishlinsky referred to the first loading threshold discovered by Euler as the static threshold, and the subsequent ones were called dynamic thresholds; they can be attained under impact loading if the pulse growth time is less than the system relaxation time. Later, the buckling mechanism in this case and the arising parametric resonance were studied in detail by Academician Morozov and his colleagues. In this paper, we complete and develop the approach to studying dynamic rod systems suggested by Morozov; in particular, we construct exact and approximate analytic solutions by using a system of special functions generalizing the Jacobi elliptic functions. We obtain approximate analytic solutions of the nonlinear dynamic problem of flexible rod deformation under longitudinal loading with regard to the boundary conditions and show that the analytic solution of static rod system stability problems in a geometrically nonlinear statement permits exactly determining all possible shapes of the bent rod and the complete system of buckling thresholds. The study of approximate analytic solutions of dynamic problems of nonlinear vibrations of rod systems loaded by lumped forces after buckling in the deformed state allows one to determine the vibration frequencies and then the parametric resonance thresholds.
Interpretation of the nonlinear mode excitation in the ITER gyrotron
International Nuclear Information System (INIS)
Nusinovich, G. S.; Sinitsyn, O. V.
2007-01-01
This study was motivated by an interesting physical effect observed in experiments with a 1 MW, 170 GHz, continuous-wave gyrotron developed at the Japan Atomic Energy Agency for plasma heating and current drive in ITER [see, e.g., Fusion Eng. Des. 55, issues 2-3 (2001)]. In these experiments, the gyrotron switching from a parasitic mode to the operating one was observed with the increase in external magnetic field in the region of hard self-excitation of the operating mode where it cannot be excited from the noise level in the absence of other modes. Below, the theory describing this effect is developed. The switching mechanism caused by merging and disappearance of two (one stable and another unstable) equilibrium states with nonzero amplitudes of both modes is proposed. It is found that the present theory can correctly interpret experimental results qualitatively, but the lack of experimental data does not let the authors carry out some simulations more adequate to experimental conditions
Robust discrete-time nonlinear sliding mode controller with plant ...
African Journals Online (AJOL)
user
multi-output linear systems with matched conditions. Some of the concepts and theoretical advances of continuous time sliding mode control are covered in literature (Won et al., 1995, Bandhyopadhyay et al., 2009) and the references there in. Due to flexibility of implementation, large classes of continuous systems are ...
Spatial stability of jets - the nonaxisymmetric fundamental and reflection modes
International Nuclear Information System (INIS)
Hardee, P.E.
1987-01-01
A spatial stability analysis of the relativistic dispersion relation governing the growth and propagation of harmonic components comprising a perturbation to the surface of a cylindrical jet is performed. The spatial growth of harmonic components associated with the nonaxisymmetric fundamental solution and reflection solutions of several Fourier modes are analyzed. Approximate analytical expressions describing resonant frequencies and wavelengths, and maximum growth rates at resonance applicable to relativistic jets are found from the dispersion relation, and the nature of the resonances is explored. On transonic jets there is only a fundamental solution for each Fourier mode with no resonance or maximum growth rate. On supersonic jets there is a fundamental solution and reflection solutions for each Fourier mode, and each solution contains a resonance at which the growth rate is a maximum. A numerical analysis of the fundamental and first three reflection solutions of the axisymmetric and first three nonaxisymmetric Fourier modes is performed. The numerical analysis is restricted to nonrelativistic flows but otherwise covers a broad range of Mach numbers and jet densities. The numerical results are used along with the analytical results to obtain accurate expressions for resonant frequencies, wavelengths, and growth rates as a function of Mach numnber and jet density. In all cases the fastest spatial growth rate at a given frequency is of harmonic components associated with the fundamental solution of one of the nonaxisymmetric Fourier modes. The application of these results to jet structure and implication of these results for jet structure in extragalactic radio sources are considered. 23 references
The simplex method for nonlinear sliding mode control
Directory of Open Access Journals (Sweden)
Bartolini G.
1998-01-01
Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
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.
Evolutionary stability in continuous nonlinear public goods games.
Molina, Chai; Earn, David J D
2017-01-01
We investigate a type of public goods games played in groups of individuals who choose how much to contribute towards the production of a common good, at a cost to themselves. In these games, the common good is produced based on the sum of contributions from all group members, then equally distributed among them. In applications, the dependence of the common good on the total contribution is often nonlinear (e.g., exhibiting synergy or diminishing returns). To date, most theoretical and experimental studies have addressed scenarios in which the set of possible contributions is discrete. However, in many real-world situations, contributions are continuous (e.g., individuals volunteering their time). The "n-player snowdrift games" that we analyze involve continuously varying contributions. We establish under what conditions populations of contributing (or "cooperating") individuals can evolve and persist. Previous work on snowdrift games, using adaptive dynamics, has found that what we term an "equally cooperative" strategy is locally convergently and evolutionarily stable. Using static evolutionary game theory, we find conditions under which this strategy is actually globally evolutionarily stable. All these results refer to stability to invasion by a single mutant. We broaden the scope of existing stability results by showing that the equally cooperative strategy is locally stable to potentially large population perturbations, i.e., allowing for the possibility that mutants make up a non-negligible proportion of the population (due, for example, to genetic drift, environmental variability or dispersal).
Remarks on the stabilization of the systems a single unstable leading mode
International Nuclear Information System (INIS)
Cotsaftis, M.
1978-07-01
Different types of stabilization were proposed for cancelling the plasma motion due to instabilities. The problem of the conventional feedback systems of 'passive' type currently used is rediscussed. The analysis is dealing with the simple case of a plasma with a single leading unstable mode. It is shown that whereas the usual passive feedback cannot achieve a compplete stability on the full interval some other type of more convenient control loops can be used in such a way that the plasma comes back to its original state after a given time, with a power consumption much weaker than in the first case. These properties are also shown to be saved under rather large assumptions in more general situations including the adjunction of delay terms, nonlinear or decoupling terms in the evolution equations of the plasma system [fr
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
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.
Edge localized mode rotation and the nonlinear dynamics of filaments
Czech Academy of Sciences Publication Activity Database
Morales, J.A.; Bécoulet, M.; Garbet, X.; Orain, F.; Dif-Pradalier, G.; Hoelzl, M.; Pamela, S.; Huijsmans, G.T.A.; Cahyna, Pavel; Fil, A.; Nardon, E.; Passeron, C.; Latu, G.
2016-01-01
Roč. 23, č. 4 (2016), č. článku 042513. ISSN 1070-664X EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : Edge Localized Modes (ELMs) * MHD * tokamak * ITER Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.115, year: 2016 http://scitation.aip.org/content/aip/journal/pop/23/4/10.1063/1.4947201
Edge localized mode rotation and the nonlinear dynamics of filaments
Czech Academy of Sciences Publication Activity Database
Morales, J.A.; Bécoulet, M.; Garbet, X.; Orain, F.; Dif-Pradalier, G.; Hoelzl, M.; Pamela, S.; Huijsmans, G.T.A.; Cahyna, Pavel; Fil, A.; Nardon, E.; Passeron, C.; Latu, G.
2016-01-01
Roč. 23, č. 4 (2016), č. článku 042513. ISSN 1070-664X EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : Edge Localized Modes (ELMs) * MHD * tokamak * ITER Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.115, year: 2016 http://scitation.aip.org/content/aip/journal/ pop /23/4/10.1063/1.4947201
Exponential stability of nonlinear time-varying differential equations and applications
Directory of Open Access Journals (Sweden)
N. M. Linh
2001-05-01
Full Text Available In this paper, we give sufficient conditions for the exponential stability of a class of nonlinear time-varying differential equations. We use the Lyapunov method with functions that are not necessarily differentiable; hence we extend previous results. We also provide an application to exponential stability for nonlinear time-varying control systems.
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.
Directory of Open Access Journals (Sweden)
Te-Jen Su
2016-12-01
Full Text Available The objective of this article is to optimize parameters of a hybrid sliding mode controller based on fireworks algorithm for a nonlinear inverted pendulum system. The proposed controller is a combination of two modified types of the classical sliding mode controller, namely, baseline sliding mode controller and fast output sampling discrete sliding mode controller. The simulation process is carried out with MATLAB/Simulink. The results are compared with a published hybrid method using proportional–integral–derivative and linear quadratic regulator controllers. The simulation results show a better performance of the proposed controller.
Nonlinear and subharmonic stability analysis in film-driven morphological patterns
Bertagni, Matteo Bernard; Camporeale, Carlo
2017-11-01
The interaction of a gravity-driven water film with an evolving solid substrate (calcite or ice) results in the formation of fascinating wavy patterns similar both in caves and in ice-falls. Due to their remarkable similarity, we adopt a unified approach in the study of pattern formation of longitudinally oriented organ-pipe-like structures, called flutings. Since the morphogenesis of cave patterns can evolve for millennia, they have an additional value as silent repositories of past climates. Fluting formation is studied with the aid of gradient expansion and center manifold projection. In particular, through gradient expansion, a Benney-type equation accounting for the movable boundary is obtained. The coupling with a wall evolution equation provides a morphodynamic model for fluting formation, explored through linear and nonlinear analyses. In this way, closed relationships for the selected wave number and for the finite amplitude are achieved. However, as finite-amplitude monochromatic waves may be destabilized by nonlinear interactions with other modes, we verify, through center manifold projection, the stability of the fundamental to subharmonic disturbances. Conclusively, we perform numerical simulations of the fully nonlinear equations to validate the theory results.
Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability
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.
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.
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.
A Nonlinear evolution of tearing mode with resistivity and hyper-resistivity
Li, Ding; Yang, Wen; Xu, Xueqiao
2017-10-01
A quasilinear model has been developed for nonlinear tearing mode with resistivity and hyper-resistivity in which only the quasilinear current effect has been taken into account. The nonlinear evolution equation has been derived analytically by using the perturbation method. It is shown that the nonlinear evolution of flux perturbation depends on both resistivity term and hyper-resistivity term. It is found that the hyper-resistivity plays a destabilizing effect. Supported by Strategic Priority Research Program of Chinese Academy of Sciences and National Natural Science Foundation of China.
International Nuclear Information System (INIS)
Assadi, S.
1994-01-01
Linear and nonlinear magnetohydrodynamic (MHD) stability of current-driven modes are studied in the MST reversed field pinch. Measured low frequency (f < 35 kHz) magnetic fluctuations are consistent with the global resistive tearing instabilities predicted by 3-D MHD simulations. At frequencies above 35 kHz, the magnetic fluctuations were detected to be localized and externally resonant. Discrete dynamo events, ''sawtooth oscillations,'' have been observed in the experimental RFP plasmas. This phenomenon causes the plasma to become unstable to m = 1 tearing modes. The modes that may be important in different phases of these oscillations are identified. These results then assist in nonlinear studies and also help to interpret the spectral broadening of the measured data during a discrete dynamo event. Three-wave nonlinear coupling of spectral Fourier modes is measured in the MST by applying bispectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 poloidal and 32 toroidal modes. Comparison to bispectra predicted by resistive MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomitant with a broadened k-spectrum. During the sawtooth formation the plasma is undergoing a pure diffusive process. The dynamo only occurs during the sawtooth crash. High frequency activity prior to a sawtooth crash is caused by nonlinear frequency (small-scale) mode coupling. Growth rate and coupling coefficients of toroidal mode spectra are calculated by statistical modeling. Temporal evolution of edge toroidal mode spectra has been predicted by transfer function analysis. The driving sources of electrostatic fields are different than for the magnetic fields. The characteristics of tearing modes can be altered by external field errors and addition of impurities to the plasma
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
Dynamic modelling of tearing mode stabilization by RF current drive
International Nuclear Information System (INIS)
Giruzzi, G.; Zabiego, M.; Gianakon, T.A.; Garbet, X.; Bernabei, S.
1998-01-01
The theory of tearing mode stabilization in toroidal plasmas by RF-driven currents that are modulated in phase with the island rotation is investigated. A time scale analysis of the phenomena involved indicates that transient effects, such as finite time response of the driven currents, island rotation during the power pulses, and the inductive response of the plasma, are intrinsically important. A dynamic model of such effects is developed, based on a 3-D Fokker-Planck code coupled to both the electric field diffusion and the island evolution equations. Extensive applications to both Electron Cyclotron and Lower Hybrid current drive in ITER are presented. (author)
Directory of Open Access Journals (Sweden)
T. G. Ritto
2014-01-01
Full Text Available This paper proposes a methodology to automatically choose the measurement locations of a nonlinear structure/equipment that needs to be monitored while operating. The response of the computational model (or experimental data is used to construct the proper orthogonal modes applying the proper orthogonal decomposition (POD, and the effective independence distribution vector (EIDV procedure is employed to eliminate, iteratively, locations that contribute less for the independence of the target proper orthogonal modes.
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
Sun, Limin; Chen, Lin
2017-10-01
Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.
On Landau damping of dipole modes by non-linear space charge and octupoles
Möhl, D
1995-01-01
The joint effect of space-charge non-linearities and octupole lenses is important for Landau damping of coherent instabilities. The octupole strength required for stabilisation can depend strongly on the sign of the excitation current of the lenses. This note tries to extend results, previously obtained for coasting beams and rigid bunches, to more general head--tail modes.
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
illustrate the design concept with a silicon-air one-dimensional photon crystal cavity that reaches an ultrasmall mode volume of V-eff similar to 7.01 x 10(-5)lambda(3) at lambda similar to 1550 nm. We show that the extreme light concentration in our design can enable ultrastrong Kerr nonlinearities, even...
Large Optical Nonlinearity of Surface Plasmon Modes on Thin Gold Films
DEFF Research Database (Denmark)
Huck, Alexander; Witthaut, Dirk; Kumar, Shailesh
2013-01-01
We investigate the optical nonlinear effects of a long-range surface plasmon polariton mode propagating on a thin gold film. These effects may play a key role in the design of future nanophotonic circuits as they allow for the realization of active plasmonic elements. We demonstrate a significant...
Scalar-vector soliton fiber laser mode-locked by nonlinear polarization rotation.
Wu, Zhichao; Liu, Deming; Fu, Songnian; Li, Lei; Tang, Ming; Zhao, Luming
2016-08-08
We report a passively mode-locked fiber laser by nonlinear polarization rotation (NPR), where both vector and scalar soliton can co-exist within the laser cavity. The mode-locked pulse evolves as a vector soliton in the strong birefringent segment and is transformed into a regular scalar soliton after the polarizer within the laser cavity. The existence of solutions in a polarization-dependent cavity comprising a periodic combination of two distinct nonlinear waves is first demonstrated and likely to be applicable to various other nonlinear systems. For very large local birefringence, our laser approaches the operation regime of vector soliton lasers, while it approaches scalar soliton fiber lasers under the condition of very small birefringence.
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)
Nonlinear disturbance observer based sliding mode control of a cable-driven rehabilitation robot.
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.
The role of pressure flattening in calculating tearing mode stability
Ham, C. J.; Connor, J. W.; Cowley, S. C.; Hastie, R. J.; Hender, T. C.; Liu, Y. Q.
2013-12-01
Calculations of tearing mode stability in tokamaks split conveniently into one in an external region, where marginally stable ideal magnetohydrodynamics (MHD) is applicable, and one in a resonant layer around the rational surface where sophisticated kinetic physics is needed. These two regions are coupled by the stability parameter Δ‧. Axisymmetric pressure and current perturbations localized around the rational surface significantly alter Δ‧. Equations governing the changes in the external solution and Δ‧ are derived for arbitrary perturbations in axisymmetric toroidal geometry. These equations can be used in two ways: (i) the Δ‧ can be calculated for a physically occurring perturbation to the pressure or current; (ii) alternatively we can use these equations to calculate Δ‧ for profiles with a pressure gradient at the rational surface in terms of the value when the perturbation removes this gradient. It is the second application we focus on here since resistive magnetohydrodynamics (MHD) codes do not contain the appropriate layer physics and therefore cannot predict stability for realistic hot plasma directly. They can, however, be used to calculate Δ‧. Existing methods (Ham et al 2012 Plasma Phys. Control. Fusion 54 025009) for extracting Δ‧ from resistive codes are unsatisfactory when there is a finite pressure gradient at the rational surface and favourable average curvature because of the Glasser stabilizing effect (Glasser et al 1975 Phys. Fluids 18 875). To overcome this difficulty we introduce a specific artificial pressure flattening function that allows the earlier approach to be used. The technique is first tested numerically in cylindrical geometry with an artificial favourable curvature. Its application to toroidal geometry is then demonstrated using the toroidal tokamak tearing mode stability code T7 (Fitzpatrick et al 1993 Nucl. Fusion 33 1533) which employs an approximate analytic equilibrium. The prospects for applying this
2014-01-01
This paper provides improved time delay-dependent stability criteria for multi-input and multi-output (MIMO) network control systems (NCSs) with nonlinear perturbations. Without the stability assumption on the neutral operator after the descriptor approach, the new proposed stability theory is less conservative than the existing stability condition. Theoretical proof is given in this paper to demonstrate the effectiveness of the proposed stability condition. PMID:24744679
Nonlinear gyrokinetic simulation of fast ion-driven modes including continuum interaction
Cole, M. D. J.; Borchardt, M.; Kleiber, R.; Könies, A.; Mishchenko, A.
2018-01-01
Energetic particle transport in toroidal magnetic confinement fusion devices can be enhanced by the particles' interaction with electromagnetic global modes. This process has been modelled numerically. The most extensive work has been with reduced models, which may use a simplified description of the bulk plasma, assuming a perturbative approximation for mode structure evolution, restrict simulation to the linear phase, or some combination. In this work, nonlinear non-perturbative simulations are performed using a fully gyrokinetic and reduced models of the bulk plasma. Previous linear investigation of a simple model tokamak case is extended to show that, at least under some conditions, dramatic qualitative differences in mode structure and saturated mode amplitude can exist due to non-perturbative response in the linear and nonlinear phases that depends upon the bulk plasma physics. This supports analytical work which has shown that the non-perturbative energetic particle response should depend upon the magnetic geometry and kinetic physics. It is also shown that energetic particle modes that dominate in the linear phase can be subdominant to a non-perturbative toroidal Alfvén eigenmode-based global structure in the nonlinear phase.
Stabilization and regulation of nonlinear systems a robust and adaptive approach
Chen, Zhiyong
2015-01-01
The core of this textbook is a systematic and self-contained treatment of the nonlinear stabilization and output regulation problems. Its coverage embraces both fundamental concepts and advanced research outcomes and includes many numerical and practical examples. Several classes of important uncertain nonlinear systems are discussed. The state-of-the art solution presented uses robust and adaptive control design ideas in an integrated approach which demonstrates connections between global stabilization and global output regulation allowing both to be treated as stabilization problems. Stabilization and Regulation of Nonlinear Systems takes advantage of rich new results to give students up-to-date instruction in the central design problems of nonlinear control, problems which are a driving force behind the furtherance of modern control theory and its application. The diversity of systems in which stabilization and output regulation become significant concerns in the mathematical formulation of practical contr...
Modeling of Neoclassical Tearing Mode Stability for Generalized Toroidal Geometry
International Nuclear Information System (INIS)
A.L. Rosenberg; D.A. Gates; A. Pletzer; J.E. Menard; S.E. Kruger; C.C. Hegna; F. Paoletti; S. Sabbagh
2002-01-01
Neoclassical tearing modes (NTMs) can lead to disruption and loss of confinement. Previous analysis of these modes used large aspect ratio, low beta (plasma pressure/magnetic pressure) approximations to determine the effect of NTMs on tokamak plasmas. A more accurate tool is needed to predict the onset of these instabilities. As a follow-up to recent theoretical work, a code has been written which computes the tearing mode island growth rate for arbitrary tokamak geometry. It calls PEST-3 [A. Pletzer et al., J. Comput. Phys. 115, 530 (1994)] to compute delta prime, the resistive magnetohydrodynamic (MHD) matching parameter. The code also calls the FLUXGRID routines in NIMROD [A.H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)] for Dnc, DI and DR [C.C. Hegna, Phys. Plasmas 6, 3980 (1999); A.H. Glasser et al., Phys. Fluids 18, 875 (1975)], which are the bootstrap current driven term and the ideal and resistive interchange mode criterion, respectively. In addition to these components, the NIMROD routines calculate alphas-H, a new correction to the Pfirsch-Schlter term. Finite parallel transport effects were added and a National Spherical Torus Experiment (NSTX) [M. Ono et al., Nucl. Fusion 40, 557 (2000)] equilibrium was analyzed. Another program takes the output of PEST-3 and allows the user to specify the rational surface, island width, and amount of detail near the perturbed surface to visualize the total helical flux. The results of this work will determine the stability of NTMs in an spherical torus (ST) [Y.-K.M. Peng et al., Nucl. Fusion 26, 769 (1986)] plasma with greater accuracy than previously achieved
Nonlinear dynamics of toroidal Alfvén eigenmodes in the presence of tearing modes
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.
Design and Simulation of Sliding Mode Fuzzy Controller for Nonlinear System
Directory of Open Access Journals (Sweden)
Ahmed Khalaf Hamoudi
2016-03-01
Full Text Available Sliding Mode Controller (SMC is a simple method and powerful technique to design a robust controller for nonlinear systems. It is an effective tool with acceptable performance. The major drawback is a classical Sliding Mode controller suffers from the chattering phenomenon which causes undesirable zigzag motion along the sliding surface. To overcome the snag of this classical approach, many methods were proposed and implemented. In this work, a Fuzzy controller was added to classical Sliding Mode controller in order to reduce the impact chattering problem. The new structure is called Sliding Mode Fuzzy controller (SMFC which will also improve the properties and performance of the classical Sliding Mode controller. A single inverted pendulum has been utilized for testing the design of the proposed controller. Programming and Simulink by Matlab have been used for the simulation results.
McKenzie, Ross Hugh
A brief overview of past experimental and theoretical investigations of the linear and nonlinear interaction of zero sound with the order parameter collective modes in superfluid ^3He-B is given before introducing the quasiclassical (QC) theory of superfluid ^3He. A new approach to calculating the linear and nonlinear response is presented. The QC propagator is calculated by expanding the low energy Dyson's equation in powers of the nonequilibrium self energy. The expression given for the expansion coefficients, involving products of pairs of equilibrium Green's functions, has a simple diagrammatic representation, and establishes a connection between the QC theory and other theoretical formalisms which have been used to investigate the collective modes. It is shown that the expansion coefficients satisfy Onsager-like relations and some identities required by gauge and galilean invariance. Consequently, this new approach to deriving dynamical equations for the collective modes is more efficient and transparent than solving the QC transport equations. This new approach is used to investigate the linear coupling of zero sound to the order parameter collective modes in weakly inhomogeneous superfluid ^3 He. It makes tractable the treatment of (nonlinear) parametric processes involving zero sound and the collective modes. It is shown that the approximate particle-hole symmetry of the ^3He Fermi liquid determines important selection rules for nonlinear acoustic processes, just as it is well known to do for linear processes. Analogues with nonlinear optics guide the derivation, solution and interpretation of the dynamical equations for a three-wave resonance between two zero sound waves and the J = 2 ^+ order parameter collective mode. It is shown that stimulated Raman scattering and two phonon absorption of zero sound by the J = 2^+ collective mode should be observable when the pump sound wave has energy density larger than about one percent of the superfluid
Extracting Leading Nonlinear Modes of Changing Climate From Global SST Time Series
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
Huang, Norden E.; Zukor, Dorothy J. (Technical Monitor)
2001-01-01
A new method for analyzing nonlinear and nonstationary data has been developed. The key part of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is defined as any function having the same numbers of zero-crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the Intrinsic Mode Functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Classical nonlinear system models are used to illustrate the roles played by the nonlinear and nonstationary effects in the energy-frequency-time distribution.
Chen, Yi-Xiang; Xu, Zhou-Xiang; Jiang, Yun-Feng; Shi, Jin; Xu, Fang-Qian
2015-07-01
We obtain exact spatial localized mode solutions of a (2+1)-dimensional nonlinear Schrödinger equation with constant diffraction and cubic-quintic nonlinearity in Script PScript T-symmetric potential, and study the linear stability of these solutions. Based on these results, we further derive exact spatial localized mode solutions in a cubic-quintic medium with harmonic and Script PScript T-symmetric potentials. Moreover, the dynamical behaviors of spatial localized modes in the exponential diffraction decreasing waveguide and the periodic distributed amplification system are investigated. Supported by the Project of Technology Office in Zhejiang Province under Grant No. 2014C32006, the Special Foundation for theoretical physics Research Program of China under Grant No. 11447124, National Natural Science Foundation of China under Grant No. 11374254 and the Higher School Visiting Scholar Development under Grant No. FX2013103
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
Multi-mode dynamics of optical oscillators based on intracavity nonlinear frequency down-conversion
Morozov, Yuri A.
2018-01-01
The transient power characteristics of two optical oscillators—a difference frequency generator (ICDFG) and a singly resonant optical parametric oscillator (ICSRO)—based on intracavity nonlinear optical frequency conversion, are described. The simulation has been performed via the rate-equation mathematical model, which features a multi-mode behavior of all optical fields. The reason for unattainability of single-mode emission in these devices without an additional frequency-selective element (e.g., a Fabry-Perot etalon) is clarified. It is shown that the dynamics of a short-wavelength emission (pump) results mainly from the nonlinear optical interaction, while that of the longer-wavelength optical fields (signal and idler) depends on selectivity of the etalon. With the suitable etalons inserted in their cavities, both devices are shown to operate dynamically single-mode under conventional experimental conditions. The nonlinear interaction makes the pump emission collapse to the single-mode operation very fast (it takes no more than a few tens of the photon lifetimes). To overcome the threshold of parametric generation, the intracavity pump power in the ICSRO has to exceed ˜ 100 W, while the ICDFG is essentially a "thresholdless" device.
International Nuclear Information System (INIS)
Yin, L.; Daughton, W.; Albright, B. J.; Bowers, K. J.; Montgomery, D. S.; Kline, J. L.; Fernandez, J. C.; Roper, Q.
2006-01-01
The backward stimulated Raman scattering (BSRS) of a laser from electron beam acoustic modes (BAM) in the presence of self-consistent non-Maxwellian velocity distributions is examined by linear theory and particle-in-cell (PIC) simulations in one and two dimensions (1D and 2D). The BAM evolve from Langmuir waves (LW) as electron trapping modifies the distribution to a non-Maxwellian form that exhibits a beam component. Linear dispersion relations using the nonlinearly modified distribution from simulations are solved for the electrostatic modes involved in the parametric coupling. Results from linear analysis agree well with electrostatic spectra from simulations. It is shown that the intersection of the Stokes root with BAM (instead of LW) determines the matching conditions for BSRS at a nonlinear stage. As the frequency of the unstable Stokes mode decreases with increasing wave number, the damping rate and the phase velocity of BAM decreases with the phase velocity of the Stokes mode, providing a self-consistently evolving plasma linear response that favors continuation of the nonlinear frequency shift. Coincident with the emergence of BAM is a rapid increase in BSRS reflectivity. The details of the wave-particle interaction region in the electron velocity distribution determine the growth/damping rate of these electrostatic modes and the nonlinear frequency shift; in modeling this behavior, the use of sufficiently large numbers of particles in the simulations is crucial. Both the reflectivity scaling with laser intensity and the spectral features from simulations are discussed and are consistent with recent Trident experiments
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.
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
Rotation in a reversed field pinch with active feedback stabilization of resistive wall modes
Cecconello, M.; Menmuir, S.; Brunsell, P. R.; Kuldkepp, M.
2006-09-01
Active feedback stabilization of multiple resistive wall modes (RWMs) has been successfully proven in the EXTRAP T2R reversed field pinch. One of the features of plasma discharges operated with active feedback stabilization, in addition to the prolongation of the plasma discharge, is the sustainment of the plasma rotation. Sustained rotation is observed both for the internally resonant tearing modes (TMs) and the intrinsic impurity oxygen ions. Good quantitative agreement between the toroidal rotation velocities of both is found: the toroidal rotation is characterized by an acceleration phase followed, after one wall time, by a deceleration phase that is slower than in standard discharges. The TMs and the impurity ions rotate in the same poloidal direction with also similar velocities. Poloidal and toroidal velocities have comparable amplitudes and a simple model of their radial profile reproduces the main features of the helical angular phase velocity. RWMs feedback does not qualitatively change the TMs behaviour and typical phenomena such as the dynamo and the 'slinky' are still observed. The improved sustainment of the plasma and TMs rotation occurs also when feedback only acts on internally non-resonant RWMs. This may be due to an indirect positive effect, through non-linear coupling between TMs and RWMs, of feedback on the TMs or to a reduced plasma-wall interaction affecting the plasma flow rotation. Electromagnetic torque calculations show that with active feedback stabilization the TMs amplitude remains well below the locking threshold condition for a thick shell. Finally, it is suggested that active feedback stabilization of RWMs and current profile control techniques can be employed simultaneously thus improving both the plasma duration and its confinement properties.
Rotation in a reversed field pinch with active feedback stabilization of resistive wall modes
Energy Technology Data Exchange (ETDEWEB)
Cecconello, M [Division of Fusion Plasma Physics, Association EURATOM -VR, Alfven Laboratory, School of Electrical Engineering, Royal Institute of Technology KTH, SE-10044 Stockholm (Sweden); Menmuir, S [Department of Physics, Association EURATOM -VR, School of Engineering Science, Royal Institute of Technology KTH, SE-10691 Stockhom (Sweden); Brunsell, P R [Division of Fusion Plasma Physics, Association EURATOM -VR, Alfven Laboratory, School of Electrical Engineering, Royal Institute of Technology KTH, SE-10044 Stockholm (Sweden); Kuldkepp, M [Department of Physics, Association EURATOM -VR, School of Engineering Science, Royal Institute of Technology KTH, SE-10691 Stockhom (Sweden)
2006-09-15
Active feedback stabilization of multiple resistive wall modes (RWMs) has been successfully proven in the EXTRAP T2R reversed field pinch. One of the features of plasma discharges operated with active feedback stabilization, in addition to the prolongation of the plasma discharge, is the sustainment of the plasma rotation. Sustained rotation is observed both for the internally resonant tearing modes (TMs) and the intrinsic impurity oxygen ions. Good quantitative agreement between the toroidal rotation velocities of both is found: the toroidal rotation is characterized by an acceleration phase followed, after one wall time, by a deceleration phase that is slower than in standard discharges. The TMs and the impurity ions rotate in the same poloidal direction with also similar velocities. Poloidal and toroidal velocities have comparable amplitudes and a simple model of their radial profile reproduces the main features of the helical angular phase velocity. RWMs feedback does not qualitatively change the TMs behaviour and typical phenomena such as the dynamo and the 'slinky' are still observed. The improved sustainment of the plasma and TMs rotation occurs also when feedback only acts on internally non-resonant RWMs. This may be due to an indirect positive effect, through non-linear coupling between TMs and RWMs, of feedback on the TMs or to a reduced plasma-wall interaction affecting the plasma flow rotation. Electromagnetic torque calculations show that with active feedback stabilization the TMs amplitude remains well below the locking threshold condition for a thick shell. Finally, it is suggested that active feedback stabilization of RWMs and current profile control techniques can be employed simultaneously thus improving both the plasma duration and its confinement properties.
Rotation in a reversed field pinch with active feedback stabilization of resistive wall modes
International Nuclear Information System (INIS)
Cecconello, M; Menmuir, S; Brunsell, P R; Kuldkepp, M
2006-01-01
Active feedback stabilization of multiple resistive wall modes (RWMs) has been successfully proven in the EXTRAP T2R reversed field pinch. One of the features of plasma discharges operated with active feedback stabilization, in addition to the prolongation of the plasma discharge, is the sustainment of the plasma rotation. Sustained rotation is observed both for the internally resonant tearing modes (TMs) and the intrinsic impurity oxygen ions. Good quantitative agreement between the toroidal rotation velocities of both is found: the toroidal rotation is characterized by an acceleration phase followed, after one wall time, by a deceleration phase that is slower than in standard discharges. The TMs and the impurity ions rotate in the same poloidal direction with also similar velocities. Poloidal and toroidal velocities have comparable amplitudes and a simple model of their radial profile reproduces the main features of the helical angular phase velocity. RWMs feedback does not qualitatively change the TMs behaviour and typical phenomena such as the dynamo and the 'slinky' are still observed. The improved sustainment of the plasma and TMs rotation occurs also when feedback only acts on internally non-resonant RWMs. This may be due to an indirect positive effect, through non-linear coupling between TMs and RWMs, of feedback on the TMs or to a reduced plasma-wall interaction affecting the plasma flow rotation. Electromagnetic torque calculations show that with active feedback stabilization the TMs amplitude remains well below the locking threshold condition for a thick shell. Finally, it is suggested that active feedback stabilization of RWMs and current profile control techniques can be employed simultaneously thus improving both the plasma duration and its confinement properties
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Antonie Arij; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched
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.
Sadri, Sobhan; Wu, Christine
2013-06-01
For the first time, this paper investigates the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom. The nonlinearity of the model comes from the third-order polynomial expression between the lateral forces on the tyres and the tyre slip angles. Comprehensive studies on both system and structural stability analyses of the vehicle model are presented. The system stability analysis includes the stability, lateral stability region, and effects of driving conditions on the lateral stability region of the vehicle model in the state space. In the structural stability analysis, the ranges of driving conditions in which the stability of the vehicle model is guaranteed are given. Moreover, through examples, the largest Lyapunov exponent is suggested as an indicator of the convergence rate in which the disturbed vehicle model returns to its stable fixed point.
Zhai, Junyong; Du, Haibo
2013-03-01
This paper investigates the problem of semi-global stabilization by output feedback for a class of nonlinear systems using homogeneous domination approach. For each subsystem, we first design an output feedback stabilizer for the nominal system without the perturbing nonlinearities. Then, based on the ideas of the homogeneous systems theory and the adding a power integrator technique, a series of homogeneous output feedback stabilizers are constructed recursively for each subsystem and the closed-loop system is rendered semi-globally asymptotically stable. The efficiency of the output feedback stabilizers is demonstrated by a simulation example. Crown Copyright © 2012. Published by Elsevier Ltd. All rights reserved.
Stability of two-dimensional spatial solitons in nonlocal nonlinear media
DEFF Research Database (Denmark)
Skupin, S.; Bang, Ole; Edmundson, D.
2006-01-01
We discuss the existence and stability of two-dimensional solitons in media with spatially nonlocal nonlinear response. We show that such systems, which include thermal nonlinearity and dipolar Bose-Einstein condensates, may support a variety of stationary localized structures, including rotating...... dipole solitons. We also demonstrate that the stability of these structures critically depends on the spatial profile of the nonlocal response function....
Turbulent transport stabilization by ICRH minority fast ions in low rotating JET ILW L-mode plasmas
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.
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.
Nondecaying linear and nonlinear modes in a periodic array of spatially localized dissipations
International Nuclear Information System (INIS)
Fernández, S C; Shchesnovich, V S
2014-01-01
We demonstrate the existence of extremely weakly decaying linear and nonlinear modes (i.e. modes immune to dissipation) in the one-dimensional periodic array of identical spatially localized dissipations, where the dissipation width is much smaller than the period of the array. We consider wave propagation governed by the one-dimensional Schrödinger equation in the array of identical Gaussian-shaped dissipations with three parameters, the integral dissipation strength Γ 0 , the width σ and the array period d. In the linear case, setting σ → 0, while keeping Γ 0 fixed, we get an array of zero-width dissipations given by the Dirac delta-functions, i.e. the complex Kronig–Penney model, where an infinite number of nondecaying modes appear with the Bloch index being either at the center, k = 0, or at the boundary, k = π/d, of an analogue of the Brillouin zone. By using numerical simulations we confirm that the weakly decaying modes persist for σ such that σ/d ≪ 1 and have the same Bloch index. The nondecaying modes persist also if a real-valued periodic potential is added to the spatially periodic array of dissipations, with the period of the dissipative array being a multiple of that of the periodic potential. We also consider evolution of the soliton-shaped pulses in the nonlinear Schrödinger equation with the spatially periodic dissipative lattice and find that when the pulse width is much larger than the lattice period and its wave number k is either at the center, k = 2π/d, or at the boundary, k = π/d, a significant fraction of the pulse escapes the dissipation forming a stationary nonlinear mode with the soliton-shaped envelope and the Fourier spectrum consisting of two peaks centered at k and −k. (paper)
Stabilization and Control Models of Systems With Hysteresis Nonlinearities
Directory of Open Access Journals (Sweden)
Mihail E. Semenov
2012-05-01
Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.
Nonlinear vibration analysis of axially moving strings based on gyroscopic modes decoupling
Yang, Xiao-Dong; Wu, Hang; Qian, Ying-Jing; Zhang, Wei; Lim, C. W.
2017-04-01
A novel idea that applies the multiple scale analysis to a discretized decoupled system of gyroscopic continua is introduced and an axial moving string is treated as an example. First, the invariant manifold method is applied to the discretized ordinary differential equations of the axially moving string. Complex gyroscopic mode functions that agree well with true analytical results are obtained. The gyroscopic modes are subsequently used for the discretized ordinary differential equations with gyroscopic and nonlinear coupling terms that yield a gyroscopically decoupled system. Further the method of multiple scales is used to obtain the equations at a slow scale. This novel procedure is compared to solutions obtained by directly applying the classical multiple scale analysis to the gyroscopically coupled system without decoupling. The modal decoupled system analysis yields better frequency with comparing to the classic method. The proposed methodology provides a novel alternative for nonlinear dynamic analysis of gyroscopic continua.
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...... of general type-2 fuzzy logic systems (GT2FLS) is utilized by the suggested controller. The suggested controller not only warranties the constancy and hardiness against uncertainties of the lumped resulted by external disturbances and un-modeled dynamics, but also considerably decreases the control...... 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...
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
Circuits and systems based on delta modulation linear, nonlinear and mixed mode processing
Zrilic, Djuro G
2005-01-01
This book is intended for students and professionals who are interested in the field of digital signal processing of delta-sigma modulated sequences. The overall focus is on the development of algorithms and circuits for linear, non-linear, and mixed mode processing of delta-sigma modulated pulse streams. The material presented here is directly relevant to applications in digital communication, DSP, instrumentation, and control.
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.
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)
Frequency domain stability analysis of nonlinear active disturbance rejection control system.
Li, Jie; Qi, Xiaohui; Xia, Yuanqing; Pu, Fan; Chang, Kai
2015-05-01
This paper applies three methods (i.e., root locus analysis, describing function method and extended circle criterion) to approach the frequency domain stability analysis of the fast tool servo system using nonlinear active disturbance rejection control (ADRC) algorithm. Root locus qualitative analysis shows that limit cycle is generated because the gain of the nonlinear function used in ADRC varies with its input. The parameters in the nonlinear function are adjustable to suppress limit cycle. In the process of root locus analysis, the nonlinear function is transformed based on the concept of equivalent gain. Then, frequency domain description of the nonlinear function via describing function is presented and limit cycle quantitative analysis including estimating prediction error is presented, which virtually and theoretically demonstrates that the describing function method cannot guarantee enough precision in this case. Furthermore, absolute stability analysis based on extended circle criterion is investigated as a complement. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2
Mohler, R. R.
1992-01-01
This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.
Nonlinear behaviour and stability of thin-walled shells
Obodan, Natalia I; Gromov, Vasilii A
2013-01-01
This book focuses on the nonlinear behaviour of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings. The dependence of critical (buckling) load upon load variability is revealed to be highly non-monotonous, showing minima when load variability is close to the eigenmode variabilities of solution branching points of the respective nonlinear boundary problem. A novel numerical approach is employed to analyze branching points and to build primary, secondary, and tertiary bifurcation paths of the nonlinear boundary problem for the case of uniform loading. The load levels of singular points belonging to the paths are considered to be critical load estimates for the case of non-uniform loadings.
Chowdhury, Sourav Das; Pal, Atasi; Chatterjee, Sayan; Sen, Ranjan; Pal, Mrinmay
2018-02-10
In this paper, we propose an all-normal-dispersion ytterbium-fiber laser with a novel ring cavity architecture having two nonlinear amplifying loop mirrors (NALM) as saturable absorbers, capable of delivering distinctly different pulses with adjustable features. By optimizing the loop lengths of the individual NALMs, the cavity can be operated to deliver Q-switched mode-locked (Q-ML) pulse bunches with adjustable repetition rates, mode-locked pulses in dissipative soliton resonance (DSR) regime or noise-like pulse (NLP) regime with tunable pulse width. The DSR pulses exhibit characteristic narrowband spectrum, while the NLPs exhibit large broadband spectrum. The operation regime of the laser can be controlled by adjusting the amplifier pump powers and the polarization controllers. To the best of the authors' knowledge, this is the first demonstration of a single mode-locked cavity where narrowband DSR pulses and broadband NLPs alongside Q-ML pulse bunches can be selectively generated by employing two NALMs.
A geometric criterion for the stability of forced oscillations in non-linear mechanics (1961)
International Nuclear Information System (INIS)
Blaquiere, A.
1961-01-01
The author completes the two-parameter diagram theory which he has previously explained, by giving a geometric criterion of stability for a non-linear system under forced conditions. After two simple geometric transformations of the diagram he obtains the separators which are the boundary conditions for the zones of stability. (author) [fr
Results on stabilization of nonlinear systems under finite data-rate constraints
Persis, Claudio De
2004-01-01
We discuss in this paper a result concerning the stabilization problem of nonlinear systems under data-rate constraints using output feedback. To put the result in a broader context, we shall first review a number of recent contributions on the stabilization problem under data-rate constraints when
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.
Davijani, Nafiseh Zare; Jahanfarnia, Gholamreza; Abharian, Amir Esmaeili
2017-01-01
One of the most important issues with respect to nuclear reactors is power control. In this study, we designed a fractional-order sliding mode controller based on a nonlinear fractional-order model of the reactor system in order to track the reference power trajectory and overcome uncertainties and external disturbances. Since not all of the variables in an operating reactor are measurable or specified in the control law, we propose a reduced-order fractional neutron point kinetic (ROFNPK) model based on measurable variables. In the design, we assume the differences between the approximated model and the real system is limited. We use the obtained model in the controller design process and use the Lyapunov method to perform a stability analysis of the closed-loop system. We simulate the proposed reduced-order fractional-order sliding mode controller (ROFOSMC) using Matlab/Simulink, and its performance is compared with that of a reduced order integer-order sliding mode controller (ROIOSMC). Our simulation results indicate an acceptable performance of the proposed approach in tracking the reference power trajectory with respect to ROIOSMC because of faster response of control effort signal and the smaller tracking error. Moreover, the results illustrate the capability of the controller in rejection of the disturbance and the noise signals and the robustness of controller against uncertainty.
Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters
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.
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
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)
On Reynolds stress and neutral azimuthal modes in the stability ...
Indian Academy of Sciences (India)
We consider the linear stability problem of inviscid, incompressible swirling flows with radius-dependent density with respect to two-dimensional disturbances. Some results of Miles on the parallel flow stability theory are extended to the swirling flow stability theory. In particular, series solutions for the stability equation for ...
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.)
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
Energy Technology Data Exchange (ETDEWEB)
Bai, Xiao-Dong; Ai, Qing; Zhang, Mei; Xiong, Jun, E-mail: junxiong@bnu.edu.cn; Yang, Guo-Jian; Deng, Fu-Guo
2015-09-15
We investigate the stability and phase transition of localized modes in Bose–Einstein Condensates (BECs) in an optical lattice with the discrete nonlinear Schrödinger model by considering both two- and three-body interactions. We find that there are three types of localized modes, bright discrete breather (DB), discrete kink (DK), and multi-breather (MUB). Moreover, both two- and three-body on-site repulsive interactions can stabilize DB, while on-site attractive three-body interactions destabilize it. There is a critical value for the three-body interaction with which both DK and MUB become the most stable ones. We give analytically the energy thresholds for the destabilization of localized states and find that they are unstable (stable) when the total energy of the system is higher (lower) than the thresholds. The stability and dynamics characters of DB and MUB are general for extended lattice systems. Our result is useful for the blocking, filtering, and transfer of the norm in nonlinear lattices for BECs with both two- and three-body interactions.
Optical fibers with low nonlinearity and low polarization-mode dispersion for terabit communications
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.
Comparison of MHD simulation codes for understanding nonlinear ELMs dynamics in KSTAR H-mode plasma
Kim, M.; Lee, J.; Park, H. K.; Yun, G. S.; Xu, X.; Jardin, S. C.; Becoulet, M.
2017-10-01
KSTAR electron cyclotron emission imaging (ECEI) systems have contributed to understanding the fundamental physics of ELMs by high-quality 2D and quasi-3D images of ELMs. However, in the highly nonlinear phase of ELM dynamics, the interpretation of ECE signals becomes complicated intrinsically. Theoretical and numerical approaches are necessary to enhance the understanding of ELM physics. Well-established MHD codes (BOUT + + , JOREK, and M3D-C1) are introduced for comparative study with the observations. The nonlinear solutions are obtained using the same equilibrium of the KSTAR H-mode plasma. Each code shows the partial difference in mode evolution, probably, due to the difference in optimized operation window of initial conditions. The nonlinear simulation results show that low- n (n qualitatively matches with the recent ECEI observation just before ELM-crash, or excitation of non-modal solitary perturbation (typically, n = 1) which is highly localized in poloidal and toroidal. Regardless of differences in details, qualitative similarity can provide inspiration to understand the triggering of ELM-crash. This work is supported by NRF of Korea under Contract No. NRF-2014M1A7A1A03029865.
Preservation of stability and synchronization in nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Fernandez-Anaya, G. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: guillermo.fernandez@uia.mx; Flores-Godoy, J.J. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: job.flores@uia.mx; Femat, R. [Division de Matematicas Aplicadas y Sistemas Computacionales, IPICyT, Camino a la Presa San Jose 2055, Col. Lomas 4a. seccion, San Luis Potosi, San Luis Potosi 78216 (Mexico)], E-mail: rfemat@ipicyt.edu.mx; Alvarez-Ramirez, J.J. [Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico)], E-mail: jjar@xanum.uam.mx
2007-11-12
Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results.
Preservation of stability and synchronization in nonlinear systems
International Nuclear Information System (INIS)
Fernandez-Anaya, G.; Flores-Godoy, J.J.; Femat, R.; Alvarez-Ramirez, J.J.
2007-01-01
Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results
Lagrangian approach to weakly nonlinear stability of elliptical flow
International Nuclear Information System (INIS)
Fukumoto, Y; Mie, Y; Hirota, M
2010-01-01
Rotating flows with elliptically strained streamlines suffer from parametric resonance instability between a pair of Kelvin waves whose azimuthal wavenumbers are separated by two. We address the weakly nonlinear amplitude evolution of three-dimensional (3D) Kelvin waves, in resonance, on a flow confined in a cylinder of elliptic cross-section. In a traditional Eulerian approach, derivation of the mean flow induced by nonlinear interaction of Kelvin waves stands as an obstacle. We show how a topological idea, or the Lagrangian approach, facilitates calculation of the wave-induced mean flow. A steady incompressible Euler flow is characterized as a state of the maximum of the total kinetic energy with respect to perturbations constrained to an isovortical sheet, and the isovortical perturbation is handled only in terms of the Lagrangian variables. The criticality in energy of a steady flow allows us to calculate the wave-induced mean flow only from the linear Lagrangian displacement. With the mean flow at hand, the Lagrangian approach provides us with a shortcut to enter into a weakly nonlinear amplitude evolution regime of 3D disturbances. Unlike the Eulerian approach, the amplitude equations are available directly in the Hamiltonian normal form.
Distributed mode filtering rod fiber amplifier delivering 292W with improved mode stability
DEFF Research Database (Denmark)
Laurila, Marko; Jørgensen, Mette Marie; Hansen, Kristian Rymann
2012-01-01
We demonstrate a high power fiber (85μm core) amplifier delivering up to 292Watts of average output power using a mode-locked 30ps source at 1032nm. Utilizing a single mode distributed mode filter bandgap rod fiber, we demonstrate 44% power improvement before the threshold-like onset of mode inst...
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.
SPORTS - a simple non-linear thermalhydraulic stability code
International Nuclear Information System (INIS)
Chatoorgoon, V.
1986-01-01
A simple code, called SPORTS, has been developed for two-phase stability studies. A novel method of solution of the finite difference equations was deviced and incorporated, and many of the approximations that are common in other stability codes are avoided. SPORTS is believed to be accurate and efficient, as small and large time-steps are permitted, and hence suitable for micro-computers. (orig.)
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.
Stabilization of nonlinear system using uniform eigenvalue assignment in linear model
Siahaan, Sahat P.; Pangaribuan, Timbang
2017-09-01
Some plant in control system has nonlinear dynamic, so it is not easy to do in analysis to see its behavior using eigenstructure assignment. From many observations which have been made, some literature give methods to design nonlinear control system. The modern control theory uses state-space method to explain the behaviour on stability of a plant. To improve the stability of the closed-loop system, designer commonly use the state feedback control law. For the case inverted pendulum plant with the nonlinear dynamics, its need to perform the nonlinear control law with the concepts of modern control theory to satisfy the closed-loop system characteristic, and all the behaviour of the closed-loop system only determined from the given linear pole specifications.
On a theory of stability for nonlinear stochastic chemical reaction networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-01-01
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms. PMID:25978877
Zhang, W.; Wang, S.; Ma, Z. W.
2017-06-01
The influences of helical driven currents on nonlinear resistive tearing mode evolution and saturation are studied by using a three-dimensional toroidal resistive magnetohydrodynamic code (CLT). We carried out three types of helical driven currents: stationary, time-dependent amplitude, and thickness. It is found that the helical driven current is much more efficient than the Gaussian driven current used in our previous study [S. Wang et al., Phys. Plasmas 23(5), 052503 (2016)]. The stationary helical driven current cannot persistently control tearing mode instabilities. For the time-dependent helical driven current with f c d = 0.01 and δ c d < 0.04 , the island size can be reduced to its saturated level that is about one third of the initial island size. However, if the total driven current increases to about 7% of the total plasma current, tearing mode instabilities will rebound again due to the excitation of the triple tearing mode. For the helical driven current with time dependent strength and thickness, the reduction speed of the radial perturbation component of the magnetic field increases with an increase in the driven current and then saturates at a quite low level. The tearing mode is always controlled even for a large driven current.
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
Algorithmic Approximation of Optimal Value Differential Stability Bounds in Nonlinear Programming,
1981-08-01
NCLASSIFIED RANO/PA6659 N IN *~4 112.0.0 ~11111,.. I32 111 IIIII 111111.25 MICROCOPY RESOLUTION TESI CHART NATIOt AL BJRLAU Of SIANDARD 1964 A * LEVEL 00 o pm...Sensitivity Analysis in Parametric Nonlinear Programming, Doctoral Dissertation, School of Engineering and Applied Science, The George Washington University...Differential Stability of the Optimal Value Function in Constrained Nonlinear Programing, Doctoral Disser- tation, School of Engineering and Applied
Effects of nonlinear forces on dynamic mode atomic force microscopy and spectroscopy.
Das, Soma; Sreeram, P A; Raychaudhuri, A K
2007-06-01
In this paper, we describe the effects of nonlinear tip-sample forces on dynamic mode atomic force microscopy and spectroscopy. The jumps and hysteresis observed in the vibration amplitude (A) versus tip-sample distance (h) curves have been traced to bistability in the resonance curve. A numerical analysis of the basic dynamic equation was used to explain the hysteresis in the experimental curve. It has been found that the location of the hysteresis in the A-h curve depends on the frequency of the forced oscillation relative to the natural frequency of the cantilever.
Stability of coupled tearing and twisting modes in tokamaks
International Nuclear Information System (INIS)
Fitzpatrick, R.
1994-03-01
A dispersion relation is derived for resistive modes of arbitrary parity in a tokamak plasma. At low mode amplitude, tearing and twisting modes which have nonideal MHD behavior at only one rational surface at a time in the plasma are decoupled via sheared rotation and diamagnetic flows. At higher amplitude, more unstable open-quote compound close-quote modes develop which have nonideal behavior simultaneously at many surfaces. Such modes possess tearing parity layers at some of the nonideal surfaces, and twisting parity layers at others, but mixed parity layers are generally disallowed. At low mode number, open-quote compound close-quote modes are likely to have tearing parity layers at all of the nonideal surfaces in a very low-β plasma, but twisting parity layers become more probable as the plasma β is increased. At high mode number, unstable twisting modes which exceed a critical amplitude drive conventional magnetic island chains on alternate rational surfaces, to form an interlocking structure in which the O-points and X-points of neighboring chains line up
Stability analysis for stochastic BAM nonlinear neural network with delays
Lv, Z. W.; Shu, H. S.; Wei, G. L.
2008-02-01
In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.
Directory of Open Access Journals (Sweden)
Bijan Bagchi
2014-04-01
Full Text Available The relevance of parity and time reversal (PT-symmetric structures in optical systems has been known for some time with the correspondence existing between the Schrödinger equation and the paraxial equation of diffraction, where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrödinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation characterized by the parameter of perturbative growth rate passing through zero, where a transition to imaginary eigenvalues occurs.
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
Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions
BoŻek, Piotr
2018-03-01
The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.
Directory of Open Access Journals (Sweden)
Faten Baklouti
2016-01-01
Full Text Available The trajectory tracking of underactuated nonlinear system with two degrees of freedom is tackled by an adaptive fuzzy hierarchical sliding mode controller. The proposed control law solves the problem of coupling using a hierarchical structure of the sliding surfaces and chattering by adopting different reaching laws. The unknown system functions are approximated by fuzzy logic systems and free parameters can be updated online by adaptive laws based on Lyapunov theory. Two comparative studies are made in this paper. The first comparison is between three different expressions of reaching laws to compare their abilities to reduce the chattering phenomenon. The second comparison is made between the proposed adaptive fuzzy hierarchical sliding mode controller and two other control laws which keep the coupling in the underactuated system. The tracking performances of each control law are evaluated. Simulation examples including different amplitudes of external disturbances are made.
Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.
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.
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)
A novel three-ring-core few-mode fiber with large effective area and low nonlinear coefficient
Yu, Ru-yuan; Zheng, Hong-jun; Li, Xin; Bai, Cheng-lin; Hu, Wei-sheng
2018-01-01
A novel three-ring-core few-mode fiber with large effective area and low nonlinear coefficient is proposed in this paper. The fiber characteristics based on the full-vector finite element method (FEM) with perfect matched layer boundary conditions show that four supermodes with large effective area, low nonlinear coefficient and low differential mode group delay ( DMGD) are achieved. With the increase of input wavelength, the effective areas of three-ring-core few-mode fiber are increased, and the nonlinear coefficients are decreased. The bending losses are increased with the increase of input wavelength, and are decreased with the increase of bending radius. Moreover, the proposed fiber performs a nonlinear coefficient and DMGD flattened profile at a large wavelength range.
MHD stability and mode locking in pre-disruptive plasmas on TORE SUPRA
International Nuclear Information System (INIS)
Vallet, J.C.; Edery, D.; Joffrin, E.; Lecoustey, P.; Mohamed-Benkadda, M.S.; Pecquet, A.L.; Samain, A.; Talvard, M.
1991-01-01
Experiments devoted to the study of MHD activity have been carried out on TORE SUPRA. The observed disruptions are preceded by the growth of an m=2 N=1 rotating mode which locks when the magnetic field perturbation exceeds a critical value. The mode locking is interpreted as a bifurcation of the mode frequency. In addition, stabilization of the m=2 N=1 tearing mode has been obtained with the Ergodic Divertor (ED)
Directory of Open Access Journals (Sweden)
Yuanchuan SHEN
2017-06-01
Full Text Available This article presents a complete nonlinear controller design for a class of spin-stabilized canard-controlled projectiles. Uniformly ultimate boundedness and tracking are achieved, exploiting a heavily coupled, bounded uncertain and highly nonlinear model of longitudinal and lateral dynamics. In order to estimate unmeasurable states, an observer is proposed for an augmented multiple-input-multiple-output (MIMO nonlinear system with an adaptive sliding mode term against the disturbances. Under the frame of a backstepping design, an adaptive sliding mode output-feedback dynamic surface control (DSC approach is derived recursively by virtue of the estimated states. The DSC technique is adopted to overcome the problem of “explosion of complexity” and relieve the stress of the guidance loop. It is proven that all signals of the MIMO closed-loop system, including the observer and controller, are uniformly ultimately bounded, and the tracking errors converge to an arbitrarily small neighborhood of the origin. Simulation results for the observer and controller are provided to illustrate the feasibility and effectiveness of the proposed approach.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
Directory of Open Access Journals (Sweden)
Pagliari Carmen
2013-07-01
Full Text Available The traditional analysis of unemployment in relation to real output dynamics is based on some empirical evidences deducted from Okun’s studies. In particular the so called Okun’s Law is expressed in a linear mathematical formulation, which cannot explain the fluctuation of the variables involved. Linearity is an heavy limit for macroeconomic analysis and especially for every economic growth study which would consider the unemployment rate among the endogenous variables. This paper deals with an introductive study about the role of non-linearity in the investigation of unemployment dynamics. The main idea is the existence of a non-linear relation between the unemployment rate and the gap of GDP growth rate from its trend. The macroeconomic motivation of this idea moves from the consideration of two concatenate effects caused by a variation of the unemployment rate on the real output growth rate. These two effects are concatenate because there is a first effect that generates a secondary one on the same variable. When the unemployment rate changes, the first effect is the variation in the level of production in consequence of the variation in the level of such an important factor as labour force; the secondary effect is a consecutive variation in the level of production caused by the variation in the aggregate demand in consequence of the change of the individual disposal income originated by the previous variation of production itself. In this paper the analysis of unemployment dynamics is carried out by the use of the logistic map and the conditions for the existence of bifurcations (cycles are determined. The study also allows to find the range of variability of some characteristic parameters that might be avoided for not having an absolute unpredictability of unemployment dynamics (deterministic chaos: unpredictability is equivalent to uncontrollability because of the total absence of information about the future value of the variable to
On Reynolds stress and neutral azimuthal modes in the stability ...
Indian Academy of Sciences (India)
series solutions presented above play important roles in the nonlinear critical layer analysis of swirling flows with variable density. However the above results on the Reynolds stress are similar to the corresponding results of Maslowe & Nigam (2008). The main difference between our results and those of Maslowe & Nigam ...
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)
Local asymptotic stability for nonlinear quadratic functional integral equations
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2008-03-01
Full Text Available In the present study, using the characterizations of measures of noncompactness we prove a theorem on the existence and local asymptotic stability of solutions for a quadratic functional integral equation via a fixed point theorem of Darbo. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. An example is indicated to demonstrate the natural realizations of abstract result presented in the paper.
Petosić, Antonio; Ivancević, Bojan; Svilar, Dragoljub
2009-06-01
The method for measuring derived acoustic power of an ultrasound point source in the form of a sonotrode tip has been considered in the free acoustic field, according to the IEC 61847 standard. The main objective of this work is measuring averaged pressure magnitude spatial distribution of an sonotrode tip in the free acoustic field conditions at different electrical excitation levels and calculation of the derived acoustic power at excitation frequency (f0 approximately 25 kHz). Finding the derived acoustic power of an ultrasonic surgical device in the strong cavitation regime of working, even in the considered laboratory conditions (anechoic pool), will enable better understanding of the biological effects on the tissue produced during operation with the considered device. The pressure magnitude spatial distribution is measured using B&K 8103 hydrophone connected with a B&K 2626 conditioning amplifier, digital storage oscilloscope LeCroy Waverunner 474, where pressure waveforms in the field points are recorded. Using MATLAB with DSP processing toolbox, averaged power spectrum density of recorded pressure signals in different field positions is calculated. The measured pressure magnitude spatial distributions are fitted with the appropriate theoretical models. In the linear operating mode, using the acoustic reciprocity principle, the sonotrode tip is theoretically described as radially oscillating sphere (ROS) and transversely oscillating sphere (TOS) in the vicinity of pressure release boundary. The measured pressure magnitude spatial distribution is fitted with theoretical curves, describing the pressure field of the considered theoretical models. The velocity and displacement magnitudes with derived acoustic power of equivalent theoretical sources are found, and the electroacoustic efficiency factor is calculated. When the transmitter is excited at higher electrical power levels, the displacement magnitude of sonotrode tip is increased, and nonlinear behaviour
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
Nonlinear stability research on the hydraulic system of double-side rolling shear
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.
Numerical simulation of large-scale MHD-mode stability in axisymmetric mirror systems
International Nuclear Information System (INIS)
Martynov, A.A.
1989-01-01
The formulation and the results of the numeric solution of a two-dimensional problem of anisotropic pressure plasma stability relative to large-scale MHD modes are presented for a system of traps consisting of a mirror device and an anchor-antimirror device. The extreme values β in the main trap depending on β in the ancor, mode number m on the position of the conducting wall. It is shown that in the case of high β the requirements of mode stability bring about considerably weaker (as compared with low-scale modes) limitations on pressure in the main trap
Robust Stabilization of T-S Fuzzy Stochastic Descriptor Systems via Integral Sliding Modes.
Li, Jinghao; Zhang, Qingling; Yan, Xing-Gang; Spurgeon, Sarah K
2017-09-19
This paper addresses the robust stabilization problem for T-S fuzzy stochastic descriptor systems using an integral sliding mode control paradigm. A classical integral sliding mode control scheme and a nonparallel distributed compensation (Non-PDC) integral sliding mode control scheme are presented. It is shown that two restrictive assumptions previously adopted developing sliding mode controllers for Takagi-Sugeno (T-S) fuzzy stochastic systems are not required with the proposed framework. A unified framework for sliding mode control of T-S fuzzy systems is formulated. The proposed Non-PDC integral sliding mode control scheme encompasses existing schemes when the previously imposed assumptions hold. Stability of the sliding motion is analyzed and the sliding mode controller is parameterized in terms of the solutions of a set of linear matrix inequalities which facilitates design. The methodology is applied to an inverted pendulum model to validate the effectiveness of the results presented.
Frequency stabilization in nonlinear MEMS and NEMS oscillators
Lopez, Omar Daniel; Antonio, Dario
2014-09-16
An illustrative system includes an amplifier operably connected to a phase shifter. The amplifier is configured to amplify a voltage from an oscillator. The phase shifter is operably connected to a driving amplitude control, wherein the phase shifter is configured to phase shift the amplified voltage and is configured to set an amplitude of the phase shifted voltage. The oscillator is operably connected to the driving amplitude control. The phase shifted voltage drives the oscillator. The oscillator is at an internal resonance condition, based at least on the amplitude of the phase shifted voltage, that stabilizes frequency oscillations in the oscillator.
Directory of Open Access Journals (Sweden)
Awad Ahmed
2016-10-01
Full Text Available The acceleration autopilot design for skid-to-turn (STT missile faces a great challenge owing to coupling effect among planes, variation of missile velocity and its parameters, inexistence of a complete state vector, and nonlinear aerodynamics. Moreover, the autopilot should be designed for the entire flight envelope where fast variations exist. In this paper, a design of integrated roll-pitch-yaw autopilot based on global fast terminal sliding mode control (GFTSMC with a partial state nonlinear observer (PSNLO for STT nonlinear time-varying missile model, is employed to address these issues. GFTSMC with a novel sliding surface is proposed to nullify the integral error and the singularity problem without application of the sign function. The proposed autopilot consisting of two-loop structure, controls STT maneuver and stabilizes the rolling with a PSNLO in order to estimate the immeasurable states as an output while its inputs are missile measurable states and control signals. The missile model considers the velocity variation, gravity effect and parameters’ variation. Furthermore, the environmental conditions’ dynamics are modeled. PSNLO stability and the closed loop system stability are studied. Finally, numerical simulation is established to evaluate the proposed autopilot performance and to compare it with existing approaches in the literature.
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.
Stabilization of infinite dimensional port-Hamiltonian systems by nonlinear dynamic boundary control
Ramirez, Hector; Zwart, Hans; Le Gorrec, Yann
2017-01-01
The conditions for existence of solutions and stability, asymptotic and exponential, of a large class of boundary controlled systems on a 1D spatial domain subject to nonlinear dynamic boundary actuation are given. The consideration of such class of control systems is motivated by the use of
DEFF Research Database (Denmark)
Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly nonlinear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
Bonito, Andrea
2013-10-03
We establish the L2-stability of an entropy viscosity technique applied to nonlinear scalar conservation equations. First-and second-order explicit time-stepping techniques using continuous finite elements in space are considered. The method is shown to be stable independently of the polynomial degree of the space approximation under the standard CFL condition. © 2013 American Mathematical Society.
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
Directory of Open Access Journals (Sweden)
Leonid Berezansky
2005-04-01
Full Text Available We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of the scalar nonlinear delay differential equation $$ frac{dN}{dt} = r(tN(tBig[a-Big(sum_{k=1}^m b_k N(g_k(tBig^{gamma}Big], $$ where $ g_k(tleq t$.
Stabilization of the higher order nonlinear Schrödinger equation with ...
Indian Academy of Sciences (India)
18
Abstract. We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. ... cattering, respectively. (1.2) also arised in the optical communications (see [1, 8, 16]). They can be applied to the long distance communications and ultrafast signalrouting systems. The HNLS models.
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.
Linear and nonlinear stability of periodic orbits in annular billiards.
Dettmann, Carl P; Fain, Vitaly
2017-04-01
An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Suming; Nie, Zongxiu
2014-11-01
Paul trap working in the second stability region has long been recognized as a possible approach for achieving high-resolution mass spectrometry (MS), which however is still far away from the experimental implementations because of the narrow working area and inefficient ion trapping. Full understanding of the ion motional behavior is helpful for solving the problem. In this article, the ion motion in a superimposed octopole field, which was characterized by the nonlinear Mathieu equation, was solved analytically using Poincare-Lighthill-Kuo (PLK) method. This method equivalently described the nonlinear disturbance by an effective quadrupole field with perturbed Mathieu parameters, a(u) and q(u), which would bring huge convenience in the studies of nonlinear ion dynamics and was, therefore, used for rapid evaluation of the nonlinear effects of ion motion. Fourth-order Runge-Kutta method (4th R-K) indicated the error of PLK for characterizing the frequency shift of ion motion was within 15%.
Hartig, Florian; Münkemüller, Tamara; Johst, Karin; Dieckmann, Ulf
2014-01-01
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field is an equally likely explanation for the current lack of empirical observations, and that our results are limited to communities with non-overlapping generations and constant resource supply. Our study highlights the need for combining ecological and
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)
Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System
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.
Resonator stability and higher-order modes in free-electron laser oscillators
Directory of Open Access Journals (Sweden)
Abhishek Pathak
2014-08-01
Full Text Available Three-dimensional simulation codes genesis and opc are used to investigate the dependence of the resonator stability of free-electron laser (FEL oscillators on the stability parameter, laser wavelength, outcoupling hole size and mirror tilt. We find that to have stable lasing over a wide range of wavelengths, the FEL cavity configuration should be carefully chosen. Broadly, the concentric configuration gives near-Gaussian modes and the best performance. At intermediate configurations the dominant mode often switches to a higher-order mode, which kills lasing. For the same reason, the outcoupled power can also be less. We have constructed a simple analytic model to study resonator stability which gives results that are in excellent agreement with the simulations. This suggests that modes in FEL oscillators are determined more by the cavity configuration and radiation propagation than by the details of the FEL interaction. We find (as in experiments at the CLIO FEL that tilting the mirror can, for some configurations, lead to more outcoupled power than a perfectly aligned mirror because the mode is now a more compact higher-order mode, which may have implications for the mode quality for user experiments. Finally, we show that the higher-order mode obtained is usually a single Gauss-Laguerre mode, and therefore it should be possible to filter out the mode using suitable intracavity elements, leading to better FEL performance.
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
Geometrical improvements of rotational stabilization of high-n ballooning modes in tokamaks
International Nuclear Information System (INIS)
Furukawa, Masaru; Tokuda, S.
2003-01-01
We have found numerically that damping phases appear in the time evolution of the perturbation energy of high-n ballooning modes in the presence of toroidal shear flows. The damping dominates exponential growth which occurs in the bad curvature region, resulting in stabilization of ballooning modes. D-shaping of plasma cross-section, reduction of aspect ratio, and arrangement of X-point at inner side of the torus enhance the stabilization effect of the toroidal flow through this mechanism. (author)
Hou, Huazhou; Zhang, Qingling
2016-11-01
In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Expansion methods for finding nonlinear stability domains of nuclear reactor models
International Nuclear Information System (INIS)
Yang, C.Y.; Cho, N.Z.
1992-01-01
Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are described in this paper: Method A based on expansion of a Lyapunov function and Method B based on expansion of any positive definite function. The methods are established on Lyapunov's stability definitions. Method A provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most reactor systems are stiff. Method B requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for reactor systems that are stiff. These methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared. (author)
Adegoke, Oluwashina; Dhang, Prasun; Mukhopadhyay, Banibrata; Ramadevi, M. C.; Bhattacharya, Debbijoy
2018-02-01
By analyzing the time series of RXTE/PCA data, the nonlinear variabilities of compact sources have been repeatedly established. Depending on the variation in temporal classes, compact sources exhibit different nonlinear 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 nonlinear 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 nonlinearity to the underlying spectral properties of the flow when the nonlinear properties are related to the associated transport mechanisms describing the geometry of the flow? The present work is aimed at addressing this question. Based on the connection between observed spectral and nonlinear (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 (ADAF) and general advective accretion flow (GAAF). 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.
Resistive Wall Mode Stability and Control in the Reversed Field Pinch
Yadikin, Dmitriy
2006-01-01
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...
Stabilization of thin shell modes by a rotating secondary wall
International Nuclear Information System (INIS)
Gimblett, C.G.
1989-01-01
A simple model is developed to investigate if and under what circumstances the thin shell instabilities of a Reverse Field Pinch can be stabilized by a rotating secondary wall. The principles may be applicable to reactor designs that utilize a flowing liquid blanket (author)
Stabilization effect of Weibel modes due to inverse bremsstrahlung ...
Indian Academy of Sciences (India)
2016-11-04
Nov 4, 2016 ... Abstract. In this work, the Weibel instability due to inverse bremsstrahlung absorption in laser fusion plasma has been investigated. The stabilization effect due to the coupling of the self-generated magnetic field by Weibel instability with the laser wave field is explicitly showed. The main result obtained in ...
Stabilization effect of Weibel modes due to inverse bremsstrahlung ...
Indian Academy of Sciences (India)
In this work, the Weibel instability due to inverse bremsstrahlung absorption in laser fusion plasma has been investigated. The stabilization effect due to the coupling of the self-generated magnetic field by Weibel instability with the laser wave field is explicitly showed. The main result obtained in this work is that the inclusion ...
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
Directory of Open Access Journals (Sweden)
Guowei Cai
2014-01-01
Full Text Available As to strong nonlinearity of doubly fed induction generators (DFIG and uncertainty of its model, a novel rotor current controller with nonlinearity and robustness is proposed to enhance fault ride-though (FRT capacities of grid-connected DFIG. Firstly, the model error, external disturbances, and the uncertain factors were estimated by constructing extended state observer (ESO so as to achieve linearization model, which is compensated dynamically from nonlinear model. And then rotor current controller of DFIG is designed by using terminal sliding mode variable structure control theory (TSMC. The controller has superior dynamic performance and strong robustness. The simulation results show that the proposed control approach is effective.
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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.
Freed, Alan; Leonov, Arkady I.
2002-01-01
This paper, the last in the series, continues developing the nonlinear constitutive relations for non-isothermal, compressible, solid viscoelasticity. We initially discuss a single integral approach, more suitable for the glassy state of rubber-like materials, with basic functionals involved in the thermodynamic description for this type of viscoelasticity. Then we switch our attention to analyzing stability constraints, imposed on the general formulation of the nonlinear theory of solid viscoelasticity. Finally, we discuss specific (known from the literature or new) expressions for material functions that are involved in the constitutive formulations of both the rubber-like and glassy-like, complementary parts of the theory.
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
Zong, Weikai; Charpinet, Stéphane; Vauclair, Gérard; Giammichele, Noemi; Van Grootel, Valérie
2017-10-01
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.
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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.
MEASUREMENT OF THE RESISTIVE WALL MODE STABILITY IN A ROTATING PLASMA USING ACTIVE MHD SPECTROSCOPY
International Nuclear Information System (INIS)
CHU, M.S; JACKSON, G.L; LA HAYE, R.J; SCOVILLE, J.T; STRAIT, E.J
2003-01-01
The stability of the resistive-wall mode (RWM) in DIII-D plasmas above the conventional pressure limit, where toroidal plasma rotation in the order of a few percent of the Alfven velocity is sufficient to stabilize the n=1 RWM, has been probed using the technique of active MHD spectroscopy at frequencies of a few Hertz. The measured frequency spectrum of the plasma response to externally applied rotating resonant magnetic fields is well described by a single mode approach and provides an absolute measurement of the damping rate and the natural mode rotation frequency of the stable RWM
Liu, Yang; Hsu, Yung; Chow, Chi-Wai; Yang, Ling-Gang; Yeh, Chien-Hung; Lai, Yin-Chieh; Tsang, Hon-Ki
2016-03-01
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.
Costabile, Jamie D.; Gołkowski, Mark; Wall, Randall E.
2017-12-01
Experimental observations of very low frequency (VLF) triggered emissions are an important resource in investigation of nonlinear wave-particle interactions between whistler mode waves and energetic electrons in the Earth's radiation belts. Magnetospherically generated whistler mode sidebands observed during the Siple Station wave injection experiment are analyzed using a mixed modulation model and the MINUIT minimization package. The observed sidebands are found to exhibit features of both amplitude and frequency modulation of the input carrier wave with frequency modulation becoming more prominent as the observed amplitudes of the carrier and sidebands increase. A nonlinear whistler mode wave growth formulation based on phase bunching of counterstreaming electrons within a well-defined phase trap is shown to reproduce the salient features of the sideband observations. Whistler mode sideband amplitude is shown to be affected by the shape and uniformity of the trap.
Wu, Yun-Jie; Zuo, Jing-Xing; Sun, Liang-Hua
2017-11-01
In this paper, the altitude and velocity tracking control of a generic hypersonic flight vehicle (HFV) is considered. A novel adaptive terminal sliding mode controller (ATSMC) with strictly lower convex function based nonlinear disturbance observer (SDOB) is proposed for the longitudinal dynamics of HFV in presence of both parametric uncertainties and external disturbances. First, for the sake of enhancing the anti-interference capability, SDOB is presented to estimate and compensate the equivalent disturbances by introducing a strictly lower convex function. Next, the SDOB based ATSMC (SDOB-ATSMC) is proposed to guarantee the system outputs track the reference trajectory. Then, stability of the proposed control scheme is analyzed by the Lyapunov function method. Compared with other HFV control approaches, key novelties of SDOB-ATSMC are that a novel SDOB is proposed and drawn into the (virtual) control laws to compensate the disturbances and that several adaptive laws are used to deal with the differential explosion problem. Finally, it is illustrated by the simulation results that the new method exhibits an excellent robustness and a better disturbance rejection performance than the convention approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Hossein Shahinzadeh; Ladan Darougaran; Ebrahim Jalili Sani; Hamed Yavari; Mahdi Mozaffari Legha
2012-01-01
This paper present a new method for design of power system stabilizer (PSS) based on sliding mode control (SMC) technique. The control objective is to enhance stability and improve the dynamic response of the multi-machine power system. In order to test effectiveness of the proposed scheme, simulation will be carried out to analyze the small signal stability characteristics of the system about the steady state operating condition following the change in reference mechanic...
Stability and stabilization of nonlinear systems and Takagi-Sugeno's fuzzy models
Directory of Open Access Journals (Sweden)
Blanco Yann
2001-01-01
Full Text Available This paper outlines a methodology to study the stability of Takagi-Sugeno's (TS fuzzy models. The stability analysis of the TS model is performed using a quadratic Liapunov candidate function. This paper proposes a relaxation of Tanaka's stability condition: unlike related works, the equations to be solved are not Liapunov equations for each rule matrix, but a convex combination of them. The coefficients of this sums depend on the membership functions. This method is applied to the design of continuous controllers for the TS model. Three different control structures are investigated, among which the Parallel Distributed Compensation (PDC. An application to the inverted pendulum is proposed here.
DEFF Research Database (Denmark)
Yoon, Changwoo; Wang, Xiongfei; Bak, Claus Leth
2015-01-01
This paper investigates the harmonic stability of small-scale inverter-based power systems. A holistic procedure to assess the contribution of each inverter to the system stability is proposed by means of using the impedancebased stability criterion. Multiple unstable modes can be identified step......-by-step coming from the interactions among inverters and passive networks. Compared to the conventional system stability analysis, the approach is easy to implement and avoids the effect of potential unstable system dynamics on the impedance ratio derived for the stability analysis. PSCAD/ EMTDC simulations...... of a Cigre LV network Benchmark system with multiple renewable energy sources are carried out. The results confirm the validity of the proposed approach....
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
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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.
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Xinhua Zheng
2015-01-01
Full Text Available Stability of pneumatic cabin pressure regulating system with complex nonlinear characteristics is considered. The mathematical model of each component is obtained and given in detail. The governing equations of the considered system consist of 8 differential equations. In the circumstance, commonly used methods of nonlinear system analysis are not applicable. Therefore a new method is proposed to construct phase plane trajectories numerically. The calculation steps are given in detail. And convergence region of numerical calculation and limits on step size is defined. The method is applied constructing phase plane trajectories for considered cabin pressure regulating system. Phase plane analysis shows that there exists a limit cycle, which is responsible for pressure pulsating in aircraft cabin. After parameters adjustment, excellent stability characteristics are acquired. And the validity of this method is confirmed by the simulation.
Feigin, Alexander; Gavrilov, Andrey; Loskutov, Evgeny; Mukhin, Dmitry
2015-04-01
Proper decomposition of the complex system into well separated "modes" is a way to reveal and understand the mechanisms governing the system behaviour as well as discover essential feedbacks and nonlinearities. The decomposition is also natural procedure that provides to construct adequate and concurrently simplest models of both corresponding sub-systems, and of the system in whole. In recent works two new methods of decomposition of the Earth's climate system into well separated modes were discussed. The first method [1-3] is based on the MSSA (Multichannel Singular Spectral Analysis) [4] for linear expanding vector (space-distributed) time series and makes allowance delayed correlations of the processes recorded in spatially separated points. The second one [5-7] allows to construct nonlinear dynamic modes, but neglects delay of correlations. It was demonstrated [1-3] that first method provides effective separation of different time scales, but prevent from correct reduction of data dimension: slope of variance spectrum of spatio-temporal empirical orthogonal functions that are "structural material" for linear spatio-temporal modes, is too flat. The second method overcomes this problem: variance spectrum of nonlinear modes falls essentially sharply [5-7]. However neglecting time-lag correlations brings error of mode selection that is uncontrolled and increases with growth of mode time scale. In the report we combine these two methods in such a way that the developed algorithm allows constructing nonlinear spatio-temporal modes. The algorithm is applied for decomposition of (i) multi hundreds years globally distributed data generated by the INM RAS Coupled Climate Model [8], and (ii) 156 years time series of SST anomalies distributed over the globe [9]. We compare efficiency of different methods of decomposition and discuss the abilities of nonlinear spatio-temporal modes for construction of adequate and concurrently simplest ("optimal") models of climate systems
Scheme for improving laser stability via feedback control of intracavity nonlinear loss.
Jin, Pixian; Lu, Huadong; Su, Jing; Peng, Kunchi
2016-05-01
We present a novel and efficient scheme to enhance the stability of laser output via feedback control to a nonlinear loss deliberately introduced to the laser resonator. By means of the feedback control to the intracavity nonlinear loss of an all-solid-state continuous-wave single-frequency laser with high output power at 1064 nm, its intensity and frequency stabilities are significantly improved. A lithium triborate crystal is deliberately placed inside the laser resonator to be an element of the nonlinear loss, and the temperature of the crystal is feedback controlled by an electronic loop. The control signal is generated by distinguishing the deviation of the output power and used for manipulating the intracavity nonlinear loss to compensate the deviation of the laser power actively. With the feedback-control loop, the intensity and frequency fluctuations of the output laser at 1064 nm are reduced from ±0.59% and 21.82 MHz without the feedback to ±0.26% and 9.84 MHz, respectively.
Asadi, Hamed; Eynbeygi, Mehdi; Wang, Quan
2014-07-01
The instability of geometrically imperfect shape memory alloy (SMA) fibers reinforced with hybrid laminated composite (SMAHC) plates and subjected to a uniform thermal loading is analytically investigated. The material properties of the SMAHC plates are assumed to be functions of temperature. Nonlinear equations of the plates’ thermal stability are derived based on a higher order shear deformation theory incorporating von Karman geometrical nonlinearity via stationary potential energy. The structural recovery stress, which is generated by martensitic phase transformation of the prestrained SMA fibers, is calculated based on the one-dimensional thermodynamic constitutive model by Brinson. Adopting the Galerkin procedure, the governing nonlinear partial differential equations are converted into a set of nonlinear algebraic equations, in which systems of equations are solved by introducing an analytical approach. Closed-form formulations are presented to determine the load-deflection path and critical buckling temperature of the plate. Based on the developed closed-form solutions, ample numerical results are presented to provide an insight into the effects of the volume fraction, prestrain, location and orientation of the SMA fibers, composite plate geometry, geometrical imperfection and temperature dependence on the stability of the SMAHC plates. It is shown that a proper application of SMA fibers results in a considerable delay of the thermal bifurcation and controllable thermal post-buckling deflection of the SMAHC plate.
Directory of Open Access Journals (Sweden)
Huang Tingwen
2009-01-01
Full Text Available This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.
Existence and stability of the externally driven, damped nonlinear Schroedinger solitons
International Nuclear Information System (INIS)
Barashenkov, I.V.; Smirnov, Yu.S.
1997-01-01
The externally driven damped nonlinear Schroedinger (NLS) equation on the infinite line is studied. Existence and stability chart for its soliton solution is constructed on the plane of two control parameters, the forcing amplitude h and dissipation coefficient γ. For generic values of h and γ there are two coexisting solitons one of which (ψ + ) is always unstable. The bifurcation diagram of the second solution (ψ - ) depends on the dissipation coefficient: if γ cr , the ψ - is stable for small h and loses its stability via a Hopf bifurcation as h is increased; if γ>γ cr , the ψ - is stable for all h. There are no 'stability windows' in the unstable region. We show that the previously reported 'stability windows' occur only when the equation is considered on a finite (and small) spatial interval
Directory of Open Access Journals (Sweden)
Sherif Amirov
2017-08-01
Full Text Available The recent work on the solvability of the boundary value problem for the nonlinear analogue of the Boussinesq equation has been further extended to focus on the characteristics of the solution. Since this type of equation does not have a known analytical solution for arbitrary boundary conditions, the problem has been solved numerically. The stability of the solution and the effect of the input function on the stability have been investigated from the physics point of view. For the special case of a discontinuous function at the right hand side of the equation, the solution has been analyzed around the discontinuity points.
Existence and Stability of the Solution of a Nonlinear Boundary Value Problem
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Agneta M. Balint
2012-01-01
Full Text Available The purpose is to find conditions assuring the existence of solutions for a nonlinear, boundary value problem in case of the axis-symmetric Young-Laplace differential equation. The equation describes the capillary surface between two static fluids. Necessary or sufficient conditions are found for the existence of a solution. The static stability of the obtained solution is also analyzed and stability or instability results are revealed. For the NdYAG microfiber growth, by the pulling-down method, numerical illustrations are given.
Electro-optic side-chain polyimide system with large optical nonlinearity and high thermal stability
Sotoyama, Wataru; Tatsuura, Satoshi; Yoshimura, Tetsuzo
1994-04-01
We report electro-optic (EO) efficiency and thermal stability of a poled polyimide system with nonlinear optical dyes as side chains. The side-chain polyimide system is synthesized from a dianhydride containing azobenzene dye and a diamine. The dye in the polymer is chemically stable for temperatures below 250 °C. The polymer can be poled simultaneously with or after imidization of the polyamic acid. Our sample poled after imidization shows a large EO coefficient (r33=10.8 pm/V at λ=1.3 μm) and long-term thermal stability at 120 °C.
On the internal stability of non-linear dynamic inversion: application to flight control
Czech Academy of Sciences Publication Activity Database
Alam, M.; Čelikovský, Sergej
2017-01-01
Roč. 11, č. 12 (2017), s. 1849-1861 ISSN 1751-8644 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : flight control * non-linear dynamic inversion * stability Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 2.536, year: 2016 http://library.utia.cas.cz/separaty/2017/TR/celikovsky-0476150.pdf
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
A nonlinear two-species oscillatory system: bifurcation and stability analysis
Directory of Open Access Journals (Sweden)
C. G. Chakrabarti
2003-06-01
Full Text Available The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.
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)
Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays
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.
Nonlinear stability and control study of highly maneuverable high performance aircraft
Mohler, R. R.
1993-01-01
This project is intended to research and develop new nonlinear methodologies for the control and stability analysis of high-performance, high angle-of-attack aircraft such as HARV (F18). Past research (reported in our Phase 1, 2, and 3 progress reports) is summarized and more details of final Phase 3 research is provided. While research emphasis is on nonlinear control, other tasks such as associated model development, system identification, stability analysis, and simulation are performed in some detail as well. An overview of various models that were investigated for different purposes such as an approximate model reference for control adaptation, as well as another model for accurate rigid-body longitudinal motion is provided. Only a very cursory analysis was made relative to type 8 (flexible body dynamics). Standard nonlinear longitudinal airframe dynamics (type 7) with the available modified F18 stability derivatives, thrust vectoring, actuator dynamics, and control constraints are utilized for simulated flight evaluation of derived controller performance in all cases studied.
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)
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)
Finite Larmor radius effects on the stability properties of internal modes of a z-pinch
International Nuclear Information System (INIS)
Aakerstedt, H.O.
1987-01-01
From the Vlasov-fluid model a set of approximate stability equations describing the stability of a cylindrically symmetric z-pinch is derived. The equations are derived in the limit of small gyroradius and include first order kinetic effects such as finite ion Larmor radius effects and resonant ion effects. Neglecting the resonant ion terms, we explicitly solve this set of equations for a constant current density profile leading to a dispersion relation. FLR effects are shown for the case of m=1 internal mode to be stabilizing and for large wavenumbers k, using a trial function approach, absolute stabilization is found. (author)
International Nuclear Information System (INIS)
Al-Asadi, H A; Mahdi, M A; Bakar, A A A; Adikan, F R Mahamd
2011-01-01
We present a theoretical study of nonlinear phase shift through stimulated Brillouin scattering in single mode optical fiber. Analytical expressions describing the nonlinear phase shift for the pump and Stokes waves in the pump power recycling technique have been derived. The dependence of the nonlinear phase shift on the optical fiber length, the reflectivity of the optical mirror and the frequency detuning coefficient have been analyzed for different input pump power values. We found that with the recycling pump technique, the nonlinear phase shift due to stimulated Brillouin scattering reduced to less than 0.1 rad for 5 km optical fiber length and 0.65 reflectivity of the optical mirror, respectively, at an input pump power equal to 30 mW
Linear mode stability of the Kerr-Newman black hole and its quasinormal modes.
Dias, Óscar J C; Godazgar, Mahdi; Santos, Jorge E
2015-04-17
We provide strong evidence that, up to 99.999% of extremality, Kerr-Newman black holes (KNBHs) are linear mode stable within Einstein-Maxwell theory. We derive and solve, numerically, a coupled system of two partial differential equations for two gauge invariant fields that describe the most general linear perturbations of a KNBH. We determine the quasinormal mode (QNM) spectrum of the KNBH as a function of its three parameters and find no unstable modes. In addition, we find that the lowest radial overtone QNMs that are connected continuously to the gravitational ℓ=m=2 Schwarzschild QNM dominate the spectrum for all values of the parameter space (m is the azimuthal number of the wave function and ℓ measures the number of nodes along the polar direction). Furthermore, the (lowest radial overtone) QNMs with ℓ=m approach Reω=mΩH(ext) and Imω=0 at extremality; this is a universal property for any field of arbitrary spin |s|≤2 propagating on a KNBH background (ω is the wave frequency and ΩH(ext) the black hole angular velocity at extremality). We compare our results with available perturbative results in the small charge or small rotation regimes and find good agreement.
Kojima, H.; Matsumoto, H.; Omura, Y.; Tsurutani, B. T.
1989-01-01
An ion beam resonates with R-mode waves at a high-frequency RH mode and a low-frequency RL mode. The nonlinear evolution of ion beam-generated RH waves is studied here by one-dimensional hybrid computer experiments. Both wave-particle and subsequent wave-wave interactions are examined. The competing process among coexisting RH and RL mode beam instabilities and repeated decay instabilities triggered by the beam-excited RH mode waves is clarified. It is found that the quenching of the RH instability is not caused by a thermal spreading of the ion beam, but by the nonlinear wave-wave coupling process. The growing RH waves become unstable against the decay instability. This instability involves a backward-traveling RH electromagnetic wave and a forward-traveling longitudinal sound wave. The inverse cascading process is found to occur faster than the growth of the RL mode. Wave spectra decaying from the RH waves weaken as time elapses and the RL mode waves become dominant at the end of the computer experiment.
Ammar, Abdelkarim; Bourek, Amor; Benakcha, Abdelhamid
2017-03-01
This paper presents a nonlinear Direct Torque Control (DTC) strategy with Space Vector Modulation (SVM) for an induction motor. A nonlinear input-output feedback linearization (IOFL) is implemented to achieve a decoupled torque and flux control and the SVM is employed to reduce high torque and flux ripples. Furthermore, the control scheme performance is improved by inserting a super twisting speed controller in the outer loop and a load torque observer to enhance the speed regulation. The combining of dual nonlinear strategies ensures a good dynamic and robustness against parameters variation and disturbance. The system stability has been analyzed using Lyapunov stability theory. The effectiveness of the control algorithm is investigated by simulation and experimental validation using Matlab/Simulink software with real-time interface based on dSpace 1104. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Krishan, S.
2007-01-01
The Stieltjes transform has been used in place of a more common Laplace transform to determine the time evolution of the self-consistent field (SCF) of an unmagnetized semi-infinite plasma, where the plasma electrons together with a primary and a low-density secondary electron beam move perpendicular to the boundary surface. The secondary beam is produced when the primary beam strikes the grid. Such a plasma system has been investigated by Griskey and Stanzel [M. C. Grisky and R. L. Stenzel, Phys. Rev. Lett. 82, 556 (1999)]. The physical phenomenon, observed in their experiment, has been named by them as ''secondary beam instability.'' The character of the instability observed in the experiment is not the same as predicted by the conventional treatments--the field amplitude does not grow with time. In the frequency spectrum, the theory predicts peak values in the amplitude of SCF at the plasma frequency of plasma and secondary beam electrons, decreasing above and below it. The Stieltjes transform for functions, growing exponentially in the long time limit, does not exist, while the Laplace transform technique gives only exponentially growing solutions. Therefore, it should be interesting to know the kind of solutions that an otherwise physically unstable plasma will yield. In the high-frequency limit, the plasma has been found to respond to any arbitrary frequency of the initial field differentiated only by the strength of the resulting SCF. The condition required for exponential growth in the conventional treatments, and the condition for maximum amplitude (with respect to frequency) in the present treatment, have been found to be the same. Nonlinear mode coupling between the modes excited by the plasma electrons and the low-density secondary beam gives rise to two frequency-dependent peaks in the field amplitude, symmetrically located about the much stronger peak due to the plasma electrons, as predicted by the experiment
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.
Solar seismology. I - The stability of the solar p-modes
Goldreich, P.; Keeley, D. A.
1977-01-01
The stability of the radial p-modes of the sun is investigated by computing nonadiabatic eigenvalues and eigenfunctions for a solar envelope model which extends from an inner radius of about 0.3 solar radius out to an optical depth of about 0.0003. The calculations take into account in a crude fashion the response of the convective flux to the oscillation. The dynamical effect of turbulence in the convection zone is parametrized in terms of a turbulent shear viscosity. The results show that if damping by turbulent viscosity is neglected, all modes with periods longer than 6 minutes are unstable. The familiar kappa-mechanism, which operates in the H ionization-H(-) opacity region, is the dominant source of driving of the oscillations. Modes with periods shorter than 6 minutes are stabilized by radiative damping in the solar atmosphere. When turbulent dissipation of pulsational energy is included, all modes are predicted to be stable. However, the margin of stability is very small. In view of the large uncertainty that must be assigned to the estimate of turbulent damping, it is concluded that theoretical calculations cannot unequivocally resolve the question of the stability of the solar p-modes.
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)
Krishnan, Hariharan
1993-01-01
This thesis is organized in two parts. In Part 1, control systems described by a class of nonlinear differential and algebraic equations are introduced. A procedure for local stabilization based on a local state realization is developed. An alternative approach to local stabilization is developed based on a classical linearization of the nonlinear differential-algebraic equations. A theoretical framework is established for solving a tracking problem associated with the differential-algebraic system. First, a simple procedure is developed for the design of a feedback control law which ensures, at least locally, that the tracking error in the closed loop system lies within any given bound if the reference inputs are sufficiently slowly varying. Next, by imposing additional assumptions, a procedure is developed for the design of a feedback control law which ensures that the tracking error in the closed loop system approaches zero exponentially for reference inputs which are not necessarily slowly varying. The control design methodologies are used for simultaneous force and position control in constrained robot systems. The differential-algebraic equations are shown to characterize the slow dynamics of a certain nonlinear control system in nonstandard singularly perturbed form. In Part 2, the attitude stabilization (reorientation) of a rigid spacecraft using only two control torques is considered. First, the case of momentum wheel actuators is considered. The complete spacecraft dynamics are not controllable. However, the spacecraft dynamics are small time locally controllable in a reduced sense. The reduced spacecraft dynamics cannot be asymptotically stabilized using continuous feedback, but a discontinuous feedback control strategy is constructed. Next, the case of gas jet actuators is considered. If the uncontrolled principal axis is not an axis of symmetry, the complete spacecraft dynamics are small time locally controllable. However, the spacecraft attitude
Linear stability analysis of detonations via numerical computation and dynamic mode decomposition
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.
Linear stability analysis of detonations via numerical computation and dynamic mode decomposition
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.
Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides
DEFF Research Database (Denmark)
Reddy, D. V.; Raymer, M. G.; McKinstrie, C. J.
2013-01-01
We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three-wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use in a trans......We explore theoretically the feasibility of using frequency conversion by sum- or difference-frequency generation, enabled by three-wave-mixing, for selectively multiplexing orthogonal input waveforms that overlap in time and frequency. Such a process would enable a drop device for use...... in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process......, and employ Schmidt (singular-value) decompositions thereof to quantify its viability in functioning as a coherent waveform discriminator. We define a selectivity figure of merit in terms of the Schmidt coefficients, and use it to compare and contrast various parameter regimes via extensive numerical...
Harnessing intrinsic localized modes to identify impurities in nonlinear periodic systems
Thota, M.; Harne, R. L.; Wang, K. W.
2015-02-01
Intrinsic localized modes (ILMs) are concentrations of vibrational energy in periodic systems/lattices due to the combined influences of nonlinearity and discreteness. Moreover, ILMs can move within the system and may strongly interact with an impurity, such as a stiffness change, mass variation, etc. Numerous scientific fields have uncovered examples and evidence of ILMs, motivating a multidisciplinary pursuit to rigorously understand the underlying principles. In spite of the diverse technical studies, a characterization of ILM interaction behaviors with multiple impurities in dissipative lattices remains outstanding. The insights on such behaviors may be broadly useful when dynamic measurements are the only accessible features of the periodic system. For instance, one may guide an ILM within the lattice using a deliberately applied and steered impurity and harness the observed interaction behaviors with a second, static (immovable) impurity/defect to identify how the underlying lattice is different at the second, defected site, whether or not one knew the position of the defect a priori. In this spirit, this research studies, analyzes, and characterizes the interaction types amongst an ILM and multiple impurities, and devises a method to identify a static defect impurity using quantitatively and qualitatively distinct interaction phenomena. The method is found to be robust to moderate levels of lattice stiffness heterogeneity and is applicable to monitor various property changes that represent impurities. Finally, experimental studies verify that ILMs interact with multiple impurities in unique ways such that defect features may be effectively identified.
Akramov, Tohir; Baty, Hubert
2017-08-01
The nonlinear evolution of double tearing modes (DTMs) is investigated within the framework of resistive magnetohydrodynamic (MHD) simulations in a two-dimensional Cartesian geometry. We have explored the explosive reconnection phase associated with the growth of the secondary structure-driven instability for a range of resistivity values. The time scale of the explosive phase (that is of order of a few Alfvénic time scales) is shown to be quasi-independent of the resistivity, even when fast growing plasmoids develop for the highest enough Lundquist number cases. Test particle accelerations are performed using the MHD explosive simulations as input parameters. Our results show that reconnection DTM dynamics is able to provide an efficient process for accelerating charged particles far beyond characteristic thermal velocities within the reconnection layers. The main acceleration mechanism is attributed to the strong inductive electric field generated by the island structure-driven instability, with an additional smaller contribution due to the presence of plasmoids. Finally, our results are used to discuss some features of the accelerated particle spectra during flaring activity in the solar corona.
Linear and non-linear control of wind farms. Contribution to the grid stability
Energy Technology Data Exchange (ETDEWEB)
Fernandez, R.D. [Laboratorio de Electronica, Facultad de Ingenieria, Universidad Nacional de la Patagonia San Juan Bosco, Ciudad Universitaria, Km. 4, 9000, Comodoro Rivadavia (Argentina); Mantz, R.J. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900, La Plata (Argentina); Comision de Investigaciones Cientificas de la Provincia de Buenos Aires, CICpBA, La Plata (Argentina); Battaiotto, P.E. [Laboratorio de Electronica Industrial, Control e Instrumentacion (LEICI), Facultad de Ingenieria, Universidad Nacional de La Plata, CC 91, 1900, La Plata (Argentina)
2010-06-15
This paper deals with linear and non-linear control of wind farms equipped with doubly-fed induction generators (DFIG). Both, active and reactive wind farm powers are employed in two independent control laws in order to increase the damping of the oscillation modes of a power system. In this way, it presented a general strategy where two correction terms are added, one by each independent control, to the normal operating condition of a wind farm. The proposed control laws are derived from the Lyapunov approach. Meanwhile for the reactive power a non-linear correction is presented, for the wind farm active power it is demonstrated that the classical proportional and inertial laws can be considered via the Lyapunov approach if wind farms are considered as real power plants, i.e. equivalent to conventional synchronous generation. Finally, some simulations are presented in order to support the theoretical considerations demonstrating the potential contributions of both control laws. (author)
Jambunathan, V.; Murthy, V. R.
1993-01-01
A generic mathematical model that is capable of accurately modeling the multiple load path bearingless rotor blade is developed. A comprehensive, finite element based solution for the natural vibration of the rotor blade is developed. An iterative scheme based on harmonic balance is used to evaluate the nonlinear response of the rotor to control inputs and a Newton-Raphson procedure is employed to evaluate the trim of rotorcraft. Linearized perturbation model of the nonlinear system are presented. The model is validated by comparing with existing whirl tower, wind tunnel and flight test results of BMR/BO-105 helicopter. Frequencies of two bearingless rotor blades compare well with results from experiments. Nonlinear response and trim results are presented for the bearingless BMR/BO-105 rotor. Aeroelastic stability in forward flight, evaluated using floquet theory agrees with test data in general.
Sufficient stability condition for alpha-driven velocity-space modes in compression tokamak
International Nuclear Information System (INIS)
Yamazaki, K.; Okamoto, M.
1982-09-01
Magnetic compression heating may invert the velocity distribution of alpha particles, which leads to velocity-space instabilities. A sufficient stability condition is derived for these modes in compression tokamaks. High-field high-density compression scenario like Zephyr satisfies this stability condition, while medium-field high-temperature compression scheme like TFTR has some possibilities of exciting velocity-space thermonuclear instabilities. (author)
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
Stability Analysis and Design of a Nonlinear Controller for Hot Rolling Coiler
Directory of Open Access Journals (Sweden)
Rui Li
2015-01-01
Full Text Available For the new style hot rolling coiler which adopt AC asynchronous motor as the driving force and with using the algorithm based on differential geometry design nonlinear controller, precise coiling tension control in the rolling process of strip steel is achieved. In this paper, under the rotating orthogonal coordinate system, the fifth-order nonlinear motor model is selected as the controlled plant. By multi-input multioutput (MIMO exact feedback linearization (EFL algorithm, the nonlinear model is transformed to a linear one. In terms of small-gain theorem, it is the first to prove that the nonlinear coiler engine that contains the controller has characteristics of input-to-state stability. Experimental results show that the algorithm can be used for high order tracking control system with time-varying parameters. Even without the traditional flux orientation calculation, the output signals are decoupled. With this controller, the tension deviation is restricted to less than 3% and average rotational speed bias was decreased from 0.5% to 0.1% that ensure high-quality plate cut and surface of strip products.
The stability of tidally deformed neutron stars to three- and four-mode coupling
International Nuclear Information System (INIS)
Venumadhav, Tejaswi; Zimmerman, Aaron; Hirata, Christopher M.
2014-01-01
It has recently been suggested that the tidal deformation of a neutron star excites daughter p- and g-modes to large amplitudes via a quasi-static instability. This would remove energy from the tidal bulge, resulting in dissipation and possibly affecting the phase evolution of inspiralling binary neutron stars and hence the extraction of binary parameters from gravitational wave observations. This instability appears to arise because of a large three-mode interaction among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We show that additional four-mode interactions enter into the analysis at the same order as the three-mode terms previously considered. We compute these four-mode couplings by finding a volume-preserving coordinate transformation that relates the energy of a tidally deformed star to that of a radially perturbed spherical star. Using this method, we relate the four-mode coupling to three-mode couplings and show that there is a near-exact cancellation between the destabilizing effect of the three-mode interactions and the stabilizing effect of the four-mode interaction. We then show that the equilibrium tide is stable against the quasi-static decay into daughter p- and g-modes to leading order. The leading deviation from the quasi-static approximation due to orbital motion of the binary is considered; while it may slightly spoil the near-cancellation, any resulting instability timescale is at least of order the gravitational wave inspiral time. We conclude that the p-/g-mode coupling does not lead to a quasi-static instability, and does not impact the phase evolution of gravitational waves from binary neutron stars.
International Nuclear Information System (INIS)
Pelinovsky, Dmitry E.; Yang Jianke
2005-01-01
We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons
Stability of the mode-locking regime in tapered quantum-dot lasers
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.
Soliton stability criterion for generalized nonlinear Schrödinger equations.
Quintero, Niurka R; Mertens, Franz G; Bishop, A R
2015-01-01
A stability criterion for solitons of the driven nonlinear Schrödinger equation (NLSE) has been conjectured. The criterion states that p'(v)0 is a necessary condition for stability; here, v is the soliton velocity and p=P/N, where P and N are the soliton momentum and norm, respectively. To date, the curve p(v) was calculated approximately by a collective coordinate theory, and the criterion was confirmed by simulations. The goal of this paper is to calculate p(v) exactly for several classes and cases of the generalized NLSE: a soliton moving in a real potential, in particular a time-dependent ramp potential, and a time-dependent confining quadratic potential, where the nonlinearity in the NLSE also has a time-dependent coefficient. Moreover, we investigate a logarithmic and a cubic NLSE with a time-independent quadratic potential well. In the latter case, there is a bisoliton solution that consists of two solitons with asymmetric shapes, forming a bound state in which the shapes and the separation distance oscillate. Finally, we consider a cubic NLSE with parametric driving. In all cases, the p(v) curve is calculated either analytically or numerically, and the stability criterion is confirmed.
Stabilization of business cycles of finance agents using nonlinear optimal control
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.
Localized stability criterion for kink modes in systems with small shear
International Nuclear Information System (INIS)
Hastie, R.J.; Johnson, J.L.
1986-02-01
A localized magnetohydrodynamic stability criterion for ideal kink instabilities is determined for systems where the safety factor has a local minimum on a rational surface with no pressure gradient. These modes are stable in the cylindrical limit, but toroidal effects can make them unstable. They could provide a partial explanation for the rapid current penetration observed in tokamaks. 7 refs
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.
Emerson, Benjamin; Lieuwen, Tim
2017-11-01
This study investigates the forced response characteristics of axisymmetric structures in density-stratified swirling jets. The reacting, swirling jet is an important canonical flow field for modern combustion systems. This work is motivated by the combustion instability problem for such systems, where acoustically excited vortical structures may drive oscillatory heat release of combustion. Previous hydrodynamics studies have shown that the stability of helical structures is highly sensitive to the swirl number. However, the combustion literature has shown that axisymmetric structures (in contrast to helical structures) are often responsible for most of the heat release response. Therefore, this work performs a spatial stability analysis to study the swirl number sensitivity of the forced response of the axisymmetric mode. A spatio-temporal analysis is conducted in tandem to investigate the swirl number sensitivity of the impulse response of this mode. The results show that at low values of the swirl number, the axisymmetric mode stability is a weak function of the swirl number, but that new modes and stability bifurcations appear at high swirl numbers.
Shiau, Ting N.; Hwang, Jon L.; Chang, Yuan B.
1992-06-01
The stability of steady state synchronous and nonsynchronous response of a nonlinear rotor system supported by squeeze-film dampers is investigated. The nonlinear differential equations which govern the motion of rotor bearing system are obtained by using the Generalized Polynomial Expansion Method. The steady state response of system is obtained by using the hybrid numerical method which combines the merits of the harmonic balance and collocation methods. The stability of system response is examined using Floquet-Liapunov theory. Using the theory, the performance may be evaluated with the calculation of derivatives of nonlinear hydrodynamic forces of the squeeze-film damper with respect to displacement and velocity of the journal center. In some cases, these derivatives can be expressed in closed form and the prediction of the dynamic characteristic of the nonlinear rotor system will be more effective. The stability results are compared to those using a direct numerical integration method and both are in good agreement.
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
Large net-normal dispersion Er-doped fibre laser mode-locked with a nonlinear amplifying loop mirror
Bowen, Patrick; Erkintalo, Miro; Broderick, Neil G. R.
2018-03-01
We report on an environmentally stable, all-PM-fibre, Er-doped, mode-locked laser with a central wavelength of 1550 nm. Significantly, the laser possesses large net-normal dispersion such that its dynamics are comparable to that of an all-normal dispersion fibre laser at 1 μm with an analogous architecture. The laser is mode-locked with a nonlinear amplifying loop mirror to produce pulses that are externally compressible to 500 fs. Experimental results are in good agreement with numerical simulations.
International Nuclear Information System (INIS)
Sudakov, M.Yu.
2000-01-01
One studied theoretically the mode of mass-selective unstable output of ions from three-dimensional quadrupole ion trap. One developed a method represent coordinates of ions per one period of supplying HF voltage with regard to nonlinear distortions of quadrupole potential. One derived equation for an envelope of ion oscillations in the form of motion equation of mass point in the efficient force field. One explained the effect of output delay of ions at presence of the field negative even harmonics. One proved that the positive even distortions of quadrupole potential favored realization of that mode and studied the dynamics of ions in the course of output [ru
Gorbunkov, M. V.; Maslova, Yu Ya; Petukhov, V. A.; Semenov, M. A.; Shabalin, Yu V.; Tunkin, V. G.
2018-03-01
Harmonic mode-locking in a solid state laser due to optoelectronic control is studied numerically on the basis of two methods. The first one is detailed numeric simulation taking into account laser radiation fine time structure. It is shown that optimally chosen feedback delay leads to self-started mode-locking with generation of desired number of pulses in the laser cavity. The second method is based on discrete maps for short laser pulse energy. Both methods show that the application of combination of positive and negative feedback loops allows to reduce the period of regular nonlinear dynamics down to a fraction of a laser cavity round trip time.
Effect of Magnetic Shear and Plasma Compressibility on Ideal Interchange Mode Stability
Mirnov, V. V.; Hegna, C. C.
2003-10-01
We analyze the stability of a localized ideal interchange mode in a cylindrical screw pinch equilibrium. In the general case, the screw pinch magnetic configuration has magnetic shear. From the Energy Principle, it follows that the most dangerous interchange perturbations, k_||=0, are incompressible, and marginal stability is given by Suydam's criterion. In the particular case of a screw pinch without axial field (Z-pinch), the magnetic configuration is shear free and, correspondingly, the stabilizing effect of shear vanishes. In this case, the magnetic field is pure poloidal, and the resonance condition of interchange modes, k_||=0, corresponds to m=0 "sausage"-like perturbations. For these modes, the effect of plasma compressibility becomes important and, in some sense, it replaces the stabilizing effect of magnetic shear. We investigate the transition between these two stabilizing mechanisms as the equilibrium changes from one with magnetic shear to a magnetic shear free configuration. This is of interest for closed systems with rational surfaces where dq/dr arrow 0 as well as for non paraxial open traps and magnetic dipoles where the effect of plasma compression plays important role.
Photochemical stability of nonlinear optical chromophores in polymeric and crystalline materials
International Nuclear Information System (INIS)
Rezzonico, Daniele; Kwon, Seong-Ji; Figi, Harry; Kwon, O-Pil; Jazbinsek, Mojca; Guenter, Peter
2008-01-01
We compare the photochemical stability of the nonlinear optical chromophore configurationally locked polyene 2-(3-[2-(4-dimethylaminophenyl)vinyl]-5,5-dimethylcyclohex-2-enylidene) malononitrile (DAT2) embedded in a polymeric matrix and in a single-crystalline configuration. The results show that, under resonant light excitations, the polymeric compound degrades through an indirect process, while the DAT2 crystal follows a slow direct process. We show that chromophores in a crystalline environment exhibit three orders of magnitude better photostability as compared to guest-host polymer composites
A Nonlinear Observer for Estimating Transverse Stability Parameters of Marine Surface Vessels
DEFF Research Database (Denmark)
Galeazzi, Roberto; Perez, Tristan
2011-01-01
This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel’s centre of gravity due...... to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves – propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion...
Energy Technology Data Exchange (ETDEWEB)
Ryashko, Lev [Ural Federal University, Lenina, 51, Ekaterinburg, 620000 (Russian Federation)
2015-11-30
A stabilization problem of the equilibrium of stochastically forced nonlinear discrete-time system with incomplete information is considered. Our approach uses a regulator which synthesizes the required stochastic sensitivity of the equilibrium. Mathematically, this problem is reduced to the solution of some quadratic matrix equations. A description of attainability sets and algorithms for regulators design is given. The general results are applied to the suppression of unwanted large-amplitude oscillations around the equilibria of the stochastically forced Verhulst model with noisy observations.
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model
Directory of Open Access Journals (Sweden)
Anatoli F. Ivanov
2010-09-01
Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.
Photochemical stability of nonlinear optical chromophores in polymeric and crystalline materials.
Rezzonico, Daniele; Kwon, Seong-Ji; Figi, Harry; Kwon, O-Pil; Jazbinsek, Mojca; Günter, Peter
2008-03-28
We compare the photochemical stability of the nonlinear optical chromophore configurationally locked polyene 2-{3-[2-(4-dimethylaminophenyl)vinyl]-5,5-dimethylcyclohex-2-enylidene} malononitrile (DAT2) embedded in a polymeric matrix and in a single-crystalline configuration. The results show that, under resonant light excitations, the polymeric compound degrades through an indirect process, while the DAT2 crystal follows a slow direct process. We show that chromophores in a crystalline environment exhibit three orders of magnitude better photostability as compared to guest-host polymer composites.
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
Stability of the single-mode output of a laser diode array with phase conjugate feedback
DEFF Research Database (Denmark)
Juul Jensen, S.; Løbel, M.; Petersen, P.M.
2000-01-01
. The output power and the center wavelength are found to be extremely stable in a 100 h stability measurement. External feedback of the output beam into the laser is seen to decrease both the spatial and the temporal coherence of the output significantly. We outline an approach to obtain a stable single......The stability of the output of a single-mode laser diode array with frequency selective phase conjugate feedback has been investigated experimentally. Both the long-term stability of the laser output and the sensitivity to feedback generated by external reflection of the output beam are examined......-mode output when external feedback is present using spatial filtering in the path of the output beam. (C) 2000 American Institute of Physics....
Peng, Junsong; Tarasov, Nikita; Sugavanam, Srikanth; Churkin, Dmitry
2016-09-19
We report for the first time, rogue waves generation in a mode-locked fiber laser that worked in multiple-soliton state in which hundreds of solitons occupied the whole laser cavity. Using real-time spatio-temporal intensity dynamics measurements, it is unveiled that nonlinear soliton collision accounts for the formation of rogue waves in this laser state. The nature of interactions between solitons are also discussed. Our observation may suggest similar formation mechanisms of rogue waves in other systems.
Directory of Open Access Journals (Sweden)
V. N. Akimov
2017-01-01
Full Text Available One of the important problems of the designing of maneuverable unmanned aerial vehicles (UAV is to ensure aeroelastic stability with automatic control system (ACS. One of the possible types of aeroelastic instability of UAV with ACS is loss of stability in the system "surface control – actuator". A nonlinear model for the study of the stability of the system "surface control – actuator" is designed for solving problems of joint design of airframe and ACS with the requirements of aeroelasticity. The electric actuator is currently the most widely used on highly maneuverable UAV. The wide bandwidth and the availability of frequency characteristic lifts are typical for the modern electric actuator. This exacerbates the problem of providing aeroelastic stability of the UAV with ACS, including the problem of ensuring the stability of the system "surface control – actuator". In proposed model the surface control, performing bending-torsion oscillations in aerodynamic flow, in fact, is the loading for the actuator. Experimental frequency characteristics of the isolated actuator, obtained for different levels of the control signal, are used for the mathematical description of the actuator, then, as dynamic hinge moment, which is determined by aeroelastic vibrations of the surface control in the air flow, is calculated. Investigation of the stability of the system "surface control – actuator" is carried out by frequency method using frequency characteristics of the open-loop system. The undeniable advantage of the proposed model is the simplicity of obtaining the transfer functions of the isolated actuator. The experiment by its definition is a standard method of determining frequency characteristics of the actuator in contrast to time-consuming experiments for determining the dynamic stiffness of the actuator (with the surface control or the transfer function of the actuator using electromechanical simulation of aeroelastic loading of the
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.
Lim, Jinkang; Savchenkov, Anatoliy A; Dale, Elijah; Liang, Wei; Eliyahu, Danny; Ilchenko, Vladimir; Matsko, Andrey B; Maleki, Lute; Wong, Chee Wei
2017-03-31
Ultrastable high-spectral-purity lasers have served as the cornerstone behind optical atomic clocks, quantum measurements, precision optical microwave generation, high-resolution optical spectroscopy, and sensing. Hertz-level lasers stabilized to high-finesse Fabry-Pérot cavities are typically used for these studies, which are large and fragile and remain laboratory instruments. There is a clear demand for rugged miniaturized lasers with stabilities comparable to those of bulk lasers. Over the past decade, ultrahigh-Q optical whispering-gallery-mode resonators have served as a platform for low-noise microlasers but have not yet reached the stabilities defined by their fundamental noise. Here, we show the noise characteristics of whispering-gallery-mode resonators and demonstrate a resonator-stabilized laser at this limit by compensating the intrinsic thermal expansion, allowing a sub-25 Hz linewidth and a 32 Hz Allan deviation. We also reveal the environmental sensitivities of the resonator at the thermodynamical noise limit and long-term frequency drifts governed by random-walk-noise statistics.High-quality optical resonators have the potential to provide a miniaturized frequency reference for metrology and sensing but they often lack stability. Here, Lim et al. experimentally characterize the stability of whispering-gallery resonators at their fundamental noise limits.
Grain size effects on stability of nonlinear vibration with nanocrystalline NiTi shape memory alloy
Xia, Minglu; Sun, Qingping
2017-10-01
Grain size effects on stability of thermomechanical responses for a nonlinear torsional vibration system with nanocrystalline superelastic NiTi bar are investigated in the frequency and amplitude domains. NiTi bars with average grain size from 10 nm to 100 nm are fabricated through cold-rolling and subsequent annealing. Thermomechanical responses of the NiTi bar as a softening nonlinear damping spring in the torsional vibration system are obtained by synchronised acquisition of rotational angle and temperature under external sinusoidal excitation. It is shown that nonlinearity and damping capacity of the NiTi bar decrease as average grain size of the material is reduced below 100 nm. Therefore jump phenomena of thermomechanical responses become less significant or even vanish and the vibration system becomes more stable. The work in this paper provides a solid experimental base for manipulating the undesired jump phenomena of thermomechanical responses and stabilising the mechanical vibration system through grain refinement of NiTi SMA.
A stabilized complementarity formulation for nonlinear analysis of 3D bimodular materials
Zhang, L.; Zhang, H. W.; Wu, J.; Yan, B.
2016-06-01
Bi-modulus materials with different mechanical responses in tension and compression are often found in civil, composite, and biological engineering. Numerical analysis of bimodular materials is strongly nonlinear and convergence is usually a problem for traditional iterative schemes. This paper aims to develop a stabilized computational method for nonlinear analysis of 3D bimodular materials. Based on the parametric variational principle, a unified constitutive equation of 3D bimodular materials is proposed, which allows the eight principal stress states to be indicated by three parametric variables introduced in the principal stress directions. The original problem is transformed into a standard linear complementarity problem (LCP) by the parametric virtual work principle and a quadratic programming algorithm is developed by solving the LCP with the classic Lemke's algorithm. Update of elasticity and stiffness matrices is avoided and, thus, the proposed algorithm shows an excellent convergence behavior compared with traditional iterative schemes. Numerical examples show that the proposed method is valid and can accurately analyze mechanical responses of 3D bimodular materials. Also, stability of the algorithm is greatly improved.
Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P
2017-03-01
In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Large thermally induced nonlinear refraction of gold nanoparticles stabilized by cyclohexanone
Energy Technology Data Exchange (ETDEWEB)
Sarkhosh, Leila; Aleali, Hoda; Karimzadeh, Rouhollah; Mansour, Nastaran [Physics Department, Shahid Beheshti University, Evin 19839, Tehran (Iran, Islamic Republic of)
2010-10-15
Stabilized gold nanoparticle (AuNP) colloids have been fabricated by nanosecond pulsed laser ablation of a pure gold plate in cyclohexanone. The AuNPs colloid exhibits a UV-Vis absorption spectrum with a surface plasmon absorption peak at about 540 nm. Scanning electron microscopy has shown the formation of spherical AuNPs with average size about 53 nm. The shift of 24 cm{sup -1} is observed in the carbonyl band of the colloid using FTIR spectroscopy. This shift indicates that the monomer carbonyl group of cyclohexanone interacts with the surface of the AuNPs and leads to stabilizing the colloid. A large nonlinear refractive index of -2.92 x 10{sup -7} cm{sup 2}/W is measured using the Z-scan technique under continuous wave laser irradiation at 532 nm. Our results show that the large induced nonlinear refraction is attributed to the surface plasmon resonance (SPR) enhancement effect of AuNPs, high thermo-optic coefficient and low thermal conductivity of cyclohexanone. Observation of far-field diffraction ring patterns confirm a thermally induced negative lens effect and spatial self-phase modulation in the laser beam as it traverses the colloids. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control
Directory of Open Access Journals (Sweden)
Chun-xia Dou
2011-01-01
Full Text Available A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribed H∞ disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI technique, some sufficient conditions for the existence of H∞ robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimized H∞ performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.
Moeferdt, Matthias; Kiel, Thomas; Sproll, Tobias; Intravaia, Francesco; Busch, Kurt
2018-02-01
A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a discontinuous Galerkin time-domain approach, and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, second-harmonic-generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interpret the physical mechanisms that lead to corresponding field distributions, the associated linear quasielectrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes in both the linear and nonlinear regimes. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nanoantenna systems.
Directory of Open Access Journals (Sweden)
Ashfaque Ahmed Hashmani
2011-04-01
Full Text Available A long time delay due to the transmission and processing of remote signal may degrade stability of power system. This paper discusses the design of H? -based local decentralized delayed-input PSS (Power System Stabilizer controllers for a separate better damping of inter-area modes. The controllers use selected suitable remote signals from whole system as supplementary inputs. The local and remote input signals, used by the controller, are the ones in which the assigned single inter-area mode is most observable. The controller is located at a generator which is most effective in controlling the assigned mode. The controller, designed for a particular single interarea mode, also works mainly in the natural frequency of the assigned mode. Pade approximation approach is used to model time delay. The time delay model is then merged into delay-free power system model to obtain the delayed-input power system model. The controllers are then redesigned for the delayed-input system.
Effect of a static external magnetic perturbation on resistive mode stability in tokamaks
International Nuclear Information System (INIS)
Fitzpatrick, R.
1994-03-01
The influence of a general static external magnetic perturbation on the stability of resistive modes in a tokamak plasma is examined. There are three main parts to this investigation. Firstly, the vacuum perturbation is expanded as a set of well-behaved toroidal ring functions and is, thereafter, specified by the coefficients of this expansion. Secondly, a dispersion relation is derived for resistive plasma instabilities in the presence of a general external perturbation and finally, this dispersion relation is solved for the amplitudes of the tearing and twisting modes driven in the plasma by a specific perturbation. It is found that the amplitudes of driven tearing and twisting modes are negligible until a certain critical perturbation strength is exceeded. Only tearing modes are driven in low-β plasmas with εβ p p ∼>1. For error-field perturbations made up of a large number of different poloidal and toroidal harmonics the critical strength to drive locked modes has a open-quote staircase close-quote variation with edge-q, characterized by strong discontinuities as coupled rational surfaces enter or leave the plasma. For single harmonic perturbations the variation with edge-q is far smoother. Both types of behaviour have been observed experimentally. The critical perturbation strength is found to decrease strongly close to an ideal external kink stability boundary. This is also in agreement with experimental observations
Frye, Michael Takaichi
This dissertation examines the problem of global decentralized control by output feedback for large-scale uncertain nonlinear systems whose subsystems are interconnected not only by their outputs but also by their unmeasurable states. Several innovative techniques will be developed to create decentralized output feedback controllers rendering the closed-loop systems globally asymptotically stable. This is accomplished by extending an output feedback domination design that requires only limited information about the nonlinear system. We will apply our design to lower, upper, and non-triangular nonlinear systems. A time-varying output feedback controller is also constructed for use with large-scale systems that have unknown parameters. Furthermore, a mixed large-scale system consisting of both lower and upper triangular systems is shown to be stabilizable by employing a combined high and low gain domination technique. The significance of our results is that we do not need to have prior information about the nonlinearities of the system. In addition, a new design technique was developed using homogeneous system theory, which allows for the design of nonsmooth controllers and observers to stabilize a class of feedforward system with uncontrollable and unobservable linearization. An example of a large-scale system is a group of autonomous airships performing the function of a temporary mobile cell phone network. An airship mobile cell phone network is a novel solution to the problem of maintaining communication during the advent of extensive damage to the communication infrastructure; be it from a flood, earthquake, hurricane, or terrorist attack. A first principle force-based dynamic model for the Tri-Turbofan Airship was developed and will be discussed in detail. The mathematical model was based on actual flight test data that has been collected at the Gait Analysis and Innovative Technologies Laboratory. This model was developed to research autonomous airship
Improving stability and strength characteristics of framed structures with nonlinear behavior
Pezeshk, Shahram
1990-01-01
In this paper an optimal design procedure is introduced to improve the overall performance of nonlinear framed structures. The design methodology presented here is a multiple-objective optimization procedure whose objective functions involve the buckling eigenvalues and eigenvectors of the structure. A constant volume with bounds on the design variables is used in conjunction with an optimality criterion approach. The method provides a general tool for solving complex design problems and generally leads to structures with better limit strength and stability. Many algorithms have been developed to improve the limit strength of structures. In most applications geometrically linear analysis is employed with the consequence that overall strength of the design is overestimated. Directly optimizing the limit load of the structure would require a full nonlinear analysis at each iteration which would be prohibitively expensive. The objective of this paper is to develop an algorithm that can improve the limit-load of geometrically nonlinear framed structures while avoiding the nonlinear analysis. One of the novelties of the new design methodology is its ability to efficiently model and design structures under multiple loading conditions. These loading conditions can be different factored loads or any kind of loads that can be applied to the structure simultaneously or independently. Attention is focused on optimal design of space framed structures. Three-dimensional design problems are more complicated to carry out, but they yield insight into real behavior of the structure and can help avoiding some of the problems that might appear in planar design procedure such as the need for out-of-plane buckling constraint. Although researchers in the field of structural engineering generally agree that optimum design of three-dimension building frames especially in the seismic regions would be beneficial, methods have been slow to emerge. Most of the research in this area has dealt
Tilt mode stability scaling in field-reversed configurations with finite Larmor radius effect
International Nuclear Information System (INIS)
Iwasawa, Naotaka; Ishida, Akio; Steinhauer, Loren C.
2000-01-01
The marginal stability of a static plasma with finite-Larmor-radius (FLR) effects depends on a combination of the FLR effect and the ideal magnetohydrodynamic (MHD) potential energy. For the tilt mode in a field-reversed configuration (FRC) previous computations of these two factors led to a prediction of stability for S * ≤(3-5)E where S * is the macroscale parameter (separatrix radius/ion skin depth) and E is the elongation (separatrix half length/separatrix radius). This prediction explained the observed stability of most experiments. However, recent computations of actual MHD eigenfunctions indicate that the MHD growth rate has a much weaker scaling with elongation than previously believed. As a consequence, most of the long-lived, stable FRC experiments lie in the region predicted to be unstable. It appears then that the stability of FRC experiments is not explained by FLR effects in a static equilibrium. (c) 2000 American Institute of Physics
Mo, Qingkai; Zhang, Tao; Yan, Yining
2016-10-01
There are contradictions among speediness, anti-disturbance performance, and steady-state accuracy caused by traditional PID controller in the existing light source systems of thermal frequency stabilizing laser with double longitudinal modes. In this paper, a new kind of fuzzy adaptive PID controller was designed by combining fuzzy PID control technology and expert system to make frequency stabilizing system obtain the optimal performance. The experiments show that the frequency stability of the designed PID controller is similar to the existing PID controller (the magnitude of frequency stability is less than 10-9 in constant temperature and 10-7 in open air). But the preheating time is shortened obviously (from 10 minutes to 5 minutes) and the anti-disturbance capability is improved significantly (the recovery time needed after strong interference is reduced from 1 minute to 10 seconds).
Cao, Jingming; Xiaver, Jolly
2017-10-01
We manipulated the simulation and apparatus to generate the entangled quantum photons by the enhanced higher quality factor in waveguide of whispering gallery mode resonator in silica microsphere. As the several nonlinear optics effects have been validated in micro-disk (lithium niobate materials based), others micro-cavity (microfiber and micro ring on the chip) and second harmonic generation (SHG) on the surface of silica microsphere because of the characterization of enhanced higher quality factor Q and smaller volume mode in these resonator. However until now for the second third nonlinearity of spontaneous parametric down conversion (SPDC), third order nonlinearity of spontaneous parametric down conversion (TOSPDC) and spontaneous four wave mixing (SFWM) in whispering gallery mode (WGM) resonator of silica microsphere rarely have not been fully investigated and verified to generate the triple and pair entangled photons where are widely applied on the applications of biosensor, quantum communications and spectroscopy, respectively. Specially, the features of silica microsphere have attracted many applications due to the simple fabrication, simplified materials melted by silica fiber. The work we demonstrated in this paper based on the breaking of the dispersion rules to make perfect phase matching in normal dispersion in silica microsphere depending on the blue laser spectrum in visible spectrum, then manipulated the modified size of microsphere to detune the pump laser of free spectral range (FSR) and both shift the geometrical dispersion are characterized in the variation of FSR given by (see PDF for equation), where n is refractive index, R is the microspheres radius and m is mode numbers in resonator, to compensate the materials dispersion given by (see PDF for equation), where c is the speed of light and λ is pump laser wavelength to fulfill the perfect phase matching in parametric down conversion regimes and the modeling fabrication coupling results also
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)].
Enhancement of Voltage Stability of DC Smart Grid During Islanded Mode by Load Shedding Scheme
Nassor, Thabit Salim; Senjyu, Tomonobu; Yona, Atsushi
2015-10-01
This paper presents the voltage stability of a DC smart grid based on renewable energy resources during grid connected and isolated modes. During the islanded mode the load shedding, based on the state of charge of the battery and distribution line voltage, was proposed for voltage stability and reservation of critical load power. The analyzed power system comprises a wind turbine, a photovoltaic generator, storage battery as controllable load, DC loads, and power converters. A fuzzy logic control strategy was applied for power consumption control of controllable loads and the grid-connected dual active bridge series resonant converters. The proposed DC Smart Grid operation has been verified by simulation using MATLAB® and PLECS® Blockset. The obtained results show the effectiveness of the proposed method.
Stabilization of a Quadrotor With Uncertain Suspended Load Using Sliding Mode Control
Energy Technology Data Exchange (ETDEWEB)
Zhou, Xu; Liu, Rui; Zhang, Jiucai; Zhang, Xiaoli
2016-08-21
The stability and trajectory control of a quadrotor carrying a suspended load with a fixed known mass has been extensively studied in recent years. However, the load mass is not always known beforehand in practical applications. This mass uncertainty brings uncertain disturbances to the quadrotor system, causing existing controllers to have a worse performance or to be collapsed. To improve the quadrotor's stability in this situation, we investigate the impacts of the uncertain load mass on the quadrotor. By comparing the simulation results of two controllers -- the proportional-derivative (PD) controller and the sliding mode controller (SMC) driven by a sliding mode disturbance of observer (SMDO), the quadrotor's performance is verified to be worse as the uncertainty increases. The simulation results also show a controller with stronger robustness against disturbances is better for practical applications.
Implementation of model predictive control for resistive wall mode stabilization on EXTRAP T2R
Setiadi, A. C.; Brunsell, P. R.; Frassinetti, L.
2015-10-01
A model predictive control (MPC) method for stabilization of the resistive wall mode (RWM) in the EXTRAP T2R reversed-field pinch is presented. The system identification technique is used to obtain a linearized empirical model of EXTRAP T2R. MPC employs the model for prediction and computes optimal control inputs that satisfy performance criterion. The use of a linearized form of the model allows for compact formulation of MPC, implemented on a millisecond timescale, that can be used for real-time control. The design allows the user to arbitrarily suppress any selected Fourier mode. The experimental results from EXTRAP T2R show that the designed and implemented MPC successfully stabilizes the RWM.
Cho, Yonggeun
2016-05-04
This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method. © 2015 World Scientific Publishing Company
International Nuclear Information System (INIS)
Miyoshi, Takahiro; Becchaku, Masahiro; Kusano, Kanya
2008-01-01
Nonlinear dynamics of the resistive tearing instability in high magnetic Reynolds number (R m ) plasmas is studied by newly developing an accurate and robust resistive magnetohydrodynamic (MHD) scheme. The results show that reconnection processes strongly depend on R m . Particularly, in a high R m case, small-scale plasmoids induced by a secondary instability are intermittently generated and ejected accompanied by fast shocks. According to the intermittent processes, the reconnection rate increases intermittently at a later nonlinear stage. (author)
DEFF Research Database (Denmark)
Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris
2013-01-01
An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...... implementation for a simple single mode soliton propagation example. As opposed to the standard implementation, the new implementation is able to reproduce pulsed four wave mixing observed experimentally in a higher order mode fiber....
Design of directional prism resonator made DPL operate in TEM00 mode with thermal stability
Lu, Changyong; Wang, Xiaobing; Sun, Bin; Guo, Yanlong; Wang, Guchang; Lin, Yi; Wan, Qiang
2005-01-01
An alignment-free directional prism resonator that ensures the laser TEM00 mode with thermal stability in a certain range is designed by using g* parameter equivalent method. The output of all solid state laser is about of 150mJ, and the beam divergence is of 3mrad with 20Hz repetition rate, moreover, when the laser operates from 10 to 30Hz, the beam divergence is steady. This laser meets the needs of special engineering application.
Stability Analysis of a Class of Second Order Sliding Mode Control Including Delay in Input
Directory of Open Access Journals (Sweden)
Pedro R. Acosta
2013-01-01
Full Text Available This paper deals with a class of second order sliding mode systems. Based on the derivative of the sliding surface, sufficient conditions are given for stability. However, the discontinuous control signal depend neither on the derivative of sliding surface nor on its estimate. Time delay in control input is also an important issue in sliding mode control for engineering applications. Therefore, also sufficient conditions are given for the time delay size on the discontinuous input signal, so that this class of second order sliding mode systems might have amplitude bounded oscillations. Moreover, amplitude of such oscillations may be estimated. Some numerical examples are given to validate the results. At the end, some conclusions are given on the possibilities of the results as well as their limitations.
Xue, Jianghong; Xia, Fei; Ye, Jun; Zhang, Jianwen; Chen, Shuhua; Xiong, Ying; Tan, Zuyuan; Liu, Renhuai; Yuan, Hong
2017-06-30
This paper presents a multiscale approach to study the nonlinear vibration of fiber reinforced composite laminates containing an embedded, through-width delamination dividing the laminate into four sub-laminates. The equations of motion are established from macroscopic nonlinear mechanics for plates and shells and micro-mechanics of composite material to allow for the influences of large amplitude, membrane stretching in the neutral plane, and the interactions of the sublaminates. Analytical solutions obtained in this paper reveal that the interaction penalty at the interfaces plays a coupling effect between sublaminates, which eventually alters the vibration characters of the four-sublaminate lamina in macroscopic and microscopic mechanism. From a macro perspective, sub-laminates above and below the delamination vibrate in exactly the same mode in spite of their different stiffness and the four-sublaminate lamina has a consistent global vibration mode. In accompanying with the macro vibration, micro buckles occur on the interfaces of the delamination with amplitude about 10 -3 times of that of the global mode. It is found that the vibration frequency is an eigenvalue of the delaminated lamina determined only by the geometry of the delamination. Authentication of the multiscale study is fulfilled by comparing the analytical solutions with the FEA results.
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.
International Nuclear Information System (INIS)
Redi, M.H.; Johnson, J.L.; Klasky, S.; Canik, J.; Dewar, R.L.; Cooper, W.A.
2002-01-01
The radially local magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), is examined just above the ballooning beta limit with a method that can lead to estimates of global stability. Here MHD stability is analyzed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space (s,α,θ k ); s is the edge normalized toroidal flux, α is the field line variable, and θ k is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, and gives rise to new types of nonsymmetric eigenvalue isosurfaces in both the stable and unstable spectrum. For eigenvalues far above the marginal point, isosurfaces are topologically spherical, indicative of strong 'quantum chaos'. The complexity of QAS marginal isosurfaces suggests that finite Larmor radius stabilization estimates will be difficult and that fully three-dimensional, high-n MHD computations are required to predict the beta limit
Digital multi-channel stabilization of four-mode phase-sensitive parametric multicasting.
Liu, Lan; Tong, Zhi; Wiberg, Andreas O J; Kuo, Bill P P; Myslivets, Evgeny; Alic, Nikola; Radic, Stojan
2014-07-28
Stable four-mode phase-sensitive (4MPS) process was investigated as a means to enhance two-pump driven parametric multicasting conversion efficiency (CE) and signal to noise ratio (SNR). Instability of multi-beam, phase sensitive (PS) device that inherently behaves as an interferometer, with output subject to ambient induced fluctuations, was addressed theoretically and experimentally. A new stabilization technique that controls phases of three input waves of the 4MPS multicaster and maximizes CE was developed and described. Stabilization relies on digital phase-locked loop (DPLL) specifically was developed to control pump phases to guarantee stable 4MPS operation that is independent of environmental fluctuations. The technique also controls a single (signal) input phase to optimize the PS-induced improvement of the CE and SNR. The new, continuous-operation DPLL has allowed for fully stabilized PS parametric broadband multicasting, demonstrating CE improvement over 20 signal copies in excess of 10 dB.
Huang, Yong; Wang, Kehong; Zhou, Zhilan; Zhou, Xiaoxiao; Fang, Jimi
2017-03-01
The arc of gas metal arc welding (GMAW) contains abundant information about its stability and droplet transition, which can be effectively characterized by extracting the arc electrical signals. In this study, ensemble empirical mode decomposition (EEMD) was used to evaluate the stability of electrical current signals. The welding electrical signals were first decomposed by EEMD, and then transformed to a Hilbert-Huang spectrum and a marginal spectrum. The marginal spectrum is an approximate distribution of amplitude with frequency of signals, and can be described by a marginal index. Analysis of various welding process parameters showed that the marginal index of current signals increased when the welding process was more stable, and vice versa. Thus EEMD combined with the marginal index can effectively uncover the stability and droplet transition of GMAW.
Nonlinear Stability of ρ-Functional Equations in Latticetic Random Banach Lattice Spaces
Directory of Open Access Journals (Sweden)
Mohammad Maleki V.
2018-02-01
Full Text Available In this paper, we prove the generalized nonlinear stability of the first and second of the following ρ -functional equations, G ( | a | Δ A * | b | Δ B * G ( | a | Δ A * * | b | − G ( | a | Δ B * * G ( | b | = ρ ( 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 − G ( | a | Δ B * * G ( | b | , and 2 G | a | Δ A * | b | 2 Δ B * G | a | Δ A * * | b | 2 − G ( | a | Δ B * * G ( | b | = ρ G ( | a | Δ A * | b | Δ B * G ( | a | Δ A * * | b | − G ( | a | Δ B * * G ( | b | in latticetic random Banach lattice spaces, where ρ is a fixed real or complex number with ρ ≠ 1 .
On the Nonlinear Stability of Plane Parallel Shear Flow in a Coplanar Magnetic Field
Xu, Lanxi; Lan, Wanli
2017-12-01
Lyapunov direct method has been used to study the nonlinear stability of laminar flow between two parallel planes in the presence of a coplanar magnetic field for streamwise perturbations with stress-free boundary planes. Two Lyapunov functions are defined. By means of the first, it is proved that the transverse components of the perturbations decay unconditionally and asymptotically to zero for all Reynolds numbers and magnetic Reynolds numbers. By means of the second, it is showed that the other components of the perturbations decay conditionally and exponentially to zero for all Reynolds numbers and the magnetic Reynolds numbers below π ^2/2M, where M is the maximum of the absolute value of the velocity field of the laminar flow.
Grants, Ilmars; Gerbeth, Gunter
2010-07-01
The stability of a thermally stratified liquid metal flow is considered numerically. The flow is driven by a rotating magnetic field in a cylinder heated from above and cooled from below. The stable thermal stratification turns out to destabilize the flow. This is explained by the fact that a stable stratification suppresses the secondary meridional flow, thus indirectly enhancing the primary rotation. The instability in the form of Taylor-Görtler rolls is consequently promoted. These rolls can only be excited by finite disturbances in the isothermal flow. A sufficiently strong thermal stratification transforms this nonlinear bypass instability into a linear one reducing, thus, the critical value of the magnetic driving force. A weaker temperature gradient delays the linear instability but makes the bypass transition more likely. We quantify the non-normal and nonlinear components of this transition by direct numerical simulation of the flow response to noise. It is observed that the flow sensitivity to finite disturbances increases considerably under the action of a stable thermal stratification. The capabilities of the random forcing approach to identify disconnected coherent states in a general case are discussed.
Stability of orbits in nonlinear mechanics for finite but very long times
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, Ψ), such that action J is nearly constant while the angle Ψ advances almost linearly with the time. By examining the change in J during a time T 0 from many initial conditions in the open domain Ω of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain Ω 0 contained-in Ω. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10 8 turns). 10 refs., 6 figs., 1 tab
Stability of orbits in nonlinear mechanics for finite but very long times
Energy Technology Data Exchange (ETDEWEB)
Warnock, R.L.; Ruth, R.D.
1990-07-01
In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.
Ghodousi, Maryam; Shahgholi, Majid; Payganeh, Gholamhassan
2018-03-01
The objective of the present work is to investigate the nonlinear vibrations of the rotating asymmetrical nano-shafts by considering surface effect. In order to compute the surface stress tensor, the surface elasticity theory is used. The governing nonlinear equations of motion are obtained with the aid of variational approach. Bubnov-Galerkin is a very effective method for exploiting the reduced-order model of the equations of motion. The averaging method is employed to analyze the reduced-order model of the system. For this purpose, the well-known Van der Pol transformation in the complex form and angle-action transformation are utilized. The effect of surface stress on the forward and backward speeds, steady state responses of the system, fixed points, close orbits and stability of the solutions is examined. The preliminary results of the research show that the absolute values of forward and backward whirling speeds in the presence of surface effect with positive residual surface stress are higher than those of regarding the system without surface effect and in the presence of surface effect with negative residual surface stress. In addition, it is seen that the undamped rotating asymmetrical nano-shaft, for specified value of detuning parameter, in the absence or presence of surface effect has various number of stable and unstable periodic solutions. Besides, there is different number of separatrix (homoclinic orbit type). Furthermore, bifurcations, number of solutions and their stability for damped rotating asymmetrical nano-shaft are investigated. Also, the above results have been obtained for rotating symmetrical nano-shaft.
A nonlinear optimal control approach to stabilization of a macroeconomic development model
Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.
2017-11-01
A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.
The structure and binding mode of citrate in the stabilization of gold nanoparticles
Al-Johani, Hind
2017-03-27
Elucidating the binding mode of carboxylate-containing ligands to gold nanoparticles (AuNPs) is crucial to understand their stabilizing role. A detailed picture of the three-dimensional structure and coordination modes of citrate, acetate, succinate and glutarate to AuNPs is obtained by 13C and 23Na solid-state NMR in combination with computational modelling and electron microscopy. The binding between the carboxylates and the AuNP surface is found to occur in three different modes. These three modes are simultaneously present at low citrate to gold ratios, while a monocarboxylate monodentate (1κO1) mode is favoured at high citrate:gold ratios. The surface AuNP atoms are found to be predominantly in the zero oxidation state after citrate coordination, although trace amounts of Auδ+ are observed. 23Na NMR experiments show that Na+ ions are present near the gold surface, indicating that carboxylate binding occurs as a 2e− L-type interaction for each oxygen atom involved. This approach has broad potential to probe the binding of a variety of ligands to metal nanoparticles.
Ni, Junkang; Liu, Chongxin; Liu, Hang
2017-01-01
This paper presents a continuous composite control scheme to achieve fixed-time stabilization for nonlinear systems with mismatched disturbances. The composite controller is constructed in two steps: First, uniformly finite time exact disturbance observers are proposed to estimate and compensate the disturbances. Then, based on adding a power integrator technique and fixed-time stability theory, continuous fixed-time stable state feedback controller and Lyapunov functions are constructed to achieve global fixed-time system stabilization. The proposed control method extends the existing fixed-time stable control results to high order nonlinear systems with mismatched disturbances and achieves global fixed-time system stabilization. Besides, the proposed control scheme improves the disturbance rejection performance and achieves performance recovery of nominal system. Simulation results are provided to show the effectiveness, the superiority and the applicability of the proposed control scheme.
Tiofack, C. G. L.; Ndzana, F., II; Mohamadou, A.; Kofane, T. C.
2018-03-01
We investigate the existence and stability of solitons in parity-time (PT )-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution and fourth-order diffraction (FOD). For the linear case, we demonstrate numerically that the FOD parameter can alter the PT -breaking points. For nonlinear cases, the exact analytical expressions of the localized modes are obtained both in one- and two-dimensional nonlinear Schrödinger equations with self-focusing and self-defocusing Kerr nonlinearity. The effect of FOD on the stability structure of these localized modes is discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Examples of stable and unstable solutions are given. The transverse power flow density associated with these localized modes is also discussed. It is found that the relative strength of the FOD coefficient can utterly change the direction of the power flow, which may be used to control the energy exchange among gain or loss regions.
International Nuclear Information System (INIS)
Yin, L.; Albright, B.J.; Bezzerides, B.; DuBois, D.F.; Kindel, J.M.; Daughton, W.; Vu, H.X.
2006-01-01
The parametric coupling involving backward stimulated scattering of a laser and electron beam acoustic modes (BAM) is described as observed in particle-in-cell (PIC) simulations. The BAM modes evolve from Langmuir waves (LW) as the electron velocity distribution is nonlinearly modified to be non-Maxwellian by backward stimulated Raman scattering (BSRS). With a marginal damping rate, BAM can be easily excited and allow an extended chirping in frequency to occur as later SRS pulses encounter modified distributions. Coincident with the emergence of this non-Maxwellian distribution is a rapid increase in BSRS reflectivities with laser intensities. Both the reflectivity scaling with laser intensity and the observed spectral features from PIC simulations are consistent with recent Trident experiments
Nonlinear ion-mixing-mode particle transport in the dissipative trapped electron regime
International Nuclear Information System (INIS)
Ware, A.S.; Terry, P.W.
1993-09-01
The nonlinear particle transport arising from the convection of nonadiabatic electron density by ion temperature gradient driven turbulence is examined for trapped electron collisionality regimes. The renormalized dissipative nonadiabatic trapped electron phase space density response is derived and used to calculate the nonlinear particle flux along with an ansatz for the turbulently broadened frequency spectrum. In the lower temperature end of this regime, trapped electrons are collisional and all components of the quasilinear particle flux are outward (i.e., in the direction of the gradients). Nonlinear effects can alter the phase between the nonadiabatic trapped electron phase space density and the electrostatic potential, producing inward components in the particle flux. Specifically, both turbulent shifting of the peak of the frequency spectrum and nonlinear source terms in the trapped electron response can give rise to inward components. However, in the dissipative regime these terms are small and the trapped electron response remains dominantly laminar. When the trapped electrons are collisionless, there is a temperature threshold above which the electron temperature gradient driven component of the quasilinear particle flux changes sign and becomes inward. For finite amplitude turbulence, however, turbulent broadening of both the electron collisional resonance and the frequency spectrum removes tills threshold., and the temperature gradient driven component remains outward
Stabilization of the Resistive Wall Mode and Error Field Reduction by a Rotating Conducting Wall
Paz-Soldan, Carlos
2011-10-01
The hypothesis that the Resistive Wall Mode (RWM) can be stabilized by high-speed differentially-rotating conducting walls is tested in a linear device. This geometry allows the use of cylindrical solid metal walls, whereas a torus would require a flowing liquid metal. Experiments over the past year have for the first time explored RWM stability with a rotating copper wall capable of achieving speeds (rΩw) of up to 280 km/h, equivalent to a magnetic Reynolds number (Rm) of 5. The main results are: 1) Wall rotation increases the stability window of the RWM, allowing ~ 25% more plasma current (Ip) at Rm = 5 while maintaining MHD stability. 2) Error field reduction below a critical value allows the observation of initial mode rotation, followed by braking, wall-locking, and subsequent faster growth. 3) Locking is found to depend on the direction of wall rotation (Ω̂w) with respect to the intrinsic plasma rotation, with locking to both the static wall (vacuum vessel) and rotating wall observed. Additionally, indirect effects on RWM stability are observed via the effect of wall rotation on device error fields. Wall rotation shields locking error fields, which reduces the braking torque and inhibits mode-locking. The linear superposition of error fields from guide field (Bz) solenoid misalignments and current-carrying leads is also shown to break symmetry in Ω̂w , with one direction causing stronger error fields and earlier locking irrespective of plasma flow. Vacuum field measurements further show that rotation decreases the error field penetration time and advects the field to a different orientation, as predicted by theory. Experiments are conducted on the Rotating Wall Machine, a 1.2 m long and 16 cm diameter screw-pinch with Bz ~ 500 G, where hollow-cathode injectors are biased to source up to 7 kA of Ip, exciting current-driven RWMs. MHD activity is measured through 120 edge Br, Bθ, Bz probes as well as internal Bdot, Langmuir and Mach probes. RWM
International Nuclear Information System (INIS)
La Haye, R.J.; Isayama, A.; Maraschek, M.
2009-01-01
The system planned for electron cyclotron current drive (ECCD) in ITER can mitigate the deleterious effects of neoclassical tearing modes (NTMs) provided that either adequate alignment of the ECCD to the rational surface is maintained or too large a misalignment is corrected on a time scale shorter than the deleterious plasma response to 'large' islands. Resistive neoclassical tearing modes will be the principal limit on stability and performance in the ITER standard scenario as the drag from rotating island induced eddy current in the resistive wall (particularly from the m/n = 2/1 mode) can slow the plasma rotation, produce locking to the wall and cause loss of high-confinement H-mode and disruption. Continuous wave (cw) ECCD at the island rational surface is successful in stabilization and/or prevention of NTMs in ASDEX Upgrade, DIII-D and JT-60U. Modulating the ECCD so that it is absorbed only on the rotating island O-point is proving successful in recovering effectiveness in ASDEX Upgrade when the ECCD is configured for wider deposition as expected in ITER. The models for the effect of misalignment on ECCD effectiveness are applied to ITER. Tolerances for misalignment are presented to establish criteria for both the alignment (by moving mirrors in ITER) in the presence of an island, and for the accuracy of real-time ITER MHD equilibrium reconstruction in the absence of an island, i.e. alignment to the mode or to the rational surface in the absence of the mode. The narrower ECCD with front steering makes precise alignment more necessary for the most effective stabilization even though the ECCD is still relatively broad, with current density deposition (full width half maximum) almost twice the marginal island width. This places strict requirements on ECCD alignment with the expected ECCD effectiveness dropping to zero for misalignments as small as 1.7 cm. The system response time for growing islands and slowing rotation without and with ECCD (at different
Dynamics and stabilization of peak current-mode controlled buck converter with constant current load
Leng, Min-Rui; Zhou, Guo-Hua; Zhang, Kai-Tun; Li, Zhen-Hua
2015-10-01
The discrete iterative map model of peak current-mode controlled buck converter with constant current load (CCL), containing the output voltage feedback and ramp compensation, is established in this paper. Based on this model the complex dynamics of this converter is investigated by analyzing bifurcation diagrams and the Lyapunov exponent spectrum. The effects of ramp compensation and output voltage feedback on the stability of the converter are investigated. Experimental results verify the simulation and theoretical analysis. The stability boundary and chaos boundary are obtained under the theoretical conditions of period-doubling bifurcation and border collision. It is found that there are four operation regions in the peak current-mode controlled buck converter with CCL due to period-doubling bifurcation and border-collision bifurcation. Research results indicate that ramp compensation can extend the stable operation range and transfer the operating mode, and output voltage feedback can eventually eliminate the coexisting fast-slow scale instability. Project supported by the National Natural Science Foundation of China (Grant No. 61371033), the Fok Ying-Tung Education Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 142027), the Sichuan Provincial Youth Science and Technology Fund, China (Grant Nos. 2014JQ0015 and 2013JQ0033), and the Fundamental Research Funds for the Central Universities, China (Grant No. SWJTU11CX029).
Wu, Rongxing; Wang, Ji; Du, Jianke; Huang, Dejin; Yan, Wei; Hu, Yuantai
2012-01-01
We investigated the nonlinear vibrations of the coupled thickness-shear and flexural modes of quartz crystal plates with the nonlinear Mindlin plate equations, taking into consideration the kinematic and material nonlinearities. The nonlinear Mindlin plate equations for strongly coupled thickness- shear and flexural modes have been established by following Mindlin with the nonlinear constitutive relations and approximation procedures. Based on the long thickness-shear wave approximation and aided by corresponding linear solutions, the nonlinear equation of thickness-shear vibrations of quartz crystal plate has been solved by the combination of the Galerkin and homotopy analysis methods. The amplitude frequency relation we obtained showed that the nonlinear frequency of thickness-shear vibrations depends on the vibration amplitude, thickness, and length of plate, which is significantly different from the linear case. Numerical results from this study also indicated that neither kinematic nor material nonlinearities are the main factors in frequency shifts and performance fluctuation of the quartz crystal resonators we have observed. These efforts will result in applicable solution techniques for further studies of nonlinear effects of quartz plates under bias fields for the precise analysis and design of quartz crystal resonators. © 2012 IEEE
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neumann...
DEFF Research Database (Denmark)
Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.
2004-01-01
This paper considers a method of lines stability analysis for finite difference discretizations of a recently published Boussinesq method for the study of highly non-linear and extremely dispersive water waves. The analysis demonstrates the near-equivalence of classical linear Fourier (von Neuman...
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.
Niu, Jie; Yang, Qianqian; Wang, Xiaoyun; Song, Rong
2017-01-01
Robot-aided rehabilitation has become an important technology to restore and reinforce motor functions of patients with extremity impairment, whereas it can be extremely challenging to achieve satisfactory tracking performance due to uncertainties and disturbances during rehabilitation training. In this paper, a wire-driven rehabilitation robot that can work over a three-dimensional space is designed for upper-limb rehabilitation, and sliding mode control with nonlinear disturbance observer is designed for the robot to deal with the problem of unpredictable disturbances during robot-assisted training. Then, simulation and experiments of trajectory tracking are carried out to evaluate the performance of the system, the position errors, and the output forces of the designed control scheme are compared with those of the traditional sliding mode control (SMC) scheme. The results show that the designed control scheme can effectively reduce the tracking errors and chattering of the output forces as compared with the traditional SMC scheme, which indicates that the nonlinear disturbance observer can reduce the effect of unpredictable disturbances. The designed control scheme for the wire-driven rehabilitation robot has potential to assist patients with stroke in performing repetitive rehabilitation training.
Shagalov, S. V.; Rybushkina, G. V.
This study explores the nonlinear development of the barotropic instability in weakly supercritical horizontally sheared zonal currents in the presence of vertical stratification. The energy exchange between unstable normal modes and the flow is shown to be confined to the common critical layer-region where the modal wave speed matches the flow velocity. A closed system of equations governing the evolution of instability wave amplitudes and critical layer vorticity distributions is derivedwith the aid of an asymptotic procedure. The dependence of the evolutionary scenarios of the flow on the values of the supercriticality and dissipation parameters is examined within the framework of qualitative and numerical analysis of the obtained equations. Nonlinear growth and saturation of the unstable barotropic and baroclinic modes lead to development of periodic coherent structures in the vorticity distribution inside the common modal critical layer. These structures take on the appearance of two-dimensional vortex chain or three-dimensional baroclinic vortex pattern depending on the flow regime at the stage of the instability equilibration.
Directory of Open Access Journals (Sweden)
Jie Niu
2017-12-01
Full Text Available Robot-aided rehabilitation has become an important technology to restore and reinforce motor functions of patients with extremity impairment, whereas it can be extremely challenging to achieve satisfactory tracking performance due to uncertainties and disturbances during rehabilitation training. In this paper, a wire-driven rehabilitation robot that can work over a three-dimensional space is designed for upper-limb rehabilitation, and sliding mode control with nonlinear disturbance observer is designed for the robot to deal with the problem of unpredictable disturbances during robot-assisted training. Then, simulation and experiments of trajectory tracking are carried out to evaluate the performance of the system, the position errors, and the output forces of the designed control scheme are compared with those of the traditional sliding mode control (SMC scheme. The results show that the designed control scheme can effectively reduce the tracking errors and chattering of the output forces as compared with the traditional SMC scheme, which indicates that the nonlinear disturbance observer can reduce the effect of unpredictable disturbances. The designed control scheme for the wire-driven rehabilitation robot has potential to assist patients with stroke in performing repetitive rehabilitation training.
Large Eddy Simulation of a Swirl-Stabilized Pilot Combustor from Conventional to Flameless Mode
Directory of Open Access Journals (Sweden)
Ehsan Fooladgar
2016-01-01
Full Text Available This paper investigates flame and flow structure of a swirl-stabilized pilot combustor in conventional, high temperature, and flameless modes by means of a partially stirred reactor combustion model to provide a better insight into designing lean premixed combustion devices with preheating system. Finite rate chemistry combustion model with one step tuned mechanism and large eddy simulation is used to numerically simulate six cases in these modes. Results show that moving towards high temperature mode by increasing the preheating level, the combustor is prone to formation of thermal NOx with higher risks of flashback. In addition, the flame becomes shorter and thinner with higher turbulent kinetic energies. On the other hand, towards the flameless mode, leaning the preheated mixture leads to almost thermal NOx-free combustion with lower risk of flashback and thicker and longer flames. Simulations also show qualitative agreements with available experiments, indicating that the current combustion model with one step tuned mechanisms is capable of capturing main features of the turbulent flame in a wide range of mixture temperature and equivalence ratios.
International Nuclear Information System (INIS)
Kotschenreuther, M.
1985-07-01
The dynamics of ideal and kinetic ballooning modes are considered analytically including parallel ion dynamics, but without electron dissipation. For ideal modes, parallel dynamics predominantly determine the growth rate when β is within approx.30% of the ideal threshold, resulting in a substantial reduction in growth rate. Compressibility also eliminates the stabilization effects of finite Larmor radius (FLR); FLR effects (when temperature gradients are neglected) can even increase the growth rate above the MHD value. Temperature gradients accentuate this by adding a new source of free energy independent of the MHD drive, in this region of ballooning coordinate corresponding in MHD to the continuum. Analytic dispersion relations are derived demonstrating the effects above; the formalism emphasizes the similarities between the ideal MHD and kinetic cases
Stabilization of the external kink and control of the resistive wall mode in tokamaks
International Nuclear Information System (INIS)
Garofalo, A.M.; Turnbull, A.D.; Strait, E.J.
1999-01-01
One promising approach to maintaining stability of high beta tokamak plasmas is the use of a conducting wall near the plasma to stabilize low-n ideal MHD instabilities. However, with a resistive wall, either plasma rotation or active feedback control is required to stabilize the more slowly growing resistive wall modes (RWMs). Experiments in the DIII-D, PBHX-M, and HBT-EP tokamaks have demonstrated that plasmas with a nearby conducting wall can remain stable to the n = 1 ideal external kink above the beta limit predicted with the wall at infinity, with durations in DIII-D up to 30 times τ w , the resistive wall time constant. More recently, detailed, reproducible observation of the n = 1 RWM has been possible in DIII-D plasmas above the no-wall beta limit. The DIII-D measurements confirm characteristics common to several RWM theories. The mode is destabilized as the plasma rotation at the q = 3 surface decreases below a critical frequency of 1 to 7 kHz. The measured mode growth times of 2 to 8 ms agree with measurements and numerical calculations of the dominant DIII-D vessel eigenmode time constants, τ w . From its onset, the RWM has little or no toroidal rotation and rapidly reduces the plasma rotation to zero. Both DIII-D and HBT-EP have adopted the smart shell concept as an initial approach to control of these slowly growing RWMs; external coils are controlled by a feedback loop designed to make the resistive wall appear perfectly conducting by maintaining a net zero radial field at the wall. Initial experiment results from DIII-D have yielded encouraging results