Nonlinear helical MHD instability
Energy Technology Data Exchange (ETDEWEB)
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
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.
Choudhury, Prakriti Pal
2015-01-01
We perform global linear stability analysis and idealized numerical simulations in global thermal balance to understand the condensation of cold gas from hot/virial atmospheres (coronae), in particular the intracluster medium (ICM). We pay particular attention to geometry (e.g., spherical versus plane-parallel) and the nature of the gravitational potential. Global linear analysis gives a similar value for the fastest growing thermal instability modes in spherical and Cartesian geometries. Simulations and observations suggest that cooling in halos critically depends on the ratio of the cooling time to the free-fall time ($t_{cool}/t_{ff}$). Extended cold gas condenses out of the ICM only if this ratio is smaller than a threshold value close to 10. Previous works highlighted the difference between the nature of cold gas condensation in spherical and plane-parallel atmospheres; namely, cold gas condensation appeared easier in spherical atmospheres. This apparent difference due to geometry arises because the prev...
Nonlinear evolution of drift instabilities
Energy Technology Data Exchange (ETDEWEB)
Lee, W.W.; Krommes, J.A.; Oberman, C.R.; Smith, R.A.
1984-01-01
The nonlinear evolution of collisionless drift instabilities in a shear-free magnetic field has been studied by means of gyrokinetic particle simulation as well as numerical integration of model mode-coupling equations. The purpose of the investigation is to identify relevant nonlinear mechanisms responsible for the steady-state drift wave fluctuations. It is found that the saturation of the instability is mainly caused by the nonlinear E x B convection of the resonant electrons and their associated velocity space nonlinearity. The latter also induces energy exchange between the competing modes, which, in turn, gives rise to enhanced diffusion. The nonlinear E x B convection of the ions, which contributes to the nonlinear frequency shift, is also an important ingredient for the saturation.
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Modulational instability in nonlocal nonlinear Kerr media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens
2001-01-01
We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function....... For a defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
Nonlinear Instability of Liquid Layers.
Newhouse, Lori Ann
The nonlinear instability of two superposed viscous liquid layers in planar and axisymmetric configurations is investigated. In the planar configuration, the light layer fluid is bounded below by a wall and above by a heavy semiinfinite fluid. Gravity drives the instability. In the first axisymmetric configuration, the layer is confined between a cylindrical wall and a core of another fluid. In the second, a thread is suspended in an infinite fluid. Surface tension forces drive the instability in the axisymmetric configurations. The nonlinear evolution of the fluid-fluid interface is computed for layers of arbitrary thickness when their dynamics are fully coupled to those of the second fluid. Under the assumption of creeping flow, the flow field is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind for the strength of the distribution is derived and then solved using an iterative technique. The Green's functions produce flow fields which are periodic in the direction parallel to the wall and have zero velocity on the wall. For small and moderate surface tension, planar layers evolve into a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of the plumes depends on the surface tension and the ratio of the fluid viscosities. As the viscosity of the layer increases, the plumes change from a well defined drop on top of a narrow stem to a compact column of rising fluid. The capillary instability of cylindrical interfaces and interfaces in which the core thickness varies in the axial direction are investigated. In both the unbounded and wall bounded configurations, the core evolves into a periodic array of elongated fluid drops connected by thin, almost cylindrical fluid links. The characteristics of the drop-link structure depend on the core thickness, the ratio of the core radius to the wall radius, and the ratio of the fluid viscosities. The factors controlling the
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability...
Nonlinear parametric instability of wind turbine wings
DEFF Research Database (Denmark)
Larsen, Jesper Winther; Nielsen, Søren R.K.
2006-01-01
Nonlinear rotor dynamic is characterized by parametric excitation of both linear and nonlinear terms caused by centrifugal and Coriolis forces when formulated in a moving frame of reference. Assuming harmonically varying support point motions from the tower, the nonlinear parametric instability o...
FILAMENTATION INSTABILITY OF LASER BEAMS IN NONLOCAL NONLINEAR MEDIA
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2001-01-01
The filamentation instability of laser beams propagating in nonlocal nonlinear media is investigated. It is shown that the filamentation instability can occur in weakly nonlocal self-focusing media for any degree of nonlocality, and in defocusing media for the input light intensity exceeding a threshold related to the degree of nonlocality. A linear stability analysis is used to predict the initial growth rate of the instability. It is found that the nonlocality tends to suppress filamentation instability in self-focusing media and to stimulate filamentation instability in self-defocusing media. Numerical simulations confirm the results of the linear stability analysis and disclose a recurrence phenomenon in nonlocal self-focusing media analogous to the Fermi-Pasta-Ulam problem.
Modulational instability in periodic quadratic nonlinear materials
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never complete...
Nonlinear Farley-Buneman instability with Dust Impurities.
Atamaniuk, B.; Volokitin, A. S.
2009-04-01
The regimes of nonlinear stabilization of instability of low frequency waves in magnetized, weakly ionized and inhomogeneous ionospheric dusty plasma are considered. In the lower ionosphere in the E--region, a complex process transforms wind energy into currents creating the E--region electrojet. If these currents exceed a certain critical amplitude, a streaming instability called the Farley--Buneman or a collisional two-stream instability develops. When the number of cooperating waves remains small due to a competition of processes of their instability and attenuation, the turbulence appears in the result of their stochastic behavior. Then even system with finite number of interacting waves can realize a turbulent state in active media. At conditions when electrons are magnetized and characteristic time of density oscillations exceed the rate of electron ion collisions and electron dust collision the drift of electrons perpendicular to magnetic field is the main motion. Consequently, the main nonlinearity appears in result of convection of a density perturbation in one wave by another wave in the perpendicular to magnetic field and mathematically is expressed in a specific vector form The strong collisional damping of waves allow to assume that a typical perturbed state of plasma can be described as finite set of interacting waves. This allow to avoid difficulties of 3D simulations and to make full study of nonlinear stabilization and influence of the dust component in the conditions when the number of interacting waves keeps small by the strong competition of processes wave damping and instabilities Keywords: Dusty Plasmas, Farley-Buneman Instability, Nonlinear Stabilization. REFERENCES 1. M. Oppenheim and N. Otani, Geophysical Research Letters, 22, pp. 353-356, 1995. 2. A.V. Volosevich and C.V. Meister, Int. Journal of Geomagnetism and aeronomy, 3 pp.151-156, 2002 3. A. S. Volokitin and B. Atamaniuk, Reduced nonlinear description of Farley-Buneman instability
3-D nonlinear evolution of MHD instabilities
Energy Technology Data Exchange (ETDEWEB)
Bateman, G.; Hicks, H. R.; Wooten, J. W.
1977-03-01
The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed.
Nonlinear instability in simulations of Large Plasma Device turbulence
Friedman, B; Umansky, M V; Schaffner, D; Joseph, I
2013-01-01
Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model, but different axial boundary conditions. They employ either periodic, zero-value, zero-derivative, or sheath axial boundaries. The linear stability physics is different between the scenarios because the various boundary conditions allow the drift wave instability to access different axial structures, and the sheath boundary simulation contains a conducting wall mode instability which is just as unstable as the drift waves. Nevertheless, the turbulence in all the simulations is relatively similar because it is primarily driven by a robust nonlinear instability that is the same for all cases. The nonlinear instability preferentially drives $k_\\parallel = 0$ potential energy fluctuations, which then three-wave couple to $k_\\parallel \
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2008-01-01
This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.
Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Kim, J; Hong, S S; Santillan, A; Martos, M A; Kim, Jongsoo; Franco, Jose; Santillan, Alfredo; Martos, Marco A.
1999-01-01
A linear stability analysis of a multi-component and magnetized Galactic disk model is presented. The disk model uses the observed stratifications for the gas density and gravitational acceleration at the solar neighborhood and, in this sense, it can be called a realistic model. The distribution of the total gas pressure is defined by these observed stratifications, and the gaseous disk is assumed isothermal. The initial magnetic field is taken parallel to the disk, with a midplane value of 5 $\\mu$G, and its stratification along the z-axis is derived from the condition of magnetohydrostatic equilibrium in an isothermal atmosphere. The resulting isothermal sound speed is $\\sim 8.4$ km s$^{-1}$, similar to the velocity dispersion of the main gas components within 1.5 kpc from midplane. The thermal-to-magnetic pressure ratio decreases with $[z]$ and the warm model is Parker unstable. The dispersion relations show that the fastest growing mode has a wavelength of about 3 kpc, for both symmetric and antisymmetric ...
Nonlinear Kinetic Dynamics of Magnetized Weibel Instability
Palodhi, L; Pegoraro, F
2010-01-01
Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown.
Mathematical models for suspension bridges nonlinear structural instability
Gazzola, Filippo
2015-01-01
This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.
Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures
Institute of Scientific and Technical Information of China (English)
彭妙娟; 程玉民
2005-01-01
In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.
Nonlinear theory of kinetic instabilities near threshold
Energy Technology Data Exchange (ETDEWEB)
Berk, H.L.; Pekker, M.S. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies; Breizman, B.N. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies]|[Budker Inst. of Nuclear Physics, Novosibirsk (Russian Federation)
1997-05-01
A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability. The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles. With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold. The explosive solutions exhibit mode frequency shifting. For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward. For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift. The frequency shift continues even after the mode traps resonant particles.
Nonlinear spacial instability of a fluid sheet
Rangel, R. H.; Hess, C. F.
1990-01-01
The mechanism of nonlinear distortion of a fluid sheet leading to atomization is investigated numerically with the use of vortex dynamics and experimentally by means of holography. The configuration investigated consists of a planar fluid sheet emerging from a rectangular slit with and without coflowing air. The numerical model is two-dimensional, inviscid, and includes surface tension effects. The experimental results indicate the existence of well-defined three-dimensional structures. These are formed mainly by the nonlinear interaction of transverse and streamwise disturbances. The transverse disturbances are associated with the Kelvin-Helmholtz instability while the streamwise disturbances appear related to streamwise vortices possibly originating inside the nozzle.
Nonlinear Development and Secondary Instability of Traveling Crossflow Vortices
Li, Fei; Choudhari, Meelan M.; Duan, Lian; Chang, Chau-Lyan
2014-01-01
Transition research under NASA's Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable "sufficiently" accurate transition prediction and practical transition control for future vehicle concepts. This paper builds upon prior effort targeting the laminar breakdown mechanisms associated with stationary crossflow instability over a swept-wing configuration relevant to subsonic aircraft with laminar flow technology. Specifically, transition via secondary instability of traveling crossflow modes is investigated as an alternate scenario for transition. Results show that, for the parameter range investigated herein, secondary instability of traveling crossflow modes becomes insignificant in relation to the secondary instability of the stationary modes when the relative initial amplitudes of the traveling crossflow instability are lower than those of the stationary modes by approximately two orders of magnitudes or more. Linear growth predictions based on the secondary instability theory are found to agree well with those based on PSE and DNS, with the most significant discrepancies being limited to spatial regions of relatively weak secondary growth, i.e., regions where the primary disturbance amplitudes are smaller in comparison to its peak amplitude. Nonlinear effects on secondary instability evolution is also investigated and found to be initially stabilizing, prior to breakdown.
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Directory of Open Access Journals (Sweden)
Liu Chang-Jiang
2011-01-01
Full Text Available This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM with spline function method (SFM to analyze the nonlinear instability modes of dished shallow shell under circular line loads. By analyzing the nonlinear instability modes and combining with concrete computational examples, we obtained the variation rules of the maximum deflection area of initial instability with different geometric parameters and loading action positions and discussed the relationship between the initial instability area and the maximum deflection area of initial instability. The results obtained from this paper provide some theoretical basis for engineering design and instability prediction and control of shallow-shell structures.
Instability of coupled geostrophic density fronts and its nonlinear evolution
Scherer, Emilie; Zeitlin, Vladimir
Instability of coupled density fronts, and its fully nonlinear evolution are studied within the idealized reduced-gravity rotating shallow-water model. By using the collocation method, we benchmark the classical stability results on zero potential vorticity (PV) fronts and generalize them to non-zero PV fronts. In both cases, we find a series of instability zones intertwined with the stability regions along the along-front wavenumber axis, the most unstable modes being long wave. We then study the nonlinear evolution of the unstable modes with the help of a high-resolution well-balanced finite-volume numerical scheme by initializing it with the unstable modes found from the linear stability analysis. The most unstable long-wave mode evolves as follows: after a couple of inertial periods, the coupled fronts are pinched at some location and a series of weakly connected co-rotating elliptic anticyclonic vortices is formed, thus totally changing the character of the flow. The characteristics of these vortices are close to known rodon lens solutions. The shorter-wave unstable modes from the next instability zones are strongly concentrated in the frontal regions, have sharp gradients, and are saturated owing to dissipation without qualitatively changing the flow pattern.
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Rosin, M S; Rincon, F; Cowley, S C
2010-01-01
Plasmas have a natural tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius with growth rates of a fraction of the ion cyclotron frequency - much faster than either the global dynamics or local turbulence. The instabilities can dramatically modify the macroscopic dynamics of the plasma. Nonlinear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta. This nonlinear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example - the parallel firehose instability in a high-beta plasma. A closed nonlinear equation for the firehose turbulence is derived and solved. In the nonlinear regime, the instability leads to secular (~t) growth of magnetic fluctuations. The fluctuations develop a k^{-3} spectrum, extending from scales somewhat larger than r...
Sivan, Y; Fibich, G; Ilan, B; Weinstein, M I
2008-10-01
We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multidimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to a focusing instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows one to predict the stability and instability strength.
Relationship between the magnitude of singular value and nonlinear stability
Institute of Scientific and Technical Information of China (English)
穆穆; 郭欢; 王佳峰; 李勇
2001-01-01
The relationship between the magnitude of singular value and nonlinear stability or instability of the basic flow is investigated. The results show that there is a good corresponding relationship between them. The magnitude of singular value decreases as the stability (or instability) of the basic flow increases (or decreases). In the stable case, the magnitude of the maximum singular value is much smaller than in the unstable case.
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
Deterministic aspects of nonlinear modulation instability
van Groesen, E; Karjanto, N
2011-01-01
Different from statistical considerations on stochastic wave fields, this paper aims to contribute to the understanding of (some of) the underlying physical phenomena that may give rise to the occurrence of extreme, rogue, waves. To that end a specific deterministic wavefield is investigated that develops extreme waves from a uniform background. For this explicitly described nonlinear extension of the Benjamin-Feir instability, the soliton on finite background of the NLS equation, the global down-stream evolving distortions, the time signal of the extreme waves, and the local evolution near the extreme position are investigated. As part of the search for conditions to obtain extreme waves, we show that the extreme wave has a specific optimization property for the physical energy, and comment on the possible validity for more realistic situations.
THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
SHANG MEI; GUO YONG-XIN
2001-01-01
We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.
The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads
Liu Chang-Jiang; Zheng Zhou-Lian; Huang Cong-Bing; He Xiao-Ting; Sun Jun-Yi; Chen Shan-Lin
2011-01-01
This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM) with spline function method (SFM) to analyze the nonlinear instability modes of dished shallow shell under circular l...
Polyhedral (in-)stability of protein crystals
Nanev, Christo N.; Penkova, Anita N.
2002-04-01
The polyhedral (in-)stability of monoclinic hen-egg white lysozyme (HEWL) crystals, grown by means of PEG-6000, and that of orthorhombic trypsin crystals has been investigated experimentally. On the basis of a quantitative theoretical analysis, it is compared with the polyhedral (in-)stability of tetragonal HEWL and cubic ferritin crystals. The unambiguous conclusion is that the phenomenon is due to the diffusive supply of matter. This conclusion is also supported by the fact that the phenomenon has common features for both proteins and small molecular crystals.
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.
Nonlinear evolution of the modulational instability under weak forcing and damping
Directory of Open Access Journals (Sweden)
J. Touboul
2010-12-01
Full Text Available The evolution of modulational instability, or Benjamin-Feir instability is investigated within the framework of the two-dimensional fully nonlinear potential equations, modified to include wind forcing and viscous dissipation. The wind model corresponds to the Miles' theory. The introduction of dissipation in the equations is briefly discussed. Evolution of this instability in the presence of damping was considered by Segur et al. (2005a and Wu et al. (2006. Their results were extended theoretically by Kharif et al. (2010 who considered wind forcing and viscous dissipation within the framework of a forced and damped nonlinear Schrödinger equation. The marginal stability curve derived from the fully nonlinear numerical simulations coincides with the curve obtained by Kharif et al. (2010 from a linear stability analysis. Furthermore, it is found that the presence of wind forcing promotes the occurrence of a permanent frequency-downshifting without invoking damping due to breaking wave phenomenon.
On stability and instability criteria for magnetohydrodynamics.
Friedlander, Susan; Vishik, Misha M.
1995-06-01
It is shown that for most, but not all, three-dimensional magnetohydrodynamic (MHD) equilibria the second variation of the energy is indefinite. Thus the class of such equilibria whose stability might be determined by the so-called Arnold criterion is very restricted. The converse question, namely conditions under which MHD equilibria will be unstable is considered in this paper. The following sufficient condition for linear instability in the Eulerian representation is presented: The maximal real part of the spectrum of the MHD equations linearized about an equilibrium state is bounded from below by the growth rate of an operator defined by a system of local partial differential equations (PDE). This instability criterion is applied to the case of axisymmetric toroidal equilibria. Sufficient conditions for instability, stronger than those previously known, are obtained for rotating MHD. (c) 1995 American Institute of Physics.
Nonlinear instability and convection in a vertically vibrated granular bed
Shukla, P.; Ansari, I.H.; van der Meer, Roger M.; Lohse, Detlef; Alam, M.
2014-01-01
The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic
Nonlinear instability and convection in a vertically vibrated granular bed
Shukla, P.; Ansari, I.H.; Meer, van der R.M.; Lohse, D.; Alam, M.
2014-01-01
The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic shak
Annual Progress Report. [Linear and nonlinear instability theory
Energy Technology Data Exchange (ETDEWEB)
Simon, A.; Catto, P.J.
1978-09-11
A number of topics in nonlinear and linear instability theory are covered in this report. The nonlinear saturation of the dissipative trapped electron instability is evaluated and its amplitude compares well with existing experimental observations. The nonlinear saturation of the drift cyclotron loss-cone mode is carried out for a variety of empty loss-cone distributions. The saturation amplitude is predicted to be small and stable. An improved linear theory of the collisionless drift instability in sheared magnetic fields yields the surprising result that no instability occurs for a wide range of parameters. Finally, the bump-on-tail calculation is shown to be unchanged by some recent results of Case and Siewart, and a rough time scale is established for the transition from the O'Neil trapping regime to the final time-asymptotic result.
Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium
Energy Technology Data Exchange (ETDEWEB)
Moatimid, Galal M., E-mail: gal-moa@hotmail.com [Department of Mathematics, Faculty of Education, Ain Shams University, Roxy (Egypt); Alali, Elham M. M., E-mail: dr-elham-alali@hotmail.com; Ali, Hoda S. M., E-mail: hoda-ali-1@hotmail.com [Department of Mathematics, Faculty of Science (Girls Branch), University of Tabuk, Tabuk, P.O. Box 741 (Saudi Arabia)
2014-09-15
Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A.; Carvalho, Márcio; Leblond, Hervé; Malomed, Boris A.
2016-11-01
We elaborate a solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water, and optical glasses at sufficiently high intensities. We also show that the tubular, rotating, and specklelike filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Stabilization of vortex beams in Kerr media by nonlinear absorption
Porras, Miguel A; Leblond, Hervé; Malomed, Boris A
2016-01-01
We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.
Energy Technology Data Exchange (ETDEWEB)
Eliasson, B., E-mail: bengt.eliasson@strath.ac.uk [SUPA, Physics Department, John Anderson Building, Strathclyde University, Glasgow G4 0NG, Scotland (United Kingdom); Lazar, M., E-mail: mlazar@tp4.rub.de [Centre for Mathematical Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium); Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum (Germany)
2015-06-15
This paper presents a numerical study of the linear and nonlinear evolution of the electromagnetic electron-cyclotron (EMEC) instability in a bi-Kappa distributed plasma. Distributions with high energy tails described by the Kappa power-laws are often observed in collision-less plasmas (e.g., solar wind and accelerators), where wave-particle interactions control the plasma thermodynamics and keep the particle distributions out of Maxwellian equilibrium. Under certain conditions, the anisotropic bi-Kappa distribution gives rise to plasma instabilities creating low-frequency EMEC waves in the whistler branch. The instability saturates nonlinearly by reducing the temperature anisotropy until marginal stability is reached. Numerical simulations of the Vlasov-Maxwell system of equations show excellent agreement with the growth-rate and real frequency of the unstable modes predicted by linear theory. The wave-amplitude of the EMEC waves at nonlinear saturation is consistent with magnetic trapping of the electrons.
Semiconductor Lasers Stability, Instability and Chaos
Ohtsubo, Junji
2013-01-01
This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended. In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One o...
Nonlinear instabilities induced by the F coil power amplifier at FTU: Modeling and control
Energy Technology Data Exchange (ETDEWEB)
Zaccarian, L. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Boncagni, L. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Cascone, D. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Centioli, C. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Cerino, S. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Gravanti, F.; Iannone, F. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Mecocci, F.; Pangione, L. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy); Podda, S. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy); Vitale, V. [Associazione Euratom/ENEA sulla fusione, Centro Ricerche Frascati, CP 65 - 00044 Frascati (Roma) (Italy)], E-mail: vitale@frascati.enea.it; Vitelli, R. [Dip. di Informatica, Sistemi e Produzione, Universita di Roma, Tor Vergata, Via del Politecnico 1 - 00133 Roma (Italy)
2009-06-15
In this paper we focus on the instabilities caused by the nonlinear behavior of the F coil current amplifier at FTU. This behavior induces closed-loop instability of the horizontal position stabilizing loop whenever the requested current is below the circulating current level. In the paper we first illustrate a modeling phase where nonlinear dynamics are derived and identified to reproduce the open-loop responses measured by the F coil current amplifier. The derived model is shown to successfully reproduce the experimental behavior by direct comparison with experimental data. Based on this dynamic model, we then reproduce the closed-loop scenario of the experiment and show that the proposed nonlinear model successfully reproduces the nonlinear instabilities experienced in the experimental sessions. Given the simulation setup, we next propose a nonlinear control solution to this instability problem. The proposed solution is shown to recover stability in closed-loop simulations. Experimental tests are scheduled for the next experimental campaign after the FTU restart.
The Influence of Dust on the Farley-Buneman instability. Nonlinear regimes.
Atamaniuk, Barbara
In the lower ionosphere in the E-region, a complex process transforms wind energy into currents creating the E-region electrojet. If these currents exceed a certain critical amplitude, a streaming instability called the Farley-Buneman or a collisional two-stream instability develops. This instability grows more rapidly at shorter wavelengths and the waves propagate nearly perpendicular to the magnetic field. It is well known that even system with finite number of interacting waves can realize a turbulent state in active media. In such cases, when the number of cooperating waves remains small due to a competition of processes of their instability and attenuation, the turbulence appears in the result of their stochastic behavior. The perturbed ionospheric plasma is one of important example of such active media. The regimes of nonlinear stabilization of instability of low frequency waves in magnetized, weakly ionized and inhomogeneous ionospheric dusty plasma are considered. We make assumptions that the Earth magnetic field has no influence on the ions and on the dust particles so only the electrons are magnetized. If characteristic time of plasma density oscillations exceeds an electron collision frequency the basic is drift motion of electrons and, accordingly, the vector nonlinearity is the strongest. We study of nonlinear stabilization and influence of the dust component, conditions of stochasticity and the different regimes in the conditions when the number of interacting waves keeps small by the strong competition of processes wave damping and instabilities are considered. *This research is supported by KBN grant 0TOOA 01429 1. Meers Oppenheim and Niels Otani, Hybrid Simulations of the Saturated Farley-Buneman Instability in the Ionosphere, Geophysical Research Letters, 22, pp. 353-356, 1995 2. Meers Oppenheim and Niels Otani and Corrado Ronchi, Saturation of the Farley-Buneman instability via nonlinear electron ExB drifts, Journal of Geophysical Research, 101
Higher-order modulation instability in nonlinear fiber optics.
Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry
2011-12-16
We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves.
Nonlinear vibration and rippling instability for embedded carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Soltani, Payam; Mehdipour, I. [Islamic Azad University, Semnan (Iran, Islamic Republic of); Farshidianfar, A. [Ferdowsi University of Mashhad, Mashhad (Iran, Islamic Republic of); Ganji, D. D. [Babol University of Technology, Babol (Iran, Islamic Republic of)
2012-04-15
Based on the rippling deformations, a nonlinear continuum elastic model is developed to analyze the transverse vibration of single walled carbon nanotubes (SWCNTs) embedded on a Winkler elastic foundation. The nonlinear natural frequency has been derived analytically for typical boundary conditions using the perturbation method of multi-scales. The results indicate that the nonlinear resonant frequency due to the rippling is related to the stiffness of the foundation, the boundary conditions, the excitation load-to-damping ratio, and the diameter-to-length ratio. Moreover, the rippling instability of carbon nanotubes, as a structural instability, is introduced and the influences of several effective parameters on this kind of instability are widely discussed.
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
Glenohumeral arthropathy following stabilization for recurrent instability.
Papalia, Rocco; Osti, Leonardo; Del Buono, Angelo; Denaro, Vincenzo; Maffulli, Nicola
2010-01-01
Little attention has been focused on the most common risk factors for post-operative glenohumeral arthropathy in patients undergoing open and arthroscopic stabilization. We performed a literature search using Medline, Cochrane and Google Scholar using the keywords: 'Shoulder instability surgery' in combination with 'glenohumeral osteoarthrosis', 'recurrent shoulder dislocation' in combination with 'surgery' and 'complications'. We identified 33 published studies. There is evidence of long-term postoperative glenohumeral arthropathy in patients undergoing surgical management for shoulder instability. The Coleman methodology score showed great heterogeneity in terms of study design, patient characteristics, management methods and outcome assessment and generally low methodological quality. Follow-up length, age at first dislocation episode and limited external rotation have been shown to be strongly associated with shoulder arthropathy. There is no univocal outcome assessment available. To define the risk factors responsible for development of postoperative glenohumeral arthropathy, controversial findings have been detected. A common validated scale for clinical and imaging measurements for shoulder arthropathy is needed, so as to allow easier and more reliable comparison of outcomes in different studies. Patients should receive controlled imaging assessment (MR and radiographs) in addition to clinical examination. There is a need to perform appropriately powered randomized clinical trials comparing clinical and imaging related outcomes in patients undergoing open, arthroscopic and conservative management for shoulder instability. Standard diagnostic assessment, common and validated clinical and imaging scoring systems are needed.
A nonlinear variable structure stabilizer for power system stability
Energy Technology Data Exchange (ETDEWEB)
Cao, Y.; Jiang, L.; Cheng, S.; Chen, D. (Huazhong Univ. of Science and Technology, Wuhan (China). Dept. of Electrical Power Engineering); Malik, O.P.; Hope, G.S. (Univ. of Calgary, Alberta (Canada). Dept. of Electrical and Computer Engineering)
1994-09-01
A nonlinear variable structure stabilizer is proposed in this paper. Design of this stabilizer involves the nonlinear transformation technique, the variable structure control technique and the linear system theory. Performance of the proposed nonlinear variable structure controller in a single machine connected to an infinite bus power and a multi-machine system with multi-mode oscillations is simulated. The responses of the system with the proposed stabilizer are compared with those obtained with some other kinds of stabilizers when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure stabilizer gives satisfactory dynamic performance and good robustness.
Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media
Directory of Open Access Journals (Sweden)
Maxim A. Molchan
2007-08-01
Full Text Available On the basis of the competing cubic-quintic nonlinearity model, stability (instability of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.
Nonlinear stability of cosmological solutions in massive gravity
De Felice, Antonio; Lin, Chunshan; Mukohyama, Shinji
2013-01-01
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type--I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Modulation instability of broad optical beams in nonlinear media with general nonlinearity
Institute of Scientific and Technical Information of China (English)
Hongcheng Wang; Weilong She
2006-01-01
@@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.
Nonlinear Evolution of the Ion-Ion Beam Instability
DEFF Research Database (Denmark)
Pécseli, Hans; Trulsen, J.
1982-01-01
The criterion for the existence of vortexlike ion phase-space configurations, as obtained by a standard pseudopotential method, is found to coincide with the criterion for the linear instability for two (cold) counterstreaming ion beams. A nonlinear equation is derived, which demonstrates...
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Rossby Wave Instability of Thin Accretion Disks - III. Nonlinear Simulations
Li, H; Wendroff, B; Liska, R
2000-01-01
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes nonlinear? Specifically, does it lead to vortex formation? (2) What is the detailed behavior of a vortex? (3) Can the instability sustain itself and can the vortex last a long time? Among various initial equilibria that we have examined, we generally find that there are three stages of the disk evolution: (1) The exponential growth of the initial small amplitude perturbations. This is in excellent agreement with the linear theory; (2) The production of large scale vortices and their interactions with the background flow, including shocks. Significant accretion is observed due to these vortices. (3) The coupling of Rossby waves/vortices with global spiral waves, which facilitates further accretion throughout the whole disk. Even after more than 20 revolutions at the radius of vortic...
Semiconductor lasers stability, instability and chaos
Ohtsubo, Junji
2017-01-01
This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in se...
Nonlinear vibrations and stability of aerostatic bearing
Directory of Open Access Journals (Sweden)
Kozánek J.
2008-12-01
Full Text Available Bearings based on aerostatic principle belong to the new machine elements advantageous for low- and high-speed applications, but their dynamic and stability properties are not yet sufficiently known. This paper presents a new elaborated method and gained results of theoretical investigation of dynamic properties of aerostatic bearing in general dimensionless form. It is aimed also as a supporting tool for diagnostic and identification methods used at developing of new bearings proposed by TECHLAB, Prague for industrial applications. Mathematical model expresses nonlinear and evolutive properties in the entire area of bearing clearance, contains sufficient number of free parameters in functions of restoring and damping forces and can therefore describe all types of motions occurring in gas bearings as periodic, quasi-periodic, including beats and instability, which can leads to chaotic and self-excited vibrations. The influence of non-diagonal elements of stiffness and damping matrices of linearized model on the spectral properties and the stability of system is investigated, too.
Stability of fractional positive nonlinear systems
Directory of Open Access Journals (Sweden)
Kaczorek Tadeusz
2015-12-01
Full Text Available The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.
Non-Linear Aeroelastic Stability of Wind Turbines
DEFF Research Database (Denmark)
Zhang, Zili; Sichani, Mahdi Teimouri; Li, Jie;
2013-01-01
As wind turbines increase in magnitude without a proportional increase in stiffness, the risk of dynamic instability is believed to increase. Wind turbines are time dependent systems due to the coupling between degrees of freedom defined in the fixed and moving frames of reference, which may...... trigger off internal resonances. Further, the rotational speed of the rotor is not constant due to the stochastic turbulence, which may also influence the stability. In this paper, a robust measure of the dynamic stability of wind turbines is suggested, which takes the collective blade pitch control...... and non-linear aero-elasticity into consideration. The stability of the wind turbine is determined by the maximum Lyapunov exponent of the system, which is operated directly on the non-linear state vector differential equations. Numerical examples show that this approach is promising for stability...
The linear and nonlinear stability of thread-annular flow.
Walton, Andrew G
2005-05-15
The surgical technique of thread injection of medical implants is modelled by the axial pressure-gradient-driven flow between concentric cylinders with a moving core. The linear stability of the flow to both axisymmetric and asymmetric perturbations is analysed asymptotically at large Reynolds number, and computationally at finite Reynolds number. The existence of multiple regions of instability is predicted and their dependence upon radius ratio and thread velocity is determined. A discrepancy in critical Reynolds numbers and cut-off velocity is found to exist between experimental results and the predictions of the linear theory. In order to account for this discrepancy, the high Reynolds number, nonlinear stability properties of the flow are analysed and a nonlinear, equilibrium critical layer structure is found, which leads to an enhanced correction to the basic flow. The predictions of the nonlinear theory are found to be in good agreement with the experimental data.
Active control and nonlinear feedback instabilities in the earth's radiation belts
Silevitch, M. B.; Villalon, E.; Rothwell, P. L.
The stability of trapped particle fluxes are examined near the Kennel-Petschek limit. In the absence of coupling between the ionosphere and magnetosphere, it is found that both the fluxes and the associated wave intensities are stable to external perturbations. However, if the ionosphere and magnetosphere are coupled through the ducting of the waves, a positive feedback may develop depending on the efficiency of the coupling. This result is a spiky, nonlinear precipitation pattern which for electrons has a period on the order of hundreds of seconds. A linear analysis that highlights the regions of instability is given, together with a computer simulation of the nonlinear regimes.
Singh, S. N.
1982-03-01
Using the invariance principle of LaSalle (1962) sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.
Modulational instability in fractional nonlinear Schrödinger equation
Zhang, Lifu; He, Zenghui; Conti, Claudio; Wang, Zhiteng; Hu, Yonghua; Lei, Dajun; Li, Ying; Fan, Dianyuan
2017-07-01
Fractional calculus is entering the field of nonlinear optics to describe unconventional regimes, as disorder biological media and soft-matter. Here we investigate spatiotemporal modulational instability (MI) in a fractional nonlinear Schrödinger equation. We derive the MI gain spectrum in terms of the Lévy indexes and a varying number of spatial dimensions. We show theoretically and numerically that the Lévy indexes affect fastest growth frequencies and MI bandwidth and gain. Our results unveil a very rich scenario that may occur in the propagation of ultrashort pulses in random media and metamaterials, and may sustain novel kinds of propagation invariant optical bullets.
Nonlinear effects at the Fermilab Recycler e-cloud instability
Balbekov, V
2016-01-01
Theoretical analysis of e-cloud instability in the Fermilab Recycler is represented in the paper. The e-cloud in strong magnetic field is treated as a set of immovable snakes each being initiated by some proton bunch. It is shown that the instability arises because of injection errors of the bunches which increase in time and from the batch to its bunch being amplified by the e-cloud electric field. The particular attention is given to nonlinear additions to the cloud field. It is shown that the nonlinearity is the main factor which restricts growth of the bunch amplitude. Possible role of the field free parts of the Recycler id discussed as well. Results of calculations are compared with experimental data demonstrating good correlation.
Nonlinear Effects at the Fermilab Recycler e-Cloud Instability
Energy Technology Data Exchange (ETDEWEB)
Balbekov, V. [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
2016-06-10
Theoretical analysis of e-cloud instability in the Fermilab Recycler is represented in the paper. The e-cloud in strong magnetic field is treated as a set of immovable snakes each being initiated by some proton bunch. It is shown that the instability arises because of injection errors of the bunches which increase in time and from bunch to bunch along the batch being amplified by the e-cloud electric field. The particular attention is given to nonlinear additions to the cloud field. It is shown that the nonlinearity is the main factor which restricts growth of the bunch amplitude. Possible role of the field free parts of the Recycler id discussed as well. Results of calculations are compared with experimental data demonstrating good correlation.
NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS
Institute of Scientific and Technical Information of China (English)
周承倜; 王列东
2001-01-01
Hamilton Principle was uaed to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load,laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed: i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shells. So, in research of dynamic stability for laminated shells, to consider these factors is important.
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...
Modulational instability in a PT-symmetric vector nonlinear Schrödinger system
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
2016-12-01
A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.
Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam
Institute of Scientific and Technical Information of China (English)
Qing-xu Yan; Hui-chao Zou; De-xing Feng
2003-01-01
In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.
Qualitative stability of nonlinear networked systems
Angulo, Marco Tulio; Slotine, Jean-Jacques
2016-01-01
In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.
Surfactant and gravity dependent instability of two-layer Couette flows and its nonlinear saturation
Frenkel, Alexander L
2016-01-01
A horizontal flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant present at the interface, is investigated. The base Couette flow is driven by the horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The linear stability is determined by an eigenvalue problem for the normal modes. The growth rates and the amplitudes of disturbances of the interface, surfactant, velocities, and pressures are found analytically. For each wavenumber, there are two active normal modes. For each mode, the instability threshold conditions in terms of the system parameters are determined. In particular, it transpires that for certain parametric ranges, even arbitrarily stron...
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 interplay of Alfven instabilities and energetic particles in tokamaks
Biancalani, A; Cole, M; Di Troia, C; Lauber, Ph; Mishchenko, A; Scott, B; Zonca, F
2016-01-01
The confinement of energetic particles (EP) is crucial for an efficient heating of tokamak plasmas. Plasma instabilities such as Alfven Eigenmodes (AE) can redistribute the EP population making the plasma heating less effective, and leading to additional loads on the walls. The nonlinear dynamics of toroidicity induced AE (TAE) is investigated by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EP due to the wave-particle nonlinearity is studied. In particular, we focus on the nonlinear modification of the frequency, growth rate and radial structure of the TAE, depending on the evolution of the EP distribution in phase space. For the ITPA benchmark case, we find that the frequency increases when the growth rate decreases, and the mode shrinks radially. This nonlinear evolution is found to be correctly reproduced by means of a quasilinear model, namely a model where the linear effects of the nonlinearly modified EP distri...
The Non-linear Saturation of the Goldreich-Schubert-Fricke Instability
Oishi, Jeffrey; Burns, Keaton; Brown, Ben; Lecoanet, Daniel; Vasil, Geoffrey
2015-11-01
The Goldreich-Schubert-Fricke (GSF) instability is an important process in stellar interiors and possibly in exoplanetary atmospheres. While the linear phase of the instability has been explored for nearly fifty years, its non-linear saturation has not been explored in detail. The GSF is a double-diffusive instability in which Rayleigh unstable perturbations are robbed of buoyant stability by thermal diffusion. Here, we will present results from a suite of direct numerical simulations using the Spiegel-Veronis Boussinesq equations in the Dedalus framework. These DNS are designed to explore the behavior of the GSF over a range of Prandtl numbers. In stellar interiors, Pr ~=10-6 , but we are limited by computational resources to much higher values, so instead we will discuss the Pr scaling of transport and mixing. We will also discuss the impact of the Boussinesq approximation in the case where large aspect ration perturbations exceed a scale height.
ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.
A Stability Theory in Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We propose a new method for finding the local optimal points ofthe constrained nonlinear programming by Ordinary Differential Equations (ODE), and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
Assessing Spontaneous Combustion Instability with Nonlinear Time Series Analysis
Eberhart, C. J.; Casiano, M. J.
2015-01-01
Considerable interest lies in the ability to characterize the onset of spontaneous instabilities within liquid propellant rocket engine (LPRE) combustion devices. Linear techniques, such as fast Fourier transforms, various correlation parameters, and critical damping parameters, have been used at great length for over fifty years. Recently, nonlinear time series methods have been applied to deduce information pertaining to instability incipiency hidden in seemingly stochastic combustion noise. A technique commonly used in biological sciences known as the Multifractal Detrended Fluctuation Analysis has been extended to the combustion dynamics field, and is introduced here as a data analysis approach complementary to linear ones. Advancing, a modified technique is leveraged to extract artifacts of impending combustion instability that present themselves a priori growth to limit cycle amplitudes. Analysis is demonstrated on data from J-2X gas generator testing during which a distinct spontaneous instability was observed. Comparisons are made to previous work wherein the data were characterized using linear approaches. Verification of the technique is performed by examining idealized signals and comparing two separate, independently developed tools.
Nonlinear evolution and final fate of (charged) superradiant instability
Bosch, Pablo; Lehner, Luis
2016-01-01
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner--Nordstr\\"om-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeateadly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.
Dynamic stabilization of Rayleigh-Taylor instability in ablation fronts
Directory of Open Access Journals (Sweden)
Piriz A.R.
2013-11-01
Full Text Available Dynamic stabilization of Rayleigh-Taylor instability in an ablation front is studied by considering the simplest possible modulations in the acceleration. Explicit analytical expressions for the instability growth rate and for the boundaries of the stability region are obtained by considering a sequence of Dirac deltas. Besides, general square waves allow for studying the effect of the driving asymmetries on the stability region as well as the optimization process. The essential role of compressibility is phenomenologically addressed in order to find the constraints it imposes on the stability region.
Adaptive stabilization for cascade nonlinear systems
Institute of Scientific and Technical Information of China (English)
陈岚萍; 王洪元; 吴波
2004-01-01
An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF)techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.
Optimal frequency conversion in the nonlinear stage of modulation instability
Bendahmane, A; Kudlinski, A; Szriftgiser, P; Conforti, M; Wabnitz, S; Trillo, S
2015-01-01
We investigate multi-wave mixing associated with the strongly pump depleted regime of induced modulation instability (MI) in optical fibers. For a complete transfer of pump power into the sideband modes, we theoretically and experimentally demonstrate that it is necessary to use a much lower seeding modulation frequency than the peak MI gain value. Our analysis shows that a record 95 % of the input pump power is frequency converted into the comb of sidebands, in good quantitative agreement with analytical predictions based on the simplest exact breather solution of the nonlinear Schr\\"odinger equation.
Nonlinear instability and dynamic bifurcation of a planeinterface during solidification
Institute of Scientific and Technical Information of China (English)
吴金平; 侯安新; 黄定华; 鲍征宇; 高志农; 屈松生
2001-01-01
By taking average over the curvature, the temperature and its gradient, the solute con-centration and its gradient at the flange of planar interface perturbed by sinusoidal ripple during solidifi-cation, the nonlinear dynamic equations of the sinusoidal perturbation wave have been set up. Analysisof the nonlinear instability and the behaviors of dynamic bifurcation of the solutions of these equationsshows that (i) the way of dynamic bifurcation of the flat-to-cellular interface transition vades with differ-ent thermal gradients. The quasi-subcritical-lag bifurcation occurs in the small interface thermal gradientscope, the supercritical-lag bifurcation in the medium thermal gradient scope and the supercritical bifur-cation in the large thermal gradient scope. (ii) The transition of cellular-to-flat interface is realizedthrough supercritical inverse bifurcation in the rapid solidification area.
Martinez, David
2015-11-01
We investigate on the National Ignition Facility (NIF) the ablative Rayleigh-Taylor (RT) instability in the transition from linear to highly nonlinear regimes. This work is part of the Discovery Science Program on NIF and of particular importance to indirect-drive inertial confinement fusion (ICF) where careful attention to the form of the rise to final peak drive is calculated to prevent the RT instability from shredding the ablator in-flight and leading to ablator mixing into the cold fuel. The growth of the ablative RT instability was investigated using a planar plastic foil with pre-imposed two-dimensional broadband modulations and diagnosed using x-ray radiography. The foil was accelerated for 12ns by the x-ray drive created in a gas-filled Au radiation cavity with a radiative temperature plateau at 175 eV. The dependence on initial conditions was investigated by systematically changing the modulation amplitude, ablator material and the modulation pattern. For each of these cases bubble mergers were observed and the nonlinear evolution of the RT instability showed insensitivity to the initial conditions. This experiment provides critical data needed to validate current theories on the ablative RT instability for indirect drive that relies on the ablative stabilization of short-scale modulations for ICF ignition. This paper will compare the experimental data to the current nonlinear theories. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Nonlinear ion trap stability analysis
Energy Technology Data Exchange (ETDEWEB)
Mihalcea, Bogdan M; Visan, Gina G, E-mail: bmihal@infim.r [Institute for Laser, Plasma and Radiation Physics (INFLPR), Atomistilor Str. Nr. 409, 077125 Magurele-Bucharest, Jud. Ilfov (Romania)
2010-09-01
This paper investigates the dynamics of an ion confined in a nonlinear Paul trap. The equation of motion for the ion is shown to be consistent with the equation describing a damped, forced Duffing oscillator. All perturbing factors are taken into consideration in the approach. Moreover, the ion is considered to undergo interaction with an external electromagnetic field. The method is based on numerical integration of the equation of motion, as the system under investigation is highly nonlinear. Phase portraits and Poincare sections show that chaos is present in the associated dynamics. The system of interest exhibits fractal properties and strange attractors. The bifurcation diagrams emphasize qualitative changes of the dynamics and the onset of chaos.
Energy Technology Data Exchange (ETDEWEB)
Schüler, D.; Alonso, S.; Bär, M. [Physikalisch-Technische Bundesanstalt, Abbestrasse 2-12, 10587 Berlin (Germany); Torcini, A. [CNR-Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - Via Madonna del Piano 10, I-50019 Sesto Fiorentino (Italy); INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino (Italy)
2014-12-15
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.
Nonlinear theory of combustion stability in liquid rocket engine based on chemistry dynamics
Institute of Scientific and Technical Information of China (English)
黄玉辉; 王振国; 周进
2002-01-01
Detailed models of combustion instability based on chemistry dynamics are developed. The results show that large activation energy goes against the combustion stability. The heat transfer coefficient between the wall and the combust gas is an important bifurcation parameter for the combustion instability. The acoustics modes of the chamber are in competition and cooperation with each other for limited vibration energy. Thermodynamics criterion of combustion stability can be deduced from the nonlinear thermodynamics. Correlations of the theoretical results and historical experiments indicate that chemical kinetics play a critical role in the combustion instability.
Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings
DEFF Research Database (Denmark)
Corney, Joel F.; Bang, Ole
2004-01-01
We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phasematching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands....
Nonlinear evolution of drift instabilities in the presence of collisions
Energy Technology Data Exchange (ETDEWEB)
Federici, J.F.; Lee, W.W.; Tang, W.M.
1986-07-01
Nonlinear evolution of drift instabilities in the presence of electron-ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation techniques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms responsible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift wave problems in more complicated geometries. The results indicate that the electron E x B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with ephi/T/sub e/ approx. = (..omega../sub l//..cap omega../sub i/)/(k/sub perpendicular/rho/sub s/)/sup 2/. The associated quasilinear diffusion, which increases with collisionality, takes the form of D/sub ql/ approx. = ..gamma../sub l//k/sub perpendicular//sup 2/, where ..omega../sub l/ and ..gamma../sub l/ are the linear frequency and growth rate, respectively. In the steady state, the diffusion process becomes stochastic in nature. The relevant mechanisms here are related to the velocity-space nonlinearities and background fluctuations. The magnitude of the diffusion at this stage can be comparable to that of quasilinear diffusion in the presence of collisions, and it remains finite even in the collisionless limit.
Instability and dynamics of two nonlinearly coupled laser beams in a plasma
Shukla, P K; Marklund, M; Stenflo, L; Kourakis, I; Parviainen, M; Dieckmann, M E
2006-01-01
We investigate the nonlinear interaction between two laser beams in a plasma in the weakly nonlinear and relativistic regime. The evolution of the laser beams is governed by two nonlinear Schroedinger equations that are coupled with the slow plasma density response. We study the growth rates of the Raman forward and backward scattering instabilities as well of the Brillouin and self-focusing/modulational instabilities. The nonlinear evolution of the instabilities is investigated by means of direct simulations of the time-dependent system of nonlinear equations.
Reyna, Albert S
2014-01-01
We present a procedure for nonlinearity management of metal-dielectric composites. Varying the volume fraction occupied by silver nanoparticles suspended in acetone we could cancel the refractive index related to the third-order susceptibility, $\\chi_{eff}^{(3)}$, and the nonlinear refraction behavior was due to the fifth-order susceptibility, $\\chi_{eff}^{(5)}$. Hence, in a cross-phase modulation experiment, we demonstrated for the first time the effect of spatial-modulation- instability due to $\\chi_{eff}^{(5)}$. The results are corroborated with numerical calculations based on a generalized Maxwell-Garnet model.
Practical stability and instability of regime-switching diffusions
Institute of Scientific and Technical Information of China (English)
G.George YIN; Bo ZHANG; Chao ZHU
2008-01-01
This work is devoted to practical stability of a class of regime-switching diffusions.First,the notion of practical stability is introduced.Then,sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument.In addition,easily verifiable conditions on drift and diffusion coefficients are also given.Moreover,examples are supplied for demonstration purposes.
Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysis
Merchant, G. J.; Braun, R. J.; Brattkus, K.; Davis, S. H.
1992-01-01
In the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.
Directory of Open Access Journals (Sweden)
Hong Qin
2003-01-01
Full Text Available Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p two-stream instability observed in the Proton Storage Ring (PSR experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.
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.
The role of proprioception and neuromuscular stability in carpal instabilities.
Hagert, E; Lluch, A; Rein, S
2016-01-01
Carpal stability has traditionally been defined as dependent on the articular congruity of joint surfaces, the static stability maintained by intact ligaments, and the dynamic stability caused by muscle contractions resulting in a compression of joint surfaces. In the past decade, a fourth factor in carpal stability has been proposed, involving the neuromuscular and proprioceptive control of joints. The proprioception of the wrist originates from afferent signals elicited by sensory end organs (mechanoreceptors) in ligaments and joint capsules that elicit spinal reflexes for immediate joint stability, as well as higher order neuromuscular influx to the cerebellum and sensorimotor cortices for planning and executing joint control. The aim of this review is to provide an understanding of the role of proprioception and neuromuscular control in carpal instabilities by delineating the sensory innervation and the neuromuscular control of the carpus, as well as descriptions of clinical applications of proprioception in carpal instabilities.
Nonlinear Weibel Instability and Turbulence in Strong Collisionless Shocks
Energy Technology Data Exchange (ETDEWEB)
Medvedev, Mikhail M.
2008-08-31
This research project was devoted to studies of collisionless shocks, their properties, microphysics and plasma physics of underlying phenomena, such as Weibel instability and generation of small-scale fields at shocks, particle acceleration and transport in the generated random fields, radiation mechanisms from these fields in application to astrophysical phenomena and laboratory experiments (e.g., laser-plasma and beam-plasma interactions, the fast ignition and inertial confinement, etc.). Thus, this study is highly relevant to astrophysical sciences, the inertial confinement program and, in particular, the Fast Ignition concept, etc. It makes valuable contributions to the shock physics, nonlinear plasma theory, as well as to the basic plasma science, in general.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
Nonlinear Saturation Amplitude in Classical Planar Richtmyer-Meshkov Instability
Liu, Wan-Hai; Wang, Xiang; Jiang, Hong-Bin; Ma, Wen-Fang
2016-04-01
The classical planar Richtmyer-Meshkov instability (RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order, and then according to definition of nonlinear saturation amplitude (NSA) in Rayleigh-Taylor instability (RTI), the NSA in planar RMI is obtained explicitly. It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface, while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength. Without marginal influence of the initial amplitude, the NSA increases linearly with wavelength. The NSA normalized by the wavelength in planar RMI is about 0.11, larger than that corresponding to RTI. Supported by the National Natural Science Foundation of China under Grant Nos. 11472278 and 11372330, the Scientific Research Foundation of Education Department of Sichuan Province under Grant No. 15ZA0296, the Scientific Research Foundation of Mianyang Normal University under Grant Nos. QD2014A009 and 2014A02, and the National High-Tech ICF Committee
The dynamics of rapid fracture: instabilities, nonlinearities and length scales.
Bouchbinder, Eran; Goldman, Tamar; Fineberg, Jay
2014-04-01
The failure of materials and interfaces is mediated by cracks, almost singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation-the dynamic process of fracture-couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the almost singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, namely linear elastic fracture mechanics (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined 'weakly nonlinear fracture mechanics', where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, ℓnl. These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of ℓnl is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wavelength is determined by ℓnl. We conclude by delineating outstanding challenges in the field.
Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2010-01-01
Full Text Available This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.
Delucia, James
We study various aspects of the linear and 2D (helically symmetric) nonlinear development of m = 1 resistive instabilities in the cylindrical spheromak. The cylindrical spheromak is a fictitious configuration in which the toroidal spheromak has been cut and straightened out to become a circular cylinder of radius a, length 2(pi)R, and with periodic boundary conditions. It has proven to be a usefull model for studying spheromak instabilities in which toroidal effects are not important. The majority of interest in this area lies in attempting to understand the effect that the resistive interchange instability has on confinement in the spheromak, the reason being that finite pressure spheromak configurations are always unstable to this mode. Therefore, most of the results presented in this thesis pertain to the nonlinear development of the resistive interchange mode. Our goal is to understand the quasilinear modifications of the equilibrium profile due to the growth of this instability, and the subsequent effect that the equilibrium modification has on the growth rate and eigenfunctions. Our studies of the resistive interchange mode reveal that mode saturation can occur due to the quasilinear flattening of the pressure profile in the vicinity of the mode rational surface. However, this saturation process is defeated when the plasma overheats and in regions of the plasma where the shear is low. Also, we found that fluid compression plays a significant, and optomistic role in the long term nonlinear development of this mode. Finally, in a tearing mode stable cylindrical spheromak configuration with an axial beta value of 6%, complete overlap of the m = 1 islands occurs in about 3% of the resistive skin time for a magnetic Reynold's number of S = 10('5). For typical parameters of the S-1 device at Princeton, this time corresponds to nearly one millisecond. We show that incorporation of the Hall terms into the resistive MHD model can stabilize the m = 1 resistive
Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows
Schmidt, Patrick; Lucquiaud, Mathieu; Valluri, Prashant
2015-01-01
We consider the genesis and dynamics of interfacial instability in gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of three main flow parameters (density contrast between liquid and gas, film thickness, pressure drop applied to drive the gas stream) on the interfacial dynamics. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable internal mode for low density contrast. The same linear stability approach provides a quantitative prediction for the onset of (partial) liquid flow reversal in terms of the gas and liquid flow rates. ...
Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow
Hendi, S H; Panah, B Eslam; Momennia, M
2015-01-01
Motivated by the violation of Lorentz invariancy in quantum gravity, we study black hole solutions in gravity's rainbow in the context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered with an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally we investigate thermal stability conditions for these black hole solutions in context of canonical ensemble. We show that although there is not physical small black hole, large black holes are physical and enjoy thermal stability in gravity's rainbow.
NONLINEAR DYNAMIC INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES UNDER PERIODIC EXCITATION
Institute of Scientific and Technical Information of China (English)
Yiming Fu; Rengui Bi; Pu Zhang
2009-01-01
A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waais forces as well as the non-coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube (DWNT) can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.
Institute of Scientific and Technical Information of China (English)
PENG Miao-juan; CHENG Yu-min
2005-01-01
In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories.The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.
Monetary Policy and Financial (InStability
Directory of Open Access Journals (Sweden)
Adam Koronowski
2010-06-01
Full Text Available This paper presents how monetary policy, restricted only by price stability, may easily become propitious to asset inflation and – eventually – to a financial crisis. This risk is particularly high when the financial system lacks proper regulation and effective supervision. Hasty liberalization, negligence of official oversight and „Greenspan doctrine” which refuted any activist policy promoting financial stability characterized Fed’s monetary policy under the former Fed’s governor. The paper also analyses another aspect of the linkages between monetary policy and financial crises – monetary policy reaction to financial crises. It is not surprising that it consists of cutting interest rates and bail-out of insolvent, systemically important financial institutions. Such policy, especially when run too long and changed too abruptly, not only creates moral hazards but it also sets the stage for another „search for yield” and build-up of another speculative bubble. As a result, monetary policy becomes asymmetric and pro-cyclical. Fed’s reaction to the recent crisis seems to be very much in line with this pattern typical of Fed’s policy in the past. However, this time the scale of flooding the economy with liquidity and – as a consequence – the risks of future major imbalances in the financial system are unprecedented. A general conclusion of the paper says that there can’t be a sound financial and economic system unless money itself is a scarce resource. However trivial this statement is, monetary policy of some central banks seems to miss the point.
On the quantum (in)stability in cavity QED
Prants, S V
2005-01-01
The stability and instability of quantum motion is studied in the context of cavity quantum electrodynamics (QED). It is shown that the Jaynes-Cummings dynamics can be unstable in the regime of chaotic walking of an atom in the quantized field of a standing wave in the absence of any other interaction with environment. This quantum instability manifests itself in strong variations of quantum purity and entropy and in exponential sensitivity of fidelity of quantum states to small variations in the atom-field detuning. It is quantified in terms of the respective classical maximal Lyapunov exponent that can be estimated in appropriate in-out experiments.
On stability of randomly switched nonlinear systems
Chatterjee, Debasish
2007-01-01
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results therefore hold for Markov jump systems in particular. For systems with control inputs we provide explicit control s...
Energy Technology Data Exchange (ETDEWEB)
Wabnitz, Stefan, E-mail: stefan.wabnitz@unibs.it [Dipartimento di Ingegneria dell' Informazione, Università degli Studi di Brescia, via Branze 38, 25123 Brescia (Italy); Wetzel, Benjamin [INRS-EMT, 1650 Blvd. Lionel-Boulet, Varennes, Québec J3X 1S2 (Canada)
2014-07-25
We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi–Pasta–Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.
Institute of Scientific and Technical Information of China (English)
文双春; 范滇元
2002-01-01
Spatiotemporal instability in nonlinear dispersive media is investigated on the basis of the nonlinear envelope equation. A general expression for instability gain which includes the effects of space-time focusing, arbitrarily higher-order dispersions and self-steepening is obtained. It is found that, for both normal and anomalous group-velocity dispersions, space-time focusing may lead to the appearance of new instability regions and influence the original instability gain spectra mainly by shrinking their regions. The region of the original instability gain spectrum shrinks much more in normal dispersion case than in anomalous one. In the former case, space-time focusing completely suppresses the growing of higher frequency components. In addition, we find that all the oddth-order dispersions contribute none to instability, while all the eventh-order dispersions influence instability region and do not influence the maximum instability gain, therein the fourth-order dispersion plays the same role as space-time focusing in spatiotemporal instability. The main role played by self-steepening in spatiotemporal instability is that it reduces the instability gain and exerts much more significant influence on the new instability regions resulting from space-time focusing.
Linear and nonlinear instability in vertical counter-current laminar gas-liquid flows
Schmidt, Patrick; Ó Náraigh, Lennon; Lucquiaud, Mathieu; Valluri, Prashant
2016-04-01
We consider the genesis and dynamics of interfacial instability in vertical gas-liquid flows, using as a model the two-dimensional channel flow of a thin falling film sheared by counter-current gas. The methodology is linear stability theory (Orr-Sommerfeld analysis) together with direct numerical simulation of the two-phase flow in the case of nonlinear disturbances. We investigate the influence of two main flow parameters on the interfacial dynamics, namely the film thickness and pressure drop applied to drive the gas stream. To make contact with existing studies in the literature, the effect of various density contrasts is also examined. Energy budget analyses based on the Orr-Sommerfeld theory reveal various coexisting unstable modes (interfacial, shear, internal) in the case of high density contrasts, which results in mode coalescence and mode competition, but only one dynamically relevant unstable interfacial mode for low density contrast. A study of absolute and convective instability for low density contrast shows that the system is absolutely unstable for all but two narrow regions of the investigated parameter space. Direct numerical simulations of the same system (low density contrast) show that linear theory holds up remarkably well upon the onset of large-amplitude waves as well as the existence of weakly nonlinear waves. For high density contrasts, corresponding more closely to an air-water-type system, linear stability theory is also successful at determining the most-dominant features in the interfacial wave dynamics at early-to-intermediate times. Nevertheless, the short waves selected by the linear theory undergo secondary instability and the wave train is no longer regular but rather exhibits chaotic motion. The same linear stability theory predicts when the direction of travel of the waves changes — from downwards to upwards. We outline the practical implications of this change in terms of loading and flooding. The change in direction of the
Morrison, Philip J; Tronko, Natalia
2013-01-01
Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical {\\delta}W criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of {\\delta}W is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instabili...
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.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Active feedback stabilization of flute instability in a mirror trap
Be'Ery, Ilan; Seemann, Omri; Fruchtman, Amnon; Fisher, Amnon; Ron, Amiram
2013-10-01
The flute instability in a table-top mirror machine has been stabilized by a feedback system consisting of optical probes, digital signal processor, and needle electrodes. The total response time of the system is 5 μs, which is considerably faster than the typical flute growth time. Simulation and a dynamic model of the plasma's response to the needle actuators were tested against cyclic bias experiments. The plasma density is increased by the stabilization by a factor of two and is limited by other decay processes.
Korycansky, D. G.
1991-01-01
Two-dimensional nonlinear hydrodynamic calculations are presented which may help assess the effectiveness of the instability in transporting angular momentum in the equatorial zones of stars and planets which are stably stratified with respect to convection. The calculations were made by numerically integrating the 2D axisymmetric Navier-Stokes equations, including viscosity and heat conduction. The instability was followed into the nonlinear regime. The maximum rms velocity amplitude was found to correlate well with the product of the linear growth rate and radial length scale of the instability, consistent with the idea that the instability grows to an amplitude such that an eddy turnover time becomes equal to the growth time defined by the inverse of the growth rate. The time scale for angular momentum to be redistributed to a state of marginal stability was consistent with this picture. The results suggest that in physical situations a state of marginal stability will be maintained, since departures from such a state will be rapidly corrected.
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
Bentley, Sean J; Heebner, John E; Boyd, Robert W
2006-04-01
We describe observations of various transverse instabilities that occur when two laser beams intersect in nonlinear optical liquids. Patterns that we observe include two types of conical emission and the generation of a linear array of spots. These results can be understood in terms of the physical processes of self-diffraction, two-beam-excited conical emission, and seeded modulational instability.
Modulational stability and dark solitons in periodic quadratic nonlinear media
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2000-01-01
We show that stable dark solitons exist in quadratic nonlinear media with periodic linear and nonlinear susceptibilities. We investigate the modulational stability of plane waves in such systems, a necessary condition for stable dark solitons....
Study on Roll Instability Mechanism and Stability Index of Articulated Steering Vehicles
Directory of Open Access Journals (Sweden)
Xuefei Li
2016-01-01
Full Text Available This study examines the roll instability mechanism and stability index of articulated steering vehicles (ASVs by taking wheel loaders as the research object. A seven-degree-of-freedom nonlinear dynamics model of the ASVs is built on the basis of multibody dynamics. A physical prototype model of an ASV is designed and manufactured to validate the dynamic model. Test results reasonably agree with the simulation results, which indicates that the established dynamic model can reasonably describe ASV movements. Detailed analysis of the rollover stability of the wheel loader is performed with the use of the established dynamic model. Analysis results show that rollover will occur when the roll angular velocity exceeds a critical threshold, which is affected by lateral acceleration and slope angle. On this basis, a dynamic stability index applicable to the ASVs is presented.
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
New results in global stabilization for stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
Modulation instability, solitons and beam propagation in spatially nonlocal nonlinear media
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Nikolov, Nikola Ivanov
2004-01-01
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction...
Non-Linear Stability of an Electrified Plane Interface in Porous Media
El-Dib, Yusry O.; Moatimid, Galal M.
2004-03-01
The non-linear electrohydrodynamic stability of capillary-gravity waves on the interface between two semi-infinite dielectric fluids is investigated. The system is stressed by a vertical electric field in the presence of surface charges. The work examines a few representative porous media configurations. The analysis includes Rayleigh-Taylor and Kelvin-Helmholtz instabilities. The boundary - value problem leads to a non-linear equation governing the surface evolution. Taylor theory is adopted to expand this equation, in the light of multiple scales, in order to obtain a non-linear Schr¨odinger equation describing the behavior of the perturbed interface. The latter equation, representing the amplitude of the quasi-monochromatic traveling wave, is used to describe the stability criteria. These criteria are discussed both analytically and numerically. In order to identifiy regions of stability and instability, the electric field intensity is plotted versus the wave number. Through a linear stability approach it is found that Darcy's coefficients have a destabilizing influence, while in the non-linear scope these coefficients as well as the electric field intensity play a dual role on the stability.
Linear stability analysis of capillary instabilities for concentric cylindrical shells
Liang, X; Nave, J -C; Johnson, S G
2010-01-01
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of N fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier--Stokes problem. Generalising previous work by Tomotika (N=2), Stone & Brenner (N=3, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalised eigenproblem in the Stokes case. Furthermore, we demonstrate by Plateau-style geometrical arguments that only axisymmetric instabilities need be considered. We show that the N=3 case is already sufficient to obtain several interesting phenomena: limiting cases of thin shells or low shell viscosity that reduce to N=2 problems, and a system with competing breakup processes at very different length scales. The latter is demonstrated with full 3-dimensional simulations. Many $N > 3$ c...
Stabilization of beam-weibel instability by equilibrium density ripples
Energy Technology Data Exchange (ETDEWEB)
Mishra, S. K., E-mail: nishfeb@gmail.com; Kaw, Predhiman; Das, A.; Sengupta, S. [Institute for Plasma Research (IPR), Gandhinagar 382428 (India); Ravindra Kumar, G. [Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005 (India)
2014-01-15
In this paper, we present an approach to achieve suppression/complete stabilization of the transverse electromagnetic beam Weibel instability in counter streaming electron beams by modifying the background plasma with an equilibrium density ripple, shorter than the skin depth; this weakening is more pronounced when thermal effects are included. On the basis of a linear two stream fluid model, it is shown that the growth rate of transverse electromagnetic instabilities can be reduced to zero value provided certain threshold values for ripple parameters are exceeded. We point out the relevance of the work to recent experimental investigations on sustained (long length) collimation of fast electron beams and integral beam transport for laser induced fast ignition schemes, where beam divergence is suppressed with the assistance of carbon nano-tubes.
Bifurcation and stability for a nonlinear parabolic partial differential equation
Chafee, N.
1973-01-01
Theorems are developed to support bifurcation and stability of nonlinear parabolic partial differential equations in the solution of the asymptotic behavior of functions with certain specified properties.
Robust stabilization of general nonlinear systems with structural uncertainty
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
Chaves Filho, V. L.; Lima, R. P. A.; Lyra, M. L.
2015-06-01
We investigate the modulational instability of uniform wavepackets governed by the discrete nonlinear Schrodinger equation in finite linear chains and square lattices. We show that, while the critical nonlinear coupling χMI above which modulational instability occurs remains finite in square lattices, it decays as 1/L in linear chains. In square lattices, there is a direct transition between the regime of stable uniform wavefunctions and the regime of asymptotically localized solutions with stationary probability distributions. On the other hand, there is an intermediate regime in linear chains for which the wavefunction dynamics develops complex breathing patterns. We analytically compute the critical nonlinear strengths for modulational instability in both lattices, as well as the characteristic time τ governing the exponential increase of perturbations in the vicinity of the transition. We unveil that the interplay between modulational instability and self-trapping phenomena is responsible for the distinct wavefunction dynamics in linear and square lattices.
Linear and Nonlinear Evolution and Diffusion Layer Selection in Electrokinetic Instability
Demekhin, E A; Polyanskikh, S V
2011-01-01
In the present work fournontrivial stages of electrokinetic instability are identified by direct numerical simulation (DNS) of the full Nernst-Planck-Poisson-Stokes (NPPS) system: i) The stage of the influence of the initial conditions (milliseconds); ii) 1D self-similar evolution (milliseconds-seconds); iii) The primary instability of the self-similar solution (seconds); iv) The nonlinear stage with secondary instabilities. The self-similar character of evolution at intermediately large times is confirmed. Rubinstein and Zaltzman instability and noise-driven nonlinear evolution to over-limiting regimes in ion-exchange membranes are numerically simulated and compared with theoretical and experimental predictions. The primary instability which happens during this stage is found to arrest self-similar growth of the diffusion layer and specifies its characteristic length as was first experimentally predicted by Yossifon and Chang (PRL 101, 254501 (2008)). A novel principle for the characteristic wave number sele...
A Weakly Nonlinear Model for Kelvin-Helmholtz Instability in Incompressible Fluids
Institute of Scientific and Technical Information of China (English)
WANG Li-Feng; YE Wen-Hua; FAN Zheng-Feng; XUE Chuang; LI Ying-Jun
2009-01-01
A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling.
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...
Energy Technology Data Exchange (ETDEWEB)
Kilkenny, J.D.
1994-08-04
As shown elsewhere an ablatively imploded shell is hydrodynamically unstable, the dominant instability being the well known Rayleigh-Taylor instability with growth rate {gamma} = {radical}Akg where k = 2{pi}/{lambda} is the wave number, g is the acceleration and A the Attwood number ({rho}{sub hi} {minus} {rho}{sub lo})/({rho}{sub hi} + {rho}{sub lo}) where {rho}{sub hi} is the density of the heavier fluid and {rho}{sub lo} is the density of the lighter fluid. A theoretical understanding of ablative stabilization has gradually evolved, confirmed over the last five years by experiments. The linear growth is very well understood with excellent agreement between experiment and simulation for planar geometry with wavelengths in the region of 30--100{mu}m. There is an accurate, albeit phenomenological dispersion relation. The non-linear growth has been measured and agrees with calculations. In this lecture, the authors go into the fundamentals of the Rayleigh-Taylor instability and the experimental measurements that show it is stabilized sufficiently by ablation in regimes relevant to ICF.
Nonlinear evolution of mirror instability in the Earth's magnetosheath in pic simulations
Ahmadi, Narges
Mirror modes are large amplitude non-propagating structures frequently observed in the magnetosheath and they are generated in space plasma environments with proton temperature anisotropy of larger than one. The proton temperature anisotropy also drives the proton cyclotron instability which has larger linear growth rate than that of the mirror instability. Linear dispersion theory predicts that electron temperature anisotropy can enhance the mirror instability growth rate while leaving the proton cyclotron instability largely unaffected. Contrary to the hypothesis, electron temperature anisotropy leads to excitement of the electron whistler instability. Our results show that the electron whistler instability grows much faster than the mirror instability and quickly consumes the electron free energy, so that there is not enough electron temperature anisotropy left to significantly impact the evolution of the mirror instability. Observational studies have shown that the shape of mirror structures is related to local plasma parameters and distance to the mirror instability threshold. Mirror structures in the form of magnetic holes are observed when plasma is mirror stable or marginally mirror unstable and magnetic peaks are observed when plasma is mirror unstable. Mirror structures are created downstream of the quasi-perpendicular bow shock and they are convected toward the magnetopause. In the middle magnetosheath, where plasma is mirror unstable, mirror structures are dominated by magnetic peaks. Close to the magnetopause, plasma expansion makes the region mirror stable and magnetic peaks evolve to magnetic holes. We investigate the nonlinear evolution of mirror instability using expanding box Particle-in-Cell simulations. We change the plasma conditions by artificially enlarging the simulation box over time to make the plasma mirror stable and investigate the final nonlinear state of the mirror structures. We show that the direct nonlinear evolution of the mirror
Theoretical and experimental research on nonlinear hydrodynamic stability and transition is presented. Bifurcations, amplitude equations, pattern in experiments, and shear flows are considered. Particular attention is given to bifurcations of plane viscous fluid flow and transition to turbulence, chaotic traveling wave covection, chaotic behavior of parametrically excited surface waves in square geometry, amplitude analysis of the Swift-Hohenberg equation, traveling wave convection in finite containers, focus instability in axisymmetric Rayleigh-Benard convection, scaling and pattern formation in flowing sand, dynamical behavior of instabilities in spherical gap flows, and nonlinear short-wavelength Taylor vortices. Also discussed are stability of a flow past a two-dimensional grid, inertia wave breakdown in a precessing fluid, flow-induced instabilities in directional solidification, structure and dynamical properties of convection in binary fluid mixtures, and instability competition for convecting superfluid mixtures.
Wan, Xiaoliang; Yu, Haijun; Weinan, E.
2015-05-01
In this work, we study the nonlinear instability of two-dimensional (2D) wall-bounded shear flows from the large deviation point of view. The main idea is to consider the Navier-Stokes equations perturbed by small noise in force and then examine the noise-induced transitions between the two coexisting stable solutions due to the subcritical bifurcation. When the amplitude of the noise goes to zero, the Freidlin-Wentzell (F-W) theory of large deviations defines the most probable transition path in the phase space, which is the minimizer of the F-W action functional and characterizes the development of the nonlinear instability subject to small random perturbations. Based on such a transition path we can define a critical Reynolds number for the nonlinear instability in the probabilistic sense. Then the action-based stability theory is applied to study the 2D Poiseuille flow in a short channel.
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.
Stability Analysis for Class of Switched Nonlinear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza; How, Jonathan P.
2010-01-01
Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which...
ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Zuoxin; HAN Jingqing; ZHAO Suxia; WU Yongxian
2002-01-01
In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by Lyapunov function approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.
Dynamic stabilization for degenerative spondylolisthesis and lumbar spinal instability.
Ohtonari, Tatsuya; Nishihara, Nobuharu; Suwa, Katsuyasu; Ota, Taisei; Koyama, Tsunemaro
2014-01-01
Lumbar interbody fusion is a widely accepted surgical procedure for patients with lumbar degenerative spondylolisthesis and lumbar spinal instability in the active age group. However, in elderly patients, it is often questionable whether it is truly necessary to construct rigid fixation for a short period of time. In recent years, we have been occasionally performing posterior dynamic stabilization in elderly patients with such lumbar disorders. Posterior dynamic stabilization was performed in 12 patients (6 women, 70.9 ± 5.6 years old at the time of operation) with lumbar degenerative spondylolisthesis in whom % slip was less than 20% or instability associated with lumbar disc herniation between March 2011 and March 2013. Movement occurs through the connector linked to the pedicle screw. In practice, 9 pairs of D connector system where the rod moves in the perpendicular direction alone and 8 pairs of Dynamic connector system where the connector linked to the pedicle screw rotates in the sagittal direction were installed. The observation period was 77-479 days, and the mean recovery rate of lumbar Japanese Orthopedic Association (JOA) score was 65.6 ± 20.8%. There was progression of slippage due to slight loosening in a case with lumbar degenerative spondylolisthesis, but this did not lead to exacerbation of the symptoms. Although follow-up was short, there were no symptomatic adjacent vertebral and disc disorders during this period. Posterior dynamic stabilization may diminish the development of adjacent vertebral or disc disorders due to lumbar interbody fusion, especially in elderly patients, and it may be a useful procedure that facilitates decompression and ensures a certain degree of spinal stabilization.
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
2011-01-01
This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Stability Analysis and Design for Nonlinear Singular Systems
Yang, Chunyu; Zhou, Linna
2013-01-01
Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability f...
Energy Technology Data Exchange (ETDEWEB)
Prill, Dennis; Class, Andreas G. [Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen (Germany). AREVA Nuclear Professional School (ANPS)
2013-07-01
Unexpected non-linear boiling water reactor (BWR) instability events in various plants, e.g. LaSalle II in 1988 and Oskarshamn II in 1990 amongst others, emphasize the major safety relevance and the existence of parameter regions with unstable behavior. A detailed description of the complete dynamical non-linear behavior is of paramount importance for BWR operation. An extension of state-of-the-art methodology towards a more general stability description, also applicable in the non-linear region, could lead to a deeper understanding of non-linear BWR stability phenomena. With the intention of a full non-linear stability analysis of the two-phase BWR system, the present paper aims at a general non-linear methodology capable to achieve reliable and numerical stable reduced order models (ROMs), representing the dynamical behavior of an original system based on a small number of transients. Model-specific options and aspects of the proposed methodology are focused on and illustrated by means of a strongly non-linear dynamical system showing complex oscillating behavior. Prediction capability of the proposed methodology is also addressed. (orig.)
The K-Stability of Nonlinear Delay Systems
Institute of Scientific and Technical Information of China (English)
章毅; 张毅; 王联
1994-01-01
In this paper,we study the K-stability theory of nonlinear delay systems.In the more general case,we establish two nonlinear delay differential inequalities.Therefore,to study the X-stability,a powerful method is provided.By making use of the foregoing inequalities,we analyse and investigate some K-stabiiity conditions of nonlinear delay systems.Finally,some examples are given to illustrate our theory.
Contribution to stability analysis of nonlinear control systems
Directory of Open Access Journals (Sweden)
varc Ivan
2003-12-01
Full Text Available The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The table includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically.Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.
Stabilization and utilization of nonlinear phenomena based on bifurcation control for slow dynamics
Yabuno, Hiroshi
2008-08-01
Mechanical systems may experience undesirable and unexpected behavior and instability due to the effects of nonlinearity of the systems. Many kinds of control methods to decrease or eliminate the effects have been studied. In particular, bifurcation control to stabilize or utilize nonlinear phenomena is currently an active topic in the field of nonlinear dynamics. This article presents some types of bifurcation control methods with the aim of realizing vibration control and motion control for mechanical systems. It is also indicated through every control method that slowly varying components in the dynamics play important roles for the control and the utilizations of nonlinear phenomena. In the first part, we deal with stabilization control methods for nonlinear resonance which is the 1/3-order subharmonic resonance in a nonlinear spring-mass-damper system and the self-excited oscillation (hunting motion) in a railway vehicle wheelset. The second part deals with positive utilizations of nonlinear phenomena by the generation and the modification of bifurcation phenomena. We propose the amplitude control method of the cantilever probe of an atomic force microscope (AFM) by increasing the nonlinearity in the system. Also, the motion control of a two link underactuated manipulator with a free link and an active link is considered by actuating the bifurcations produced under high-frequency excitation. This article is a discussion on the bifurcation control methods presented by the author and co-researchers by focusing on the actuation of the slowly varying components included in the original dynamics.
Stabilization of a class of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) ByrnesIsidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented.Finally, as an application the stability of switched lorenz systems is investigated.
Nonlinear electron-magnetohydrodynamic simulations of three dimensional current shear instability
Energy Technology Data Exchange (ETDEWEB)
Jain, Neeraj [Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau (Germany); Das, Amita; Sengupta, Sudip; Kaw, Predhiman [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2012-09-15
This paper deals with detailed nonlinear electron-magnetohydrodynamic simulations of a three dimensional current shear driven instability in slab geometry. The simulations show the development of the instability in the current shear layer in the linear regime leading to the generation of electromagnetic turbulence in the nonlinear regime. The electromagnetic turbulence is first generated in the unstable shear layer and then spreads into the stable regions. The turbulence spectrum shows a new kind of anisotropy in which power transfer towards shorter scales occurs preferentially in the direction perpendicular to the electron flow. Results of the present three dimensional simulations of the current shear instability are compared with those of our earlier two dimensional simulations of sausage instability. It is found that the flattening of the mean velocity profile and thus reduction in the electron current due to generation of electromagnetic turbulence in the three dimensional case is more effective as compared to that in the two dimensional case.
Chin, Siu A
2007-01-01
Since the kinetic and the potential energy term of the real time nonlinear Schr\\"odinger equation can each be solved exactly, the entire equation can be solved to any order via splitting algorithms. We verified the fourth-order convergence of some well known algorithms by solving the Gross-Pitaevskii equation numerically. All such splitting algorithms suffer from a latent numerical instability even when the total energy is very well conserved. A detail error analysis reveals that the noise, or elementary excitations of the nonlinear Schr\\"odinger, obeys the Bogoliubov spectrum and the instability is due to the exponential growth of high wave number noises caused by the splitting process. For a continuum wave function, this instability is unavoidable no matter how small the time step. For a discrete wave function, the instability can be avoided only for $\\dt k_{max}^2{<\\atop\\sim}2 \\pi$, where $k_{max}=\\pi/\\Delta x$.
Indian Academy of Sciences (India)
R Ganapathy; V C Kuriakose
2002-04-01
We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
NONLINEAR STABILITY OF BALANCED ROTOR DUE TO EFFECT OF BALL BEARING INTERNAL CLEARANCE
Institute of Scientific and Technical Information of China (English)
BAI Chang-qing; XU Qing-yu; ZHANG Xiao-long
2006-01-01
Stability and dynamic characteristics of a ball bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Floquet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution.The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.
Directory of Open Access Journals (Sweden)
Ghader Rezazadeh
2007-07-01
Full Text Available In this paper, the effect of residual stress on divergence instability of a rectangular microplate subjected to a nonlinear electrostatic pressure for different geometrical properties has been presented. After deriving the governing equation and using of Step-by-Step Linearization Method (SSLM, the governing nonlinear equation has been linearized. By applying the finite difference method (FDM to a rectangular mesh, the linearized equation has been discretized. The results show, residual stresses have considerable effects on Pull-in phenomena. Tensile residual stresses increase pull-in voltage and compressive decrease it. The effect of different geometrical properties on divergence instability has also been studied.
Robust stabilization for a class of nonlinear networked control systems
Institute of Scientific and Technical Information of China (English)
Jinfeng GAO; Hongye SU; Xiaofu JI; Jian CHU
2008-01-01
The problem of robust stabilization for a class of uncertain networked control systems(NCSs)with nonlinearities satisfying a given sector condition is investigated in this paper.By introducing a new model of NCSs with parameter uncertainty,network.induced delay,nonlinearity and data packet dropout in the transmission,a strict linear matrix inequality(LMI)criterion is proposed for robust stabilization of the uncenmn nonlinear NCSs based on the Lyapunov stability theory.The maximum allowable transfer interval(MATI)can be derived by solving the feasibility problem of the corresponding LMI.Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.
STEADY-STATE RESPONSES AND THEIR STABILITY OF NONLINEAR VIBRATION OF AN AXIALLY ACCELERATING STRING
Institute of Scientific and Technical Information of China (English)
吴俊; 陈立群
2004-01-01
The steady-state transverse vibration of an axially moving string with geometric nonlinearity was investigated. The transport speed was assumed to be a constant mean speed with small harmonic variations. The nonlinear partial-differential equation that governs the transverse vibration of the string was derived by use of the Hamilton principle. The method of multiple scales was applied directly to the equation. The solvability condition of eliminating the secular terms was established. Closed form solutions for the amplitude and the existence conditions of nontrivial steady-state response of the two-to-one parametric resonance were obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation were presented. The Liapunov linearized stability theory was employed to derive the instability conditions of the trivial solution and the nontrivial solutions for the two-to-one parametric resonance. Some numerical examples highlighting influences of the related parameters on the instability conditions were presented.
Massive gravity: nonlinear instability of the homogeneous and isotropic universe
De Felice, Antonio; Mukohyama, Shinji
2012-01-01
We study the propagating modes for nonlinear massive gravity on a Bianchi type--I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. Since this ghost mode can be considered as a leading nonlinear perturbation around a homogeneous and isotropic background, we conclude that the universe in this theory must be either inhomogeneous or anisotropic.
Stability and nonlinear regimes of flow over a saturated porous medium
Directory of Open Access Journals (Sweden)
T. P. Lyubimova
2013-07-01
Full Text Available The paper deals with the investigation of stability and nonlinear regimes of flow over the saturated porous medium applied to the problem of stability of water flow over the bottom covered with vegetation. It is shown that the velocity profile of steady plane-parallel flow has two inflection points, which results in instability of this flow. The neutral stability curves, the dependencies of critical Reynolds number and the wave number of most dangerous perturbations on the ratio of porous layer thickness to the total thickness are obtained. The nonlinear flow regimes are investigated numerically by finite difference method. It is found that at supercritical parameter values waves travelling in the direction of the base flow take place.
A steady-state solver and stability calculator for nonlinear internal wave flows
Viner, Kevin C.; Epifanio, Craig C.; Doyle, James D.
2013-10-01
A steady solver and stability calculator is presented for the problem of nonlinear internal gravity waves forced by topography. Steady-state solutions are obtained using Newton's method, as applied to a finite-difference discretization in terrain-following coordinates. The iteration is initialized using a boundary-inflation scheme, in which the nonlinearity of the flow is gradually increased over the first few Newton steps. The resulting method is shown to be robust over the full range of nonhydrostatic and rotating parameter space. Examples are given for both nonhydrostatic and rotating flows, as well as flows with realistic upstream shear and static stability profiles. With a modest extension, the solver also allows for a linear stability analysis of the steady-state wave fields. Unstable modes are computed using a shifted-inverse method, combined with a parameter-space search over a set of realistic target values. An example is given showing resonant instability in a nonhydrostatic mountain wave.
Directory of Open Access Journals (Sweden)
Cha'o-Kuang Chen
2009-01-01
Full Text Available The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the method of multiple scales. The Ginzburg-Landau equation is determined to discuss the necessary condition for the existence of such flow pattern. The results indicate that the superctitical instability region increases, and the subcritical stability region decreases with the increase of the rotation number or the radius of circular disk. It is found that the rotation number and the radius of circular disk not only play the significant roles in destabilizing the flow in the linear stability analysis but also shrink the area of supercritical stability region at high Reynolds number in the weakly nonlinear stability analysis.
Stabilization of nonlinear excitations by disorder
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
Using analytical and numerical techniques we analyze the static and dynamical properties of solitonlike excitations in the presence of parametric disorder in the one-dimensional nonlinear Schrodinger equation with a homogeneous power nonlinearity. Both the continuum and the discrete problem are i...
AN INSTABILITY THEOREM FOR A KIND OF SEVENTH ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
This paper considers a kind of seventh order nonlinear differential equations with a deviating argument.By means of the Lyapunov direct method,some sufficient conditions are established to show the instability of the zero solution to the equation.Our result is new and complements the corresponding result of [5].
Effect of four-dimensional variational data assimilation in case of nonlinear instability
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The effect of four-dimensional variational data assimilation on the reduction of the forecast errors is investigated for both stable and unstable flows. Numerical results show that the effect is generally positive. Particularly,its effect is much more significant in the presence of nonlinear instability
Passamonti, A
2011-01-01
We study the damping of the gravitational radiation-driven f-mode instability in ro- tating neutron stars by nonlinear bulk viscosity in the so-called supra-thermal regime. In this regime the dissipative action of bulk viscosity is known to be enhanced as a result of nonlinear contributions with respect to the oscillation amplitude. Our anal- ysis of the f-mode instability is based on a time-domain code that evolves linear perturbations of rapidly rotating polytropic neutron star models. The extracted mode frequency and eigenfunctions are subsequently used in standard energy integrals for the gravitational wave growth and viscous damping. We find that nonlinear bulk vis- cosity has a moderate impact on the size of the f-mode instability window, becoming an important factor and saturating the mode's growth at a relatively large oscillation amplitude. We show that a similar result holds for the damping of the inertial r-mode instability by nonlinear bulk viscosity. In addition, we show that the action of bulk v...
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)
The nonlinear saturation of the non-resonant kinetically driven streaming instability
Gargate, L; Niemiec, J; Pohl, M; Bingham, R; Silva, L O
2010-01-01
A non-resonant instability for the amplification of the interstellar magnetic field in young Supernova Remnant (SNR) shocks was predicted by Bell (2004), and is thought to be relevant for the acceleration of cosmic ray (CR) particles. For this instability, the CRs streaming ahead of SNR shock fronts drive electromagnetic waves with wavelengths much shorter than the typical CR Larmor radius, by inducing a current parallel to the background magnetic field. We explore the nonlinear regime of the non-resonant mode using Particle-in-Cell (PIC) hybrid simulations, with kinetic ions and fluid electrons, and analyze the saturation mechanism for realistic CR and background plasma parameters. In the linear regime, the observed growth rates and wavelengths match the theoretical predictions; the nonlinear stage of the instability shows a strong reaction of both the background plasma and the CR particles, with the saturation level of the magnetic field varying with the CR parameters. The simulations with CR-to-background ...
Stability of Nonlinear Force-Free Magnetic Fields
Institute of Scientific and Technical Information of China (English)
胡友秋
2001-01-01
Based on the magnetohydrodynamic energy principle, it is proved that Gold-Hoyle's nonlinear force-free magnetic field is unstable. This disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Kriiger that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue associated with the domain of interest.
Weakly nonlinear stability of ultra-thin slipping films
Institute of Scientific and Technical Information of China (English)
HU Guohui
2005-01-01
A weakly nonlinear theory is presented to study the effects of slippage on the stability of the ultra-thin polymer films.The nonlinear mathematical model is constructed for perturbations of small finite amplitude based on hydrodynamic equations with the long wave approximation. Results reveal that the nonlinearity always accelerates the rupture of the films. The influences of the slip length, film thickness, and initial amplitude of perturbations on the rupture of the films are investigated.
STABILITY AND INSTABILITY OF SOLITARY WAVES FOR ABSTRACT COMPLEX HAMILTONIAN SYSTEM
Institute of Scientific and Technical Information of China (English)
Zhao Ye
2005-01-01
This paper is concerned with the orbital stability and orbital instability of solitary waves for some complex Hamiltonian systems in abstract form. Under some assumptions on the spectra of the related operator and the decaying estimates of the semigroup, the sufficient conditions on orbital stability and instability are obtained.
Existence,Orbital Stability and Instability of Solitary Waves for Coupled BBM Equations
Institute of Scientific and Technical Information of China (English)
Li-wei Cui
2009-01-01
This paper is concerned with the orbital stability/instability of solitary waves for coupled BBM equations which have Hamiltonian form.The explicit solitary wave solutions will be worked out first.Then by detailed spectral analysis and decaying estimates of solutions for the initial value problem,we obtain the orbital stability/instability of solitary waves.
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
Uniform Stability of Damped Nonlinear Vibrations of an Elastic String
Indian Academy of Sciences (India)
Ganesh C Gorain; Sujit K Bose
2003-11-01
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 achieved by considering an energy-like Lyapunov functional for the system.
AdS nonlinear instability: moving beyond spherical symmetry
Dias, Oscar J C
2016-01-01
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.
Nonlinear effects of energetic particle driven instabilities in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Bruedgam, Michael
2010-03-25
In a tokamak plasma, a population of superthermal particles generated by heating methods can lead to a destabilization of various MHD modes. Due to nonlinear wave-particle interactions, a consequential fast particle redistribution reduces the plasma heating and can cause severe damages to the wall of the fusion device. In order to describe the wave-particle interaction, the drift-kinetic perturbative HAGIS code is applied which evolves the particle trajectories and the waves nonlinearly. For a simulation speed-up, the 6-d particle phase-space is reduced by the guiding centre approach to a 5-d description. The eigenfunction of the wave is assumed to be invariant, but its amplitude and phase is altered in time. A sophisticated {delta}/f-method is employed to model the change in the fast particle distribution so that numerical noise and the excessive number of simulated Monte-Carlo points are reduced significantly. The original code can only calculate the particle redistribution inside the plasma region. Therefore, a code extension has been developed during this thesis which enlarges the simulation region up to the vessel wall. By means of numerical simulations, this thesis addresses the problem of nonlinear waveparticle interactions in the presence of multiple MHD modes with significantly different eigenfrequencies and the corresponding fast particle transport inside the plasma. In this context, a new coupling mechanism between resonant particles and waves has been identified that leads to enhanced mode amplitudes and fast particle losses. The extension of the code provides for the first time the possibility of a quantitative and qualitative comparison between simulation results and recent measurements in the experiment. The findings of the comparison serve as a validation of both the theoretical model and the interpretation of the experimental results. Thus, a powerful interface tool has been developed for a deeper insight of nonlinear wave-particle interaction
Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative
Directory of Open Access Journals (Sweden)
Fengrong Zhang
2011-01-01
Full Text Available This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some other sufficient conditions on stability are also presented.
Global stabilization of nonlinear systems with uncertain structure
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The global stabilization problem of nonlinear systems with uncertain structure is dealt with. Based on control Lyapunov function (CLF), a sufficient and necessary condition for Lyapunov stabilization is given. From the condition,several simply sufficient conditions for the globally asymptotical stability are deduced. A state feedback control law is designed to globally asymptotically stabilize the equilibrium of the closed system. Last, a simulation shows the effectiveness of the method.
Non-linear Study of Bell's Cosmic Ray Current-driven Instability
Riquelme, Mario A
2008-01-01
The cosmic ray current-driven (CRCD) instability, predicted by Bell (2004), consists of non-resonant, growing plasma waves driven by the electric current of cosmic rays (CRs) that stream along the magnetic field ahead of both relativistic and non-relativistic shocks. Combining an analytic, kinetic model with one-, two-, and three-dimensional particle-in-cell simulations, we confirm the existence of this instability in the kinetic regime and determine its saturation mechanisms. In the linear regime, we show that, if the background plasma is well magnetized, the CRCD waves grow exponentially at the rates and wavelengths predicted by the analytic dispersion relation. The magnetization condition implies that the growth rate of the instability is much smaller than the ion cyclotron frequency. As the instability becomes non-linear, significant turbulence forms in the plasma. This turbulence reduces the growth rate of the field and damps the shortest wavelength modes, making the dominant wavelength, \\lambda_d, grow ...
The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities
Chang, Philip; Lamberts, Astrid
2014-01-01
Very-high energy gamma-rays from extragalactic sources pair-produce off of the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the "oblique" instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here, we show with numerical calculations that the effective damping rate is $8\\times 10^{-4}$ of the growth rate of the linear instability, which is sufficient for the "oblique" instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wavenumber and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to ap...
Barker, Adrian J
2016-01-01
I present results from the first global hydrodynamical simulations of the elliptical instability in a tidally deformed gaseous planet (or star) with a free surface. The elliptical instability is potentially important for tidal evolution of the shortest-period hot Jupiters. I model the planet as a spin-orbit aligned or anti-aligned, and non-synchronously rotating, tidally deformed, homogeneous fluid body. A companion paper presented an analysis of the global modes and instabilities of such a planet. Here I focus on the nonlinear evolution of the elliptical instability. This is observed to produce bursts of turbulence that drive the planet towards synchronism with its orbit in an erratic manner. If the planetary spin is initially anti-aligned, the elliptical instability also drives spin-orbit alignment on a similar timescale as the spin synchronisation. The instability generates differential rotation inside the planet in the form of zonal flows, which play an important role in the saturation of the instability,...
Remarks on the relationship between ℒp stability and internal stability of nonlinear systems
Wang, Xu; Grip, H°avard Fjær; Saberi, Ali A.; Stoorvogel, Anton A.; Saberi, Ingmar
2013-01-01
In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic
Remarks on the relationship between ℒp stability and internal stability of nonlinear systems
Wang, Xu; Grip, H°avard Fjær; Saberi, Ali; Stoorvogel, Anton A.; Saberi, Ingmar
2011-01-01
In this paper, we investigate the relationship between ℒp stability and internal stability of nonlinear systems. It is shown that under certain conditions, ℒp stability without finite gain implies attractivity of the equilibrium, and that local ℒp stability with finite gain implies local asymptotic
AdS nonlinear instability: moving beyond spherical symmetry
Dias, Óscar J. C.; Santos, Jorge E.
2016-12-01
Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation (Dafermos and Holzegel 2006 Seminar at DAMTP (University of Cambridge) available at https://dpmms.cam.ac.uk/~md384/ADSinstability.pdf, Bizon and Rostworowski 2011 Phys. Rev. Lett. 107 031102). We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied by Bizon and Rostworowski. In contrast with Bizon and Rostworowski, we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied by Bizon and Rostworowski. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of Bizon and Rostworowski. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.
Nonlinear Rayleigh--Taylor instability of the cylindrical fluid flow with mass and heat transfer
Indian Academy of Sciences (India)
ALY R SEADAWY; K EL-RASHIDY
2016-08-01
The nonlinear Rayleigh--Taylor stability of the cylindrical interface between the vapour and liquid phases of a fluid is studied. The phases enclosed between two cylindrical surfaces coaxial with mass and heat transfer is derived from nonlinear Ginzburg--Landau equation. The F-expansion method is used to get exactsolutions for a nonlinear Ginzburg--Landau equation. The region of solutions is displayed graphically.
ASYMPTOTIC STABILITY OF SINGULAR NONLINEAR DIFFERENTIAL SYSTEMS WITH UNBOUNDED DELAYS
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,the asymptotic stability of singular nonlinear differential systems with unbounded delays is considered.The stability criteria are derived based on a kind of Lyapunov-functional and some technique of matrix inequalities.The criteria are described as matrix equation and matrix inequalities,which are computationally flexible and efficient.Two examples are given to illustrate the results.
Control Lyapunov Stabilization of Nonlinear Systems with Structural Uncertainty
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; TANG Hou-jun
2005-01-01
This paper deals with global stabilization problem for the nonlinear systems with structural uncertainty.Based on control Lyapunov function, a sufficient and necessary condition for the globally and asymptotically stabilizing the equailibrium of the closed system is given. Moreovery, an almost smooth state feedback control law is constructed. The simulation shows the effectiveness of the method.
Nonlinear {omega}*-stabilization of the m = 1 mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Rogers, B. [Univ. of Maryland, College Park, MD (United States). Inst. for Plasma Research; Zakharov, L. [Princeton Univ., NJ (United States). Plasma Physics Lab.
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 {omega}*{sub 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.
Nariyuki, Y; Nariyuki, Yasuhiro; Hada, Tohru
2006-01-01
Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfven waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation.
A nonlinear dynamical system for combustion instability in a pulse model combustor
Takagi, Kazushi; Gotoda, Hiroshi
2016-11-01
We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.
Palodhi, L; Pegoraro, F; 10.1088/0741-3335/51/12/125006
2010-01-01
The nonlinear evolution of the Weibel instability driven by the anisotropy of the electron distribution function in a collisionless plasma is investigated in a spatially one-dimensional configuration with a Vlasov code in a two-dimensional velocity space. It is found that the electromagnetic fields generated by this instability cause a strong deformation of the electron distribution function in phase space, corresponding to highly filamented magnetic vortices. Eventually, these deformations lead to the generation of short wavelength Langmuir modes that form highly localized electrostatic structures corresponding to jumps of the electrostatic potential.
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
Directory of Open Access Journals (Sweden)
Bo Wang
2012-10-01
Full Text Available In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
ON NONLINEAR STABILITY IN NONPARALLEL BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
TANG Deng-bin; WANG Wei-zhi
2004-01-01
The nonlinear stability problem in nonparallel boundary layer flow for two-dimensional disturbances was studied by using a newly presented method called Parabolic Stability Equations (PSE). A series of new modes generated by the nonlinear interaction of disturbance waves were tabulately analyzed, and the Mean Flow Distortion (MFD) was numerically given. The computational techniques developed, including the higher-order spectral method and the more effective algebraic mapping, increased greatly the numerical accuracy and the rate of convergence. With the predictor-corrector approach in the marching procedure, the normalization condition was satisfied, and the stability of numerical calculation could be ensured. With different initial amplitudes, the nonlinear stability of disturbance wave was studied. The results of examples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
Robust Stabilization of a Class of passive Nonlinear Systems
Joshi, Suresh M.; Kelkar, Atul G.
1996-01-01
The problem of feedback stabilization is considered for a class of nonlinear, finite dimensional, time invariant passive systems that are affine in control. Using extensions of the Kalman-Yakubovch lemma, it is shown that such systems can be stabilized by a class of finite demensional, linear, time-invariant controllers which are strictly positive real in the weak or marginal sense. The stability holds regardless of model uncertainties, and is therefore, robust.
Simulations and model of the nonlinear Richtmyer-Meshkov instability (U)
Energy Technology Data Exchange (ETDEWEB)
Dimonte, Guy [Los Alamos National Laboratory
2009-01-01
The nonlinear evolution of the Richtmyer-Meshkov (RM) instability is investigated using numerical simulations with the FLASH code in two-dimensions (20). The purpose of the simulations is to develop a nonlinear model of the RM instability that is accurate to the regime of inertial confinement fusion (ICF) and ejecta formation, namely, at large Atwood number A and initial amplitude kh{sub o} (k {triple_bond} wavenumber) of the perturbation. The FLASH code is first validated by obtaining excellent agreement with RM experiments well into the nonlinear regime. The results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A and kh{sub o} but not for the values characteristic of ICF and ejecta formation. As a result, a new nonlinear model is developed that captures the simulation results consistent with potential flow and for a broader range of A and kh{sub o}.
Baum, J. D.; Levine, J. N.
1980-01-01
The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.
Investigation of nonlinear effects in the instabilities and noise radiation of supersonic jets
Janjua, S. I.; McLaughlin, D. K.
1985-01-01
The nonlinear interactions of fluctuating components which produce noise in supersonic jet flows were studied experimentally. Attention was given to spectral components interactions and the spectral effects of increasing Re. A jet exhausted in perfectly expanded conditions was monitored by microphones in the maximum noise emission direction. Trials were run at Mach 1.4 and 2.1 and the Re was varied from 5000-20,000 and 9000-25,000, respectively. Hot-wire data were gathered to examine the mode-mode interactions and a point glow discharge was used to excite the jets. The noise was found to exhibit discrete frequency components and a single tone instability at Re below 10,000. Mode interactions were found to weaken after the instabilities reached a crescendo and then decayed, leading to a nonlinear spectral broadening effect.
Gianni, G; Paganini, E; Sello, S
2003-01-01
The onset of thermoacoustic instabilities in lean-premixed gas-turbine combustors is a crucial problem leading to degradation in engine and emissions performance and shortened component life. The main aim of this study is to propose a methodology based both on concepts of nonlinear dynamics and on geometric-topological invariants, for the characterization of attractors related to measurements based on the flame spontaneous light emission, like OH* radical, in order to classify different phases of the combustion process and to better recognize the transition mechanisms leading to the thermoacoustic instabilities. Preliminary results, clearly show the powerfulness of the approach to show the dynamical evolution of the flame and to evidence the onset of the thermoacoustic instabilities: in particular the topological invariant index (genus and related quantities) appear s as the best candidate for an early indicator of the dynamical transition, characterized by the onset of a more persistent, low entropy torus (q...
ORBITAL INSTABILITY OF STANDING WAVES FOR THE COUPLED NONLINEAR KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
Gan Zaihui; Guo Boling; Zhang Jian
2008-01-01
This paper deals with a type of standing waves for the coupled nonlin-ear Klein-Gordon equations in three space dimensions. First we construct a suitable constrained variational problem and obtain the existence of the standing waves with ground state by using variational argument. Then we prove the orbital instability of the standing waves by defining invariant sets and applying some priori estimates.
DEFF Research Database (Denmark)
Mamaev, A.V.; Saffman, M.; Zozulya, A.A.
1996-01-01
We analyze the evolution of (1+1) dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate....... Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay into a set of optical vortices....
THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES
Energy Technology Data Exchange (ETDEWEB)
Chang, Philip; Lamberts, Astrid [Department of Physics, University of Wisconsin-Milwaukee, 1900 E. Kenwood Boulevard, Milwaukee, WI 53211 (United States); Broderick, Avery E.; Shalaby, Mohamad [Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5 (Canada); Pfrommer, Christoph [Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, D-69118 Heidelberg (Germany); Puchwein, Ewald, E-mail: chang65@uwm.edu [Institute of Astronomy and Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge CB3 0HA (United Kingdom)
2014-12-20
Very high energy gamma-rays from extragalactic sources produce pairs from the extragalactic background light, yielding an electron-positron pair beam. This pair beam is unstable to various plasma instabilities, especially the ''oblique'' instability, which can be the dominant cooling mechanism for the beam. However, recently, it has been claimed that nonlinear Landau damping renders it physically irrelevant by reducing the effective damping rate to a low level. Here we show with numerical calculations that the effective damping rate is 8 × 10{sup –4} the growth rate of the linear instability, which is sufficient for the ''oblique'' instability to be the dominant cooling mechanism of these pair beams. In particular, we show that previous estimates of this rate ignored the exponential cutoff in the scattering amplitude at large wave numbers and assumed that the damping of scattered waves entirely depends on collisions, ignoring collisionless processes. We find that the total wave energy eventually grows to approximate equipartition with the beam by increasingly depositing energy into long-wavelength modes. As we have not included the effect of nonlinear wave-wave interactions on these long-wavelength modes, this scenario represents the ''worst case'' scenario for the oblique instability. As it continues to drain energy from the beam at a faster rate than other processes, we conclude that the ''oblique'' instability is sufficiently strong to make it the physically dominant cooling mechanism for high-energy pair beams in the intergalactic medium.
Non-linear simulations of combustion instabilities with a quasi-1D Navier-Stokes code
Haugen, Nils Erland L; Sannan, Sigurd
2010-01-01
As lean premixed combustion systems are more susceptible to combustion instabilities than non-premixed systems, there is an increasing demand for improved numerical design tools that can predict the occurrence of combustion instabilities with high accuracy. The inherent non-linearities in combustion instabilities can be of crucial importance, and we here propose an approach in which the one-dimensional Navier-Stokes and scalar transport equations are solved for geometries of variable cross-section. The focus is on attached flames, and for this purpose a new phenomenological model for the unsteady heat release from a flame front is introduced. In the attached flame method (AFM) the heat release occurs over the full length of the flame. The non-linear code with the use of the AFM approach is validated against results from an experimental study of thermoacoustic instabilities in oxy-fuel flames by Ditaranto and Hals [Combustion and Flame, 146, 493-512 (2006)]. The numerical simulations are in accordance with the...
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.
Dey, Pinkee; Suslov, Sergey A.
2016-12-01
A finite amplitude instability has been analysed to discover the exact mechanism leading to the appearance of stationary magnetoconvection patterns in a vertical layer of a non-conducting ferrofluid heated from the side and placed in an external magnetic field perpendicular to the walls. The physical results have been obtained using a version of a weakly nonlinear analysis that is based on the disturbance amplitude expansion. It enables a low-dimensional reduction of a full nonlinear problem in supercritical regimes away from a bifurcation point. The details of the reduction are given in comparison with traditional small-parameter expansions. It is also demonstrated that Squire’s transformation can be introduced for higher-order nonlinear terms thus reducing the full three-dimensional problem to its equivalent two-dimensional counterpart and enabling significant computational savings. The full three-dimensional instability patterns are subsequently recovered using the inverse transforms The analysed stationary thermomagnetic instability is shown to occur as a result of a supercritical pitchfork bifurcation.
Yang, Jianke
2016-01-01
Stability of soliton families in one-dimensional nonlinear Schroedinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets $(\\lambda, -\\lambda, \\lambda^*, -\\lambda^*)$, similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non-PT-symmetric systems, and it has far-reaching consequences ...
Nonlinear stabilization of tokamak microturbulence by fast ions
Citrin, J; Garcia, J; Haverkort, J W; Hogeweij, G M D; Jenko, F; Johnson, T; Mantica, P; Pueschel, M J; Told, D; contributors, JET-EFDA
2013-01-01
Nonlinear electromagnetic stabilization by suprathermal pressure gradients found in specific regimes is shown to be a key factor in reducing tokamak microturbulence, augmenting significantly the thermal pressure electromagnetic stabilization. Based on nonlinear gyrokinetic simulations investigating a set of ion heat transport experiments on the JET tokamak, described by Mantica et al. [Phys. Rev. Lett. 107 135004 (2011)], this result explains the experimentally observed ion heat flux and stiffness reduction. These findings are expected to improve the extrapolation of advanced tokamak scenarios to reactor relevant regimes.
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.
Stabilization of nonlinear systems based on robust control Lyapunov function
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; LU Gan-yun
2007-01-01
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization (robust practical stabilization) is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunov function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
Stabilization of a Nonlinear Delay System
Directory of Open Access Journals (Sweden)
Walid Arouri
2012-01-01
Full Text Available Problem statement: The analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. This can affect their significantly operations. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also affect the establishment of the command. Several studies have investigated the stability of delay systems under the assumption that the delay is a variable phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system. In this study we propose a modelling of delayed system by using the multimodels and switched system theory. The analysis of stability is based on the use of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequalities impossible to resolve. Thats why we propose the same original relaxations to come over this difficulty, an example of induction machine is given to illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabilisation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pessimistic than the used classical methods.
Two-dimensional nonlinear dynamics of bidirectional beam-plasma instability
Pavan, J.; Ziebell, L. F.; Gaelzer, R.; Yoon, P. H.
2009-01-01
Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present paper, this problem is revisited by extending the analysis to two dimensions. The classic bump-on-tail instability involves a single electron beam interacting with the background population. The bidirectional or counterstreaming beams excite Langmuir turbulence initially propagating in opposite directions. It is found that the nonlinear mode coupling leads to the redistribution of wave moments along concentric arcs in wave number space, somewhat similar to the earlier findings by Ziebell et al. (2008) in the case of one beam-plasma instability. However, the present result also shows distinctive features. The similarities and differences in the nonlinear wave dynamics are discussed. It is also found that the initial bidirectional beams undergo plateau formation and broadening in perpendicular velocity space. However, the anisotropy persists in the nonlinear stage, implying that an additional pitch angle scattering by transverse electromagnetic fluctuations is necessary in order to bring the system to a truly isotropic state.
Non-linear Evolution of Rayleigh-Taylor Instability in a Radiation Supported Atmosphere
Jiang, Yan-Fei; Stone, James
2012-01-01
The non-linear regime of Rayleigh-Taylor instability (RTI) in a radiation supported atmosphere, consisting of two uniform fluids with different densities, is studied numerically. We perform simulations using our recently developed numerical algorithm for multi-dimensional radiation hydrodynamics based on a variable Eddington tensor as implemented in Athena, focusing on the regime where scattering opacity greatly exceeds absorption opacity. We find that the radiation field can reduce the growth and mixing rate of RTI, but this reduction is only significant when radiation pressure significantly exceeds gas pressure. Small scale structures are also suppressed in this case. In the non-linear regime, dense fingers sink faster than rarefied bubbles can rise, leading to asymmetric structures about the interface. By comparing the calculations that use a variable Eddington tensor (VET) versus the Eddington approximation, we demonstrate that anisotropy in the radiation field can affect the non-linear development of RTI...
Nonlinear regime of the mode-coupling instability in 2D plasma crystals
Röcker, T B; Zhdanov, S K; Nosenko, V; Ivlev, A V; Thomas, H M; Morfill, G E
2014-01-01
The transition between linear and nonlinear regimes of the mode-coupling instability (MCI) operating in a monolayer plasma crystal is studied. The mode coupling is triggered at the centre of the crystal and a melting front is formed, which travels through the crystal. At the nonlinear stage, the mode coupling results in synchronisation of the particle motion and the kinetic temperature of the particles grows exponentially. After melting of the crystalline structure, the mean kinetic energy of the particles continued to grow further, preventing recrystallisation of the melted phase. The effect could not be reproduced in simulations employing a simple point-like wake model. This shows that at the nonlinear stage of the MCI a heating mechanism is working which was not considered so far.
The weakly nonlinear magnetorotational instability in a global, cylindrical Taylor-Couette flow
Clark, S E
2016-01-01
We conduct a global, weakly nonlinear analysis of the magnetorotational instability (MRI) in a Taylor-Couette flow. This is a multiscale perturbative treatment of the nonideal, axisymmetric MRI near threshold, subject to realistic radial boundary conditions and cylindrical geometry. We analyze both the standard MRI, initialized by a constant vertical background magnetic field, and the helical MRI, with an azimuthal background field component. This is the first weakly nonlinear analysis of the MRI in a global Taylor-Couette geometry, as well as the first weakly nonlinear analysis of the helical MRI. We find that the evolution of the amplitude of the standard MRI is described by a real Ginzburg-Landau equation (GLE), while the amplitude of the helical MRI takes the form of a complex GLE. This suggests that the saturated state of the helical MRI may itself be unstable on long spatial and temporal scales.
Compositional Finite-Time Stability analysis of nonlinear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....
Stabilization of nonlinear systems by similarity transformations
Directory of Open Access Journals (Sweden)
Irina E. Zuber
1998-01-01
Full Text Available For a system x˙=A(x+b(xu, u(x=s∗(xx, x∈ℝn, where the pair (A(x,b(x is given, we obtain the feedback vector s(x to stabilize the corresponding closed loop system. For an arbitrarily chosen constant vector g, a sufficient condition of the existence and an explicit form of a similarity transformation T(A(x,b(x,g is established. The latter transforms matrix A(x into the Frobenius matrix, vector b(x into g, and an unknown feedback vector s(x into the first unit vector. The boundaries of A˜(y,g are determined by the boundaries of {∂kA(x∂xk,∂kb(x∂xk}, k=0,n−1¯. The stabilization of the transformed system is subject to the choice of the constant vector g.
Asymptotic Stability of Uniformly Bounded Nonlinear Switched Systems
Jouan, Philippe; Naciri, Said
2012-01-01
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of inputs with dwell-time, and the class of general ones. For each of them we provide some sufficient conditions for asymptotic stability in terms of the geometry of certain sets. The results, which extend those of Balde, Jouan about linear systems, are illustrated...
Stabilization of discrete nonlinear systems based on control Lyapunov functions
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The stabilization of discrete nonlinear systems is studied.Based on control Lyapunov functions,asufficient and necessary condition for a quadratic function to be a control Lyapunov function is given.From this condition,a continuous state feedback law is constructed explicitly.It can globally asymptotically stabilize the equilibrium of the closed-loop system.A simulation example shows the effectiveness of the proposed method.
Spencer, B. J.; Voorhees, P. W.; Davis, S. H.
1993-01-01
The morphological instability of a growing epitaxially strained dislocation-free solid film is analyzed. An evolution equation for the film surface is derived in the dilute limit of vacancies based on surface diffusion driven by a stress-dependent chemical potential. From the time-dependent linear stability problem the conditions for which a growing film is unstable are determined. It is found that the instability is driven by the lattice mismatch between the film and the substrate; however, low temperatures as well as elastically stiff substrates are stabilizing influences. The results also reveal that the critical film thickness for instability depends on the growth rate of the film itself. Detailed comparison with experimental observations indicates that the instability described exhibits many of the observed features of the onset of the 'island instability'.
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.
Discontinuous stabilization of nonlinear systems : Quantized and switching controls
Ceragioli, Francesca; De Persis, Claudio
2007-01-01
In this paper we consider the classical problem of stabilizing nonlinear systems in the case the control laws take values in a discrete set. First, we present a robust control approach to the problem. Then, we focus on the class of dissipative systems and rephrase classical results available for thi
Sheykhi, A.; Hajkhalili, S.
2015-11-01
We study topological dilaton black holes of Einstein gravity in the presence of exponential nonlinear electrodynamics. The event horizons of these black holes can be a two-dimensional positive, zero or negative constant curvature surface. We analyze thermodynamics of these solutions by calculating all conserved and thermodynamic quantities and showing that the first law holds on the black hole horizon. Then, we perform the stability analysis in both canonical and grand canonical ensemble and disclose the effects of the dilaton and nonlinear electrodynamics on the thermal stability of the solutions. Finally, we study the phase transition points of these black holes in the thermodynamic geometry approach.
Properties and stability of freely propagating nonlinear density waves in accretion disks
Fromang, S
2007-01-01
In this paper, we study the propagation and stability of nonlinear sound waves in accretion disks. Using the shearing box approximation, we derive the form of these waves using a semi-analytic approach and go on to study their stability. The results are compared to those of numerical simulations performed using finite difference approaches such as employed by ZEUS as well as Godunov methods. When the wave frequency is between Omega and two Omega (where Omega is the disk orbital angular velocity), it can couple resonantly with a pair of linear inertial waves and thus undergo a parametric instability. Neglecting the disk vertical stratification, we derive an expression for the growth rate when the amplitude of the background wave is small. Good agreement is found with the results of numerical simulations performed both with finite difference and Godunov codes. During the nonlinear phase of the instability, the flow remains well organised if the amplitude of the background wave is small. However, strongly nonlin...
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
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.
Kinetic plasma turbulence during the nonlinear stage of the Kelvin-Helmholtz instability
Kemel, Koen; Lapenta, Giovanni; Califano, Francesco; Markidis, Stefano
2014-01-01
Using a full kinetic, implicit particle-in-cell code, iPiC3D, we studied the properties of plasma kinetic turbulence, such as would be found at the interface between the solar wind and the Earth magnetosphere at low latitude during northwards periods. In this case, in the presence of a magnetic field B oriented mostly perpendicular to the velocity shear, turbulence is fed by the disruption of a Kelvin-Helmholtz vortex chain via secondary instabilities, vortex pairing and non-linear interactions. We found that the magnetic energy spectral cascade between ion and electron inertial scales, $d_i$ and $d_e$, is in agreement with satellite observations and other previous numerical simulations; however, in our case the spectrum ends with a peak beyond $d_e$ due to the occurrence of the lower hybrid drift instability. The electric energy spectrum is influenced by effects of secondary instabilities: anomalous resistivity, fed by the development of the lower hybrid drift instability, steepens the spectral decay and, de...
Energy Technology Data Exchange (ETDEWEB)
Gaur, Gurudatt; Das, Amita [Institute for Plasma Research, Bhat, Gandhinagar 382428 (India)
2012-07-15
The study of electron velocity shear driven instability in electron magnetohydrodynamics (EMHD) regime in three dimensions has been carried out. It is well known that the instability is non-local in the plane defined by the flow direction and that of the shear, which is the usual Kelvin-Helmholtz mode, often termed as the sausage mode in the context of EMHD. On the other hand, a local instability with perturbations in the plane defined by the shear and the magnetic field direction exists which is termed as kink mode. The interplay of these two modes for simple sheared flow case as well as that when an external magnetic field exists has been studied extensively in the present manuscript in both linear and nonlinear regimes. Finally, these instability processes have been investigated for the exact 2D dipole solutions of EMHD equations [M. B. Isichenko and A. N. Marnachev, Sov. Phys. JETP 66, 702 (1987)] for which the electron flow velocity is sheared. It has been shown that dipoles are very robust and stable against the sausage mode as the unstable wavelengths are typically longer than the dipole size. However, we observe that they do get destabilized by the local kink mode.
Analytic approach to nonlinear hydrodynamic instabilities driven by time-dependent accelerations
Energy Technology Data Exchange (ETDEWEB)
Mikaelian, K O
2009-09-28
We extend our earlier model for Rayleigh-Taylor and Richtmyer-Meshkov instabilities to the more general class of hydrodynamic instabilities driven by a time-dependent acceleration g(t) . Explicit analytic solutions for linear as well as nonlinear amplitudes are obtained for several g(t)'s by solving a Schroedinger-like equation d{sup 2}{eta}/dt{sup 2} - g(t)kA{eta} = 0 where A is the Atwood number and k is the wavenumber of the perturbation amplitude {eta}(t). In our model a simple transformation k {yields} k{sub L} and A {yields} A{sub L} connects the linear to the nonlinear amplitudes: {eta}{sup nonlinear} (k,A) {approx} (1/k{sub L})ln{eta}{sup linear} (k{sub L}, A{sub L}). The model is found to be in very good agreement with direct numerical simulations. Bubble amplitudes for a variety of accelerations are seen to scale with s defined by s = {integral} {radical}g(t)dt, while spike amplitudes prefer scaling with displacement {Delta}x = {integral}[{integral}g(t)dt]dt.
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 gyro with harmonic nonlinearity in spinning vehicle
Singh, S. N.
1983-03-01
The stability analysis of a rate gyro mounted in a vehicle which is spinning with uncertain angular velocity about the spin axis of the gyro is presented. The complete nonlinear equation of the motion of the gimbal is considered, retaining the fundamental and second harmonic nonlinear terms which are functions of the angular velocity of the vehicle about the spin axis of the gyro. Using the circle criterion for the case of time-varying angular momentum and the Lyapunov approach for the case of uncertain constant angular velocity, conditions for asymptotic stability and global asymptotic stability are obtained. Stable regions in parameter space of the gyro and state space are obtained, and analytical relations for the selection of gyro parameters are derived.
ANALYSIS OF NONLINEAR DYNAMIC STABILITY OF LIQUID-CONVEYING PIPES
Institute of Scientific and Technical Information of China (English)
张立翔; 黄文虎
2002-01-01
Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson,Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different.
Instability Suppression in a Swirl-Stabilized Combustor Using Microjet Air Injection
LaBry, Zachary
2010-01-04
In this study, we examine the effectiveness of microjet air injection as a means of suppressing thermoacoustic instabilities in a swirl-stabilized, lean-premixed propane/air combustor. High-speed stereo PIV measurements, taken to explore the mechanism of combustion instability, reveal that the inner recirculation zone plays a dominant role in the coupling of acoustics and heat release that leads to combustion instability. Six microjet injector configurations were designed to modify the inner and outer recirculation zones with the intent of decoupling the mechanism leading to instability. Microjets that injected air into the inner recirculation zone, swirling in the opposite sense to the primary swirl were effective in suppressing combustion instability, reducing the overall sound pressure level by up to 17 dB within a certain window of operating conditions. Stabilization was achieved near an equivalence ratio of 0.65, corresponding to the region where the combustor transitions from a 40 Hz instability mode to a 110 Hz instability mode. PIV measurements made of the stabilized flow revealed significant modification of the inner recirculation zone and substantial weakening of the outer recirculation zone.
Nonlinear dynamics of beam-plasma instability in a finite magnetic field
Bogdankevich, I. L.; Goncharov, P. Yu.; Gusein-zade, N. G.; Ignatov, A. M.
2017-06-01
The nonlinear dynamics of beam-plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam-plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B 0 = 4.5 kG (Ω ω B p ) and 20 kG (Ω B ≫ ωp). For B 0 = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.
Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability.
Bosch, Pablo; Green, Stephen R; Lehner, Luis
2016-04-08
We describe the full nonlinear development of the superradiant instability for a charged massless scalar field coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordström-anti-de Sitter black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.
Nonlinear Marangoni instability of a liquid jet in the presence of electric field
Energy Technology Data Exchange (ETDEWEB)
Zakaria, Kadry; Sirwah, Magdy A.; Assaf, Achmed [Tanta Univ. (Egypt). Dept. of Mathematics
2009-11-15
The work discusses the linear and nonlinear stability of cylindrical surface deformations between two incompressible fluids. The interface is carrying a uniform surface charge. The inner fluid is assumed to be a liquid jet. Both fluids are modeled as a special type of a Newtonian viscous fluid. Furthermore, the effect of surface adsorption is taken into account. Both fluids are assumed to be dielectric and the stability is discussed in the presence of a constant electric field in axial direction. The analysis is performed along the lines of a multiple scale perturbation expansion with additional slow time and space variables. The various stability criteria are discussed both analytically and numerically. The results are displayed in many plots showing the stability criteria in various parameter planes. The results show the dual role of the electric field and the negative rate of change of surface tension with the concentration of surfactant on the system stability, in both the linear and nonlinear steps. The nonlinear theory, when used to investigate the stability of liquid jet, appears accurately to predict new unstable regions. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Ham, J. van; Beer, R.J. van; Builtjes, P.J.H.; Roemer, M.G.M. [TNO Inst. of Environmental Sciences, Delft (Netherlands); Koennen, G.P. [KNMI, Royal Netherlands Meteorological Inst., de Bilt (Netherlands); Oerlemans, J. [Utrecht Univ. (Netherlands). Inst. for Meteorological and Atmospheric Research
1995-12-31
In this presentation part of an investigation is described into risks for climate change which are presently not adequately covered in General Circulation Models. In the concept of climate change as a result of the enhanced greenhouse effect it is generally assumed that the radiative forcings from increased concentrations of greenhouse gases (GHG) will result in a proportional or quasilinear global warming. Though correlations of this kind are known from palaeoclimate research, the variability of the climate seems to prevent the direct proof of a causal relation between recent greenhouse gas concentrations and temperature observations. In order to resolve the issue the use of General Circulation Models (GCMs), though still inadequate at present, is indispensable. Around the world some 10 leading GCMs exist which have been the subject of evaluation and intercomparison in a number of studies. Their results are regularly assessed in the IPCC process. A discussion on their performance in simulating present or past climates and the causes of their weak points shows that the depiction of clouds is a major weakness of GCMs. A second element which is virtually absent in GCMs are the feedbacks from natural biogeochemical cycles. These cycles are influenced by man in a number of ways. GCMs have a limited performance in simulating regional effects on climate. Moreover, albedo instability, in part due to its interaction with cloudiness, is only roughly represented. Apparently, not all relevant processes have been included in the GCMs. That situation constitutes a risk, since it cannot be ruled out that a missing process could cause or trigger a non-linear climate change. In the study non-linear climate change is connected with those processes which could provide feedbacks with a risk for non-monotonous or discontinuous behaviour of the climate system, or which are unpredictable or could cause rapid transitions
Extension to nonlinear stability theory of the circular Couette flow
Yau, Pun Wong; Wang, Shixiao; Rusak, Zvi
2016-11-01
A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol'd energy-Casimir function Ard of Wang (2009). We show that all the inviscid flow effects as well as all the viscous-dependent terms related to the flow boundaries vanish. The evolution of ΔArd depends solely on the viscous effects of the perturbation's dynamics inside the flow domain. The requirement for the temporal decay of ΔArd leads to novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (1933) and significantly extend the classical nonlinear stability results of Serrin (1959) and Joseph & Hung (1971). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the setup of the rotating cylinders. This study provides new physical insights into a classical flow problem that was studied for decades.
Synchrophasor-Assisted Prediction of Stability/Instability of a Power System
Saha Roy, Biman Kumar; Sinha, Avinash Kumar; Pradhan, Ashok Kumar
2013-05-01
This paper presents a technique for real-time prediction of stability/instability of a power system based on synchrophasor measurements obtained from phasor measurement units (PMUs) at generator buses. For stability assessment the technique makes use of system severity indices developed using bus voltage magnitude obtained from PMUs and generator electrical power. Generator power is computed using system information and PMU information like voltage and current phasors obtained from PMU. System stability/instability is predicted when the indices exceeds a threshold value. A case study is carried out on New England 10-generator, 39-bus system to validate the performance of the technique.
A nonlinear lattice model for Heisenberg helimagnet and spin wave instabilities
Ludvin Felcy, A.; Latha, M. M.; Christal Vasanthi, C.
2016-10-01
We study the dynamics of a Heisenberg helimagnet by presenting a square lattice model and proposing the Hamiltonian associated with it. The corresponding equation of motion is constructed after averaging the Hamiltonian using a suitable wavefunction. The stability of the spin wave is discussed by means of Modulational Instability (MI) analysis. The influence of various types of inhomogeneities in the lattice is also investigated by improving the model.
Stabilizing model predictive control for constrained nonlinear distributed delay systems.
Mahboobi Esfanjani, R; Nikravesh, S K Y
2011-04-01
In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.
The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability
Wang, Yanjin
2011-01-01
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh-Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.
Non-linear Dynamics in ETG Mode Saturation and Beam-Plasma Instabilities
Tokluoglu, Erinc K.
Non-linear mechanisms arise frequently in plasmas and beam-plasma systems resulting in dynamics not predicted by linear theory. The non-linear mechanisms can influence the time evolution of plasma instabilities and can be used to describe their saturation. Furthermore time and space averaged non-linear fields generated by instabilities can lead to collisionless transport and plasma heating. In the case of beam-plasma systems counter-intuitive beam defocusing and scaling behavior which are interesting areas of study for both Low-Temperature and High Energy Density physics. The non-linear mode interactions in form of phase coupling can describe energy transfer to other modes and can be used to describe the saturation of plasma instabilities. In the first part of this thesis, a theoretical model was formulated to explain the saturation mechanism of Slab Electron Temperature Gradient (ETG) mode observed in the Columbia Linear Machine (CLM), based on experimental time-series data collected through probe diagnostics [1]. ETG modes are considered to be a major player in the unexplained high levels of electron transport observed in tokamak fusion experiments and the saturation mechanism of these modes is still an active area of investigation. The data in the frequency space indicated phase coupling between 3 modes, through a higher order spectral correlation coefficient known as bicoherence. The resulting model is similar to [2], which was a treatment for ITG modes observed in the CLM and correctly predicts the observed saturation level of the ETG turbulence. The scenario is further supported by the fact that the observed mode frequencies are in close alignment with those predicted theoretical dispersion relations. Non-linear effects arise frequently in beam-plasma systems and can be important for both low temperature plasma devices commonly used for material processing as well as High Energy Density applications relevant to inertial fusion. The non-linear time averaged
Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems.
Trillo, S; Gongora, J S Totero; Fratalocchi, A
2014-12-03
We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems
Trillo, S.
2014-12-03
We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
Stability properties of a general class of nonlinear dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br
2001-05-04
We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)
Stability and instability of a hot and dilute nuclear droplet
Nörenberg, W; Rozmej, P
2000-01-01
The diabatic approach to collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with the same growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and ...
QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Hui-ping; XUE Yu-sheng; CHEN Yu-shu
2005-01-01
Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quanttative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point (DCP) of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP's kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal beatings with nonlinear suspensionare are determined.
Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability
Energy Technology Data Exchange (ETDEWEB)
Saito, Shinji, E-mail: saito@stelab.nagoya-u.ac.jp [Graduate School of Science, Nagoya University, Nagoya (Japan); Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan); Nariyuki, Yasuhiro, E-mail: nariyuki@edu.u-toyama.ac.jp [Faculty of Human Development, University of Toyama, Toyama (Japan); Umeda, Takayuki, E-mail: umeda@stelab.nagoya-u.ac.jp [Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya (Japan)
2015-07-15
A two-dimensional, fully kinetic, particle-in-cell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates short-scale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified two-stream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSI-driven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.
Yang, Yunqing; Malomed, Boris A
2015-01-01
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and Lakshmanan-Porsezian-Daniel (LPD) equations. We present continuous-wave (CW) solutions and conditions for their modulation instability in the framework of this model. Applying the Darboux transformation to the CW input, novel first- and second-order RW solutions of the FONLS equation are analytically found. In particular, trajectories of motion of peaks and depressions of profiles of the first- and second-order RWs are produced by means of analytical and numerical methods. The solutions also include newly found rational and W-shaped one- and two-soliton modes. The results predict the corresponding dynamical phenomena in extended models of nonlinear fiber optics and other physically relevant integrable systems.
Strong quantum squeezing near the pull-in instability of a nonlinear beam
Passian, Ali; Siopsis, George
2016-08-01
Microscopic silicon-based suspended mechanical oscillators, constituting an extremely sensitive force probe, transducer, and actuator, are being increasingly employed in many developing microscopies, spectroscopies, and emerging optomechanical and chem-bio sensors. We predict a significant squeezing in the quantum state of motion of an oscillator constrained as a beam and subject to an electrically induced nonlinearity. By taking into account the quantum noise, the underlying nonlinear dynamics is investigated in both the transient and stationary regimes of the driving force leading to the finding that strongly squeezed states are accessible in the vicinity of the pull-in instability of the oscillator. We discuss a possible application of this strong quantum squeezing as an optomechanical method for detecting broad-spectrum single or low-count photons, and further suggest other novel sensing actions.
Philip, Jimmy; Karp, Michael; Cohen, Jacob
2016-01-01
Streaks and hairpin-vortices are experimentally generated in a laminar plane Poiseuille crossflow by injecting a continuous jet through a streamwise slot normal to the crossflow, with air as the working media. Small disturbances form stable streaks, however, higher disturbances cause the formation of streaks which undergo instability leading to the generation of hairpin vortices. Particular emphasis is placed on the flow conditions close to the generation of hairpin-vortices. Measurements are carried out in the cases of natural and phase-locked disturbance employing smoke visualisation, particle image velocimetry, and hot-wire anemometry, which include, the dominant frequency, wavelength, and the disturbance shape (or eigenfunctions) associated with the coherent part of the velocity field. A linear stability analysis for both one- and two-dimensional base-flows is carried out to understand the mechanism of instability and good agreement of wavelength and eigenfunctions are obtained when compared to the experimental data, and a slight under-prediction of the growth-rates by the linear stability analysis consistent with the final nonlinear stages in transitional flows. Furthermore, an energy analysis for both the temporal and spatial stability analysis revels the dominance of the symmetric varicose mode, again, in agreement with the experiments, which is found to be governed by the balance of the wallnormal shear and dissipative effects rather than the spanwise shear. In all cases the anti-symmetric sinuous modes governed by the spanwise shear are found to be damped both in analysis and in our experiments.
Institute of Scientific and Technical Information of China (English)
Zhong Xian-Qiong; Cheng Ke; Xiang An-Ping
2013-01-01
On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability (MI) have been analyzed and calculated for negative-refractive metamaterials (MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.
Stability Analysis of Fixed points in a Parity-time symmetric coupler with Kerr nonlinearity
Deka, Jyoti Prasad
2016-01-01
We report our study on nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. In the linear regime, the differential equations governing the dynamics of the coupler, under some parametric changes, can be solved exactly. But with the inclusion of nonlinearity, analytical solution of the system is a rather complicated job. And the sensitiveness of the system on the initial conditions is yet another critical issue. To circumvent the situation, we have employed the mathematical framework of nonlinear dynamics. Considering the parity-time threshold of the linear PT-coupler as the reference point, we find that in nonlinear coupler the parity-time symmetric threshold governs the existence of fixed points. We have found that the stability of the ground state undergoes a phase transition when the gain/loss coefficient is increased from zero to beyond the PT threshold. In the unbroken PT regime, we find that the instabilities in the initial launch conditions can trigger an exponential growth and dec...
Energy Technology Data Exchange (ETDEWEB)
Adams, Colin Stuart [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States)
2015-01-15
The Rayleigh-Taylor instability causes mixing in plasmas throughout the universe, from micron-scale plasmas in inertial confinement fusion implosions to parsec-scale supernova remnants. The evolution of this interchange instability in a plasma is influenced by the presence of viscosity and magnetic fields, both of which have the potential to stabilize short-wavelength modes. Very few experimental observations of Rayleigh-Taylor growth in plasmas with stabilizing mechanisms are reported in the literature, and those that are reported are in sub-millimeter scale plasmas that are difficult to diagnose. Experimental observations in well-characterized plasmas are important for validation of computational models used to make design predictions for inertial confinement fusion efforts. This dissertation presents observations of instability growth during the interaction between a high Mach-number, initially un-magnetized plasma jet and a stagnated, magnetized plasma. A multi-frame fast camera captures Rayleigh-Taylor-instability growth while interferometry, spectroscopy, photodiode, and magnetic probe diagnostics are employed to estimate plasma parameters in the vicinity of the collision. As the instability grows, an evolution to longer mode wavelength is observed. Comparisons of experimental data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization. These data provide the opportunity to benchmark computational models used in astrophysics and fusion research.
Energy Technology Data Exchange (ETDEWEB)
Adams, Colin Stuart [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of New Mexico, Albuquerque, NM (United States); Univ. of Washington, Seattle, WA (United States)
2015-01-15
The Rayleigh-Taylor instability causes mixing in plasmas throughout the universe, from micron-scale plasmas in inertial confinement fusion implosions to parsec-scale supernova remnants. The evolution of this interchange instability in a plasma is influenced by the presence of viscosity and magnetic fields, both of which have the potential to stabilize short-wavelength modes. Very few experimental observations of Rayleigh-Taylor growth in plasmas with stabilizing mechanisms are reported in the literature, and those that are reported are in sub-millimeter scale plasmas that are difficult to diagnose. Experimental observations in well-characterized plasmas are important for validation of computational models used to make design predictions for inertial confinement fusion efforts. This dissertation presents observations of instability growth during the interaction between a high Mach-number, initially un-magnetized plasma jet and a stagnated, magnetized plasma. A multi-frame fast camera captures Rayleigh-Taylor-instability growth while interferometry, spectroscopy, photodiode, and magnetic probe diagnostics are employed to estimate plasma parameters in the vicinity of the collision. As the instability grows, an evolution to longer mode wavelength is observed. Comparisons of experimental data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization. These data provide the opportunity to benchmark computational models used in astrophysics and fusion research.
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.
Stability Analysis of Some Nonlinear Anaerobic Digestion Models
Directory of Open Access Journals (Sweden)
Ivan Simeonov
2010-04-01
Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.
Robust stabilization of uncertain nonholonomic systems with strong nonlinear drifts
Institute of Scientific and Technical Information of China (English)
Yuqiang WU; Xiuyun ZHENG
2008-01-01
This paper investigates the robust stabilization of the nonholonomic control systems with strongly nonlinear uncertainties.In order to make the state scaling effective and to prevent the fiflite time escape phenomenon from happening.the switching control strategy based on the state measurement of the first subsystem is employed to achieve the asymptotic stabilization.The recurslve integrator backstepping technique is applied to the design of the robust controller.The simulation example demonstrates the efficiency and robust features of the proposed method.
The numerical stability of nonlinear floating body calculations
Park, Jong-Hwan
1992-01-01
The numerical stability of nonlinear body-wave interaction problems is investigated by applying potential flow assumptions to oscillating, non-wallsided two-dimensional and three-dimensional axisymmetric bodies. This body-wave interaction problem is solved using a mixed two-step Eulerian-Lagrangian method. In the first step, Laplace's equation is solved to determine the unknown potential values on the body and the unknown derivatives of the potentials on the free surface. In the second step, free surface boundary conditions are applied using the results of the first step to find the evolved free surface location and new potential values on the new location. Each step has particular mathematical characteristics (elliptic or parabolic-like), so that each step requires different numerical schemes. Consequently, the numerical stability of this body-wave interaction problem contains the characteristics of both of these two steps. The major contributions made to this body-wave interaction problem are the effects of the various parameters (i.e. time increments, panel length, etc.) and the different forms of the Boundary Integral Method (BIM) on numerical stability and accuracy. The far-field truncation requirement is met by matching the linear outer solution to the nonlinear inner solution at the truncation boundary. The intersection point is traced by the extrapolation method with a special boundary condition at the intersection point. To determine the evolution of the free surface according to a Lagrangian model, a regridding scheme is utilized to prevent the concentration of the Lagrangian markers in the vicinity of high gradients. A parameter for the numerical stability of free surface waves, the Free Surface Stability (FSS) number, is defined as a function of the time step size and the discretized panel length. The various stability regions are investigated by changing the FSS number, Green's function constant c, and numerical schemes. A nonlinear stability analysis
Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method
Ma, Jun; Qin, Hong; Yu, Zhi; Li, Dehui
2016-07-01
A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and this trend continues through all scale-lengths. The physics of this interesting nonlinear dynamics is numerically analyzed. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB111002, 2013GB105003, 2013GB111000, 2014GB124005, 2015GB111003), National Natural Science Foundation of China (Nos. 11305171, 11405208), JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC-11261140328), the Science Foundation of the Institute of Plasma Physics, Chinese Academy of Sciences (DSJJ-15-JC02) and the CAS Program for the Interdisciplinary Collaboration Team
Ryu, D; Frank, A I; Ryu, Dongsu; Frank, Adam
2000-01-01
We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memo...
Paradoxical stabilization of forced oscillations by strong nonlinear friction
Esirkepov, Timur Zh.; Bulanov, Sergei V.
2017-08-01
In a dissipative dynamic system driven by an oscillating force, a strong nonlinear highly oscillatory friction force can create a quasi-steady tug, which is always directed opposite to the ponderomotive force induced due to a spatial inhomogeneity of oscillations. When the friction-induced tug exceeds the ponderomotive force, the friction stabilizes the system oscillations near the maxima of the oscillation spatial amplitude of the driving force.
Nonlinear Evolution of the Radiation-Driven Magneto-Acoustic Instability (RMI)
Fernández, Rodrigo
2012-01-01
We examine the nonlinear development of unstable magnetosonic waves driven by a background radiative flux -- the Radiation-Driven Magneto-Acoustic Instability (RMI, a.k.a. the "photon bubble" instability). The RMI may serve as a persistent source of density, radiative flux, and magnetic field fluctuations in stably-stratified, optically-thick media. The conditions for instability are present in a variety of astrophysical environments, and do not require the radiation pressure to dominate or the magnetic field to be strong. Here we numerically study the saturation properties of the RMI, covering three orders of magnitude in the relative strength of radiation, magnetic field, and gas energies. Two-dimensional, time-dependent radiation-MHD simulations of local, stably-stratified domains are conducted with Zeus-MP in the optically-thick, highly-conducting limit. Our results confirm the theoretical expectations of Blaes and Socrates (2003) in that the RMI operates even in gas pressure-dominated environments that a...
NONLINEAR EVOLUTION OF THE RADIATION-DRIVEN MAGNETO-ACOUSTIC INSTABILITY
Energy Technology Data Exchange (ETDEWEB)
Fernandez, Rodrigo; Socrates, Aristotle [Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 (United States)
2013-04-20
We examine the nonlinear development of unstable magnetosonic waves driven by a background radiative flux-the radiation-driven magneto-acoustic instability (RMI, a.k.a. the ''photon bubble'' instability). The RMI may serve as a persistent source of density, radiative flux, and magnetic field fluctuations in stably stratified, optically thick media. The conditions for instability are present in a variety of astrophysical environments and do not require the radiation pressure to dominate or the magnetic field to be strong. Here, we numerically study the saturation properties of the RMI, covering three orders of magnitude in the relative strength of radiation, magnetic field, and gas energies. Two-dimensional, time-dependent radiation-magnetohydrodynamic simulations of local, stably stratified domains are conducted with Zeus-MP in the optically thick, highly conducting limit. Our results confirm the theoretical expectations of Blaes and Socrates in that the RMI operates even in gas-pressure-dominated environments that are weakly magnetized. The saturation amplitude is a monotonically increasing function of the ratio of radiation to gas pressure. Keeping this ratio constant, we find that the saturation amplitude peaks when the magnetic pressure is comparable to the radiation pressure. We discuss the implications of our results for the dynamics of magnetized stellar envelopes, where the RMI should act as a source of sub-photospheric perturbations.
Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results
Energy Technology Data Exchange (ETDEWEB)
Kueny, C.S.; Morrison, P.J.
1995-05-01
In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.
Dissipative parametric modulation instability and pattern formation in nonlinear optical systems
Perego, A. M.; Tarasov, N.; Churkin, D. V.; Turitsyn, S. K.; Staliunas, K.
2016-04-01
We present the essential features of the dissipative parametric instability, in the universal complex Ginzburg- Landau equation. Dissipative parametric instability is excited through a parametric modulation of frequency dependent losses in a zig-zag fashion in the spectral domain. Such damping is introduced respectively for spectral components in the +ΔF and in the -ΔF region in alternating fashion, where F can represent wavenumber or temporal frequency depending on the applications. Such a spectral modulation can destabilize the homogeneous stationary solution of the system leading to growth of spectral sidebands and to the consequent pattern formation: both stable and unstable patterns in one- and in two-dimensional systems can be excited. The dissipative parametric instability provides an useful and interesting tool for the control of pattern formation in nonlinear optical systems with potentially interesting applications in technological applications, like the design of mode- locked lasers emitting pulse trains with tunable repetition rate; but it could also find realizations in nanophotonics circuits or in dissipative polaritonic Bose-Einstein condensates.
STUDIES ON NONLINEAR STABILITY OF THREE-DIMENSIONAL H-TYPE DISTURBANCE
Institute of Scientific and Technical Information of China (English)
王伟志; 唐登斌
2003-01-01
The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE).The key initial conditions for sub-harmonic disturbances are obtained by means of the secondary instability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region,increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the "H-type"evolution are studied in detail. The results of the three-dimensional nonlinear "H-type" evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.
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.
Active feedback stabilization of multimode flute instability in a mirror trap
Be'ery, I.; Seemann, O.; Fisher, A.
2014-07-01
The flute instability in a table-top mirror machine has been stabilized by a feedback system consisting of optical sensors, a digital signal processor and charge-injecting electrodes. The use of multiple sensors and actuators enable the feedback to simultaneously stabilize two modes of the fast-growing, slowly rotating flute instability. Step function response and magnetohydrodynamic spectroscopy indicate a smooth frequency response and an inherent delayed response of the plasma drift due to the sheath resistivity. The measured feedback power is very small relative to the heating power of the plasma.
Local Stability and Global Instability in Iron-opaque Disks
Grzȩdzielski, Mikołaj; Janiuk, Agnieszka; Czerny, Bożena
2017-08-01
The thermal stability of accretion disks and the possibility of seeing a limit-cycle behavior strongly depends on the ability of the disk plasma to cool down. Various processes connected with radiation-matter interaction appearing in hot accretion disk plasma contribute to opacity. For the case of geometrically thin and optically thick accretion disks, we can estimate the influence of several different components of function κ, given by the Roseland mean. In the case of high temperatures of ˜107 K, the electron Thomson scattering is dominant. At lower temperatures, atomic processes become important. The slope d{log}κ /d{log}T can have a locally stabilizing or destabilizing effect on the disk. Although the local MHD simulation postulates the stabilizing influence of the atomic processes, only the global time-dependent model can reveal the global disk stability range estimation. This is due to the global diffusive nature of those processes. In this paper, using the previously tested GLADIS code with a modified prescription of the viscous dissipation, we examine the stabilizing effect of the iron opacity bump.
Three-Dimensional Single-Mode Nonlinear Ablative Rayleigh-Taylor Instability
Yan, R.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.
2015-11-01
The nonlinear evolution of the ablative Rayleigh-Taylor (ART) instability is studied in three dimensions for conditions relevant to inertial confinement fusion targets. The simulations are performed using our newly developed code ART3D and an astrophysical code AstroBEAR. The laser ablation can suppress the growth of the short-wavelength modes in the linear phase but may enhance their growth in the nonlinear phase because of the vortex-acceleration mechanism. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the bubble velocity grows faster than predicted in the classical 3-D theory. When compared to 2-D results, 3-D short-wavelength bubbles grow faster and do not reach saturation. The unbounded 3-D 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 into the ablated plasma filling the bubble volume. A density plateau is observed inside a nonlinear ART bubble and the plateau density is higher for shorter-wavelength modes. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
Design for robust stabilization of nonlinear systems with uncertain parameters
Institute of Scientific and Technical Information of China (English)
赖旭芝; 文静; 吴敏
2004-01-01
Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabilize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the original system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.
Renormalization, averaging, conservation laws and AdS (in)stability
Energy Technology Data Exchange (ETDEWEB)
Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University,Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Vanhoof, Joris [Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-01-21
We continue our analytic investigations of non-linear spherically symmetric perturbations around the anti-de Sitter background in gravity-scalar field systems, and focus on conservation laws restricting the (perturbatively) slow drift of energy between the different normal modes due to non-linearities. We discover two conservation laws in addition to the energy conservation previously discussed in relation to AdS instability. A similar set of three conservation laws was previously noted for a self-interacting scalar field in a non-dynamical AdS background, and we highlight the similarities of this system to the fully dynamical case of gravitational instability. The nature of these conservation laws is best understood through an appeal to averaging methods which allow one to derive an effective Lagrangian or Hamiltonian description of the slow energy transfer between the normal modes. The conservation laws in question then follow from explicit symmetries of this averaged effective theory.
Temporal (In)Stability of Employee Preferences for Rewards
Wine, Byron; Gilroy, Shawn; Hantula, Donald A.
2012-01-01
This study examined the temporal stability of employee preferences for rewards over seven monthly evaluations. Participants completed a ranking stimulus preference assessment monthly, and the latter six monthly assessments were compared to the initial assessment. Correlations of preferences from month to month ranged from r = -0.89 to 0.99.…
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Crosta, M.
2011-12-05
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Geometrical nonlinear stability analyses of cable-truss domes
Institute of Scientific and Technical Information of China (English)
高博青; 卢群鑫; 董石麟
2003-01-01
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cable-truss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rise-span ratio; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.
Geometrical nonlinear stability analyses of cable-truss domes
Institute of Scientific and Technical Information of China (English)
高博青; 卢群鑫; 董石麟
2003-01-01
The nonlinear finite element method is used to analyze the geometrical nonlinear stability of cabletruss domes with different cable distributions. The results indicate that the critical load increases evidently when cables, especially diagonal cables, are distributed in the structure. The critical loads of the structure at different rise-span ratios are also discussed in this paper. It was shown that the effect of the tensional cable is more evident at small rise-span ratio. The buckling of the structure is characterized by a global collapse at small rlse-span ratio ; that the torsional buckling of the radial truss occurs at big rise-span ratio; and that at proper rise-span ratio, the global collapse and the lateral buckling of the truss occur nearly simultaneously.
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 Feedback Stabilization of Nonlinear Systems with an Uncontrollable Critical Mode
1992-11-17
mode that is uncontrollable. The results complement previous work on the synthesis of nonlinear stabilizing control laws. The present work addresses...analysis and stabilizing control design employ results on stability of bifurcations of parametrized systems.
Quadrupole stabilization of the n = 2 rotational instability of a field-reversed theta-pinch plasma
Energy Technology Data Exchange (ETDEWEB)
Ohi, S.; Minato, T.; Kawakami, Y.; Tanjyo, M.; Okada, S.; Ito, Y.; Kako, M.; Got, S.; Ishimura, T.; It, H.
1983-09-19
The n = 2 rotational instability is the most dangerous gross instability in a field-reversed theta pinch. It is demonstrated for the first time that the instability is completely suppressed by superposing a quadrupole field which is much smaller than the axial confinement field at the separatrix. The experimental threshold intensity of the field for stabilization is about 2.5 times less than that predicted by theoretical stability analysis.
Johansen, A; Johansen, Anders; Youdin, Andrew
2007-01-01
We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag forces. We find that the initially laminar equilibrium flow spontaneously develops into turbulence in our unstratified local model. Marginally coupled solids (that couple to the gas on a Keplerian time-scale) trigger an upward cascade to large particle clumps with peak overdensities above 100. The clumps evolve dynamically by losing material downstream to the radial drift flow while receiving recycled material from upstream. Smaller, more tightly coupled solids produce weaker turbulence with more transient overdensities on smaller length scales. The net inward radial drift is decreased for marginally coupled particles, whereas the tightly coupled particles migrate faster in the saturated turbulent state. The turbulent diffusion of solid particles, measured by their random wal...
The weakly nonlinear magnetorotational instability in a thin-gap Taylor-Couette flow
Clark, S E
2016-01-01
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales analysis of the non-ideal MRI in the weakly nonlinear regime -- that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a thin-gap, Cartesian channel. Our results confirm the finding by Umurhan et al. (2007) that the perturbation amplitude follows a Ginzburg-Landau equation. We extend these results by performing a detailed force balance for the saturated azimuthal velocity and vertical magnetic field, demonstrating that even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system and demons...
Prediction of Algebraic Instabilities
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
Stabilization of the vertical instability by non-axisymmetric coils
Turnbull, A. D.; Reiman, A. H.; Lao, L. L.; Cooper, W. A.; Ferraro, N. M.; Buttery, R. J.
2016-08-01
In a published Physical Review Letter (Reiman 2007 Phys. Rev. Lett. 99 135007), it was shown that axisymmetric (or vertical) stability can be improved by placing a set of parallelogram coils above and below the plasma oriented at an angle to the constant toroidal planes. The physics of this stabilization can be understood as providing an effective additional positive stability index. The original work was based on a simplified model of a straight tokamak and is not straightforwardly applicable to a finite aspect ratio, strongly shaped plasma such as in DIII-D. Numerical calculations were performed in a real DIII-D -like configuration to provide a proof of principal that 3-D fields can, in fact raise the elongation limits as predicted. A four field period trapezioid-shaped coil set was developed in toroidal geometry and 3D equilibria were computed using trapezium coil currents of 10 kA , 100 kA , and 500 kA . The ideal magnetohydrodynamics growth rates were computed as a function of the conformal wall position for the n = 0 symmetry-preserving family. The results show an insignificant relative improvement in the stabilizing wall location for the two lower coil current cases, of the order of 10-3 and less. In contrast, the marginal wall position is increased by 7% as the coil current is increased to 500 kA , confirming the main prediction from the original study in a real geometry case. In DIII-D the shift in marginal wall position of 7% would correspond to being able to move the existing wall outward by 5 to 10 cm. While the predicted effect on the axisymmetric stability is real, it appears to require higher coil currents than could be provided in an upgrade to existing facilities. Additional optimization over the pitch of the coils, the number of field periods and the coil positions, as well as plasma parameters, such as the internal inductivity {{\\ell}\\text{i}} , β , and {{q}95} would mitigate this but seem unlikely to change the conclusion.
Nguyen, Quan M.; Peleg, Avner; Tran, Thinh P.
2015-01-01
We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that the amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability and pulse distortion. This enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides.
Spin Evolution of Accreting Neutron Stars: Nonlinear Development of the R-mode Instability
Bondarescu, Ruxandra; Wasserman, Ira
2007-01-01
The nonlinear saturation of the r-mode instability and its effects on the spin evolution of Low Mass X-ray Binaries (LMXBs) are modeled using the triplet of modes at the lowest parametric instability threshold. We solve numerically the coupled equations for the three mode amplitudes in conjunction with the spin and temperature evolution equations. We observe that very quickly the mode amplitudes settle into quasi-stationary states. Once these states are reached, the mode amplitudes can be found algebraically and the system of equations is reduced from eight to two equations: spin and temperature evolution. Eventually, the system may reach thermal equilibrium and either (1) undergo a cyclic evolution with a frequency change of at most 10%, (2) evolve toward a full equilibrium state in which the accretion torque balances the gravitational radiation emission, or (3) enter a thermogravitational runaway on a very long timescale of about $10^6$ years. Alternatively, a faster thermal runaway (timescale of about 100 ...
Delzanno, G. L.; Finn, J. M.; Lapenta, G.
2002-12-01
The nonlinear dynamics of a Penning trap plasma, including the effect of the finite length and end curvature of the plasma column, is studied. A new cylindrical particle-in-cell code, called KANDINSKY, has been implemented by using a new interpolation scheme. The principal idea is to calculate the volume of each cell from a particle volume, in the same manner as is done for the cell charge. With this new method, the density is conserved along streamlines and artificial sources of compressibility are avoided. The code has been validated with a number of tests. The code is then used to compare the dynamics of three different models: the standard Euler or drift-Poisson model, the modified drift-Poisson model [J. Finn et al. Phys. Plasmas 6, 3744 (1999); Phys. Rev. Lett. 84, 2401 (2000)] with compressional effects, and the quasigeostrophic model of geophysical fluid dynamics in the limit of the γ-plane approximation. The results of this investigation show that Penning traps can be used to simulate geophysical fluids. Moreover, the results for the m=1 diocotron instability reproduce qualitatively the experiments [C. F. Driscoll, Phy. Rev. Lett. 64, 645 (1990); C. F. Driscoll et al. Phys. Fluids B 2, 1359 (1990)]: The instability turns the plasma "inside-out" resulting at the end in a stable, monotonic profile.
Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs
Shtemler, Yuri M; Liverts, Edward
2014-01-01
The magneto-rotational decay instability (MRDI) of thin Keplerian discs threaded by poloidal magnetic fields is introduced and studied. The linear magnetohydrodynamic problem decouples into eigenvalue problems for in-plane slow- and fast- Alfv'een-Coriolis (AC), and vertical magnetosonic (MS) eigenmodes. The magnetorotational instability (MRI) is composed of a discrete number of unstable slow AC eigenmodes that is determined for each radius by the local beta. In the vicinity of the first beta threshold a parent MRI eigenmode together with a stable AC eigenmode (either slow or fast) and a stable MS eigenmode form a resonant triad. The three-wave MRDI relies on the nonlinear saturation of the parent MRI mode and the exponential growth of two daughter linearly stable waves, slow-AC and MS modes with an effective growth rate that is comparable to that of the parent MRI. If, however, the role of the AC daughter wave is played by a stable fast mode, all three modes remain bounded.
Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2).
Zhang, Ruoxun; Tian, Gang; Yang, Shiping; Cao, Hefei
2015-05-01
This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.
Schamel, Hans; Mandal, Debraj; Sharma, Devendra
2017-03-01
An outstanding notion for collisionless plasmas is the essential nonlinear character of their coherent structures, which in the stationary, weak amplitude limit are described by a continuum of cnoidal electron and ion hole modes governed by a multiparametric nonlinear dispersion relation. The well-known discrete structure of undamped linear plasma modes is seamlessly embedded in this nonlinear continuum as the microscopic texture of plasma begins to reveal itself in the high temperature collisionless plasma limit. This transforms the linear-threshold-based operating mechanism of plasma turbulence into a fundamental nonlinear, multifaceted one. Based on a comprehensive three-level description of increasing profundity, a proof of this novel dictum is presented, which makes use of the joint properties of such structures, their coherency and stationarity, and uses in succession a fluid, linear Vlasov and a full Vlasov description. It unifies discrete and continuum limits by resolving the inevitable resonant region and shows that coherent electrostatic equilibria are generally controlled by kinetic particle trapping and are hence fundamentally nonlinear. By forging a link between damped and growing wave solutions, these modes render plasma stability complex and difficult to evaluate due to the entangled pattern of the stability boundary in function and parameter space, respectively. A direct consequence is the existence of negative energy modes of arbitrarily small amplitudes in the subcritical region of the two-stream instability as well as the failure of linear Landau (Vlasov, van Kampen) theory, whenever resonant particles are involved, in addressing the onset of instability in a current-carrying plasma. Responsible for this subtle phase space behavior is hence the thresholdless omnipresence of the trapping nonlinearity originating from coherency. A high resolution, exact-mass-ratio, multispecies, and collisionless plasma simulation is employed to illustrate
Kerswell, R R
2015-01-01
We discuss the inviscid 2D instability recently uncovered by Ilin & Morgulis (2013) in the context of irrotational Taylor-Couette flow with a radial flow imposed. By finding a simplier rectilinear example of the instability - the sheared half plane, the minimal ingredients for the instability are identified and the destabilizing/stabilizing effect of the inflow/outflow boundaries clarified. The instability - christened `boundary inflow instability' here - is of critical layer type where this layer is either at the inflow wall and the growth rate is $O(\\eta^{1/2})$ (as found by Ilin & Morgulis 2013), or in the interior of the flow and the growth rate is $O(\\eta \\log(1/\\eta) )$ where $\\eta$ measures the (small) inflow-to-tangential-flow ratio. The instability is robust to changes in the rotation profile even to those which are very Rayleigh-stable and the addition of further physics such as viscosity, 3-dimensionality and compressibility but is sensitive to the boundary condition imposed on the tangenti...
Stability of rotating magnetized jets in the solar atmosphere. I. Kelvin-Helmholtz instability
Zaqarashvili, T V; Ofman, L
2015-01-01
Observations show various jets in the solar atmosphere with significant rotational motions, which may undergo instabilities leading to heat ambient plasma. We study the Kelvin-Helmholtz (KH) instability of twisted and rotating jets caused by the velocity jumps near the jet surface. We derive a dispersion equation with appropriate boundary condition for total pressure (including centrifugal force of tube rotation), which governs the dynamics of incompressible jets. Then, we obtain analytical instability criteria of Kelvin-Helmholtz instability in various cases, which were verified by numerical solutions to the dispersion equation. We find that twisted and rotating jets are unstable to KH instability when the kinetic energy of rotation is more than the magnetic energy of the twist. Our analysis shows that the azimuthal magnetic field of 1-5 G can stabilize observed rotations in spicule/macrospicules and X-ray/EUV jets. On the other hand, non-twisted jets are always unstable to KH instability. In this case, the ...
Stability analysis for nonlinear multi－variable delay perturbation problems
Institute of Scientific and Technical Information of China (English)
WangHongshan; ZhangChengjian
2003-01-01
This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP) of the form x′(t) = f(x(t),x(t - τ1(t)),…,x(t -τm(t)),y(t),y(t - τ1(t)),…,y(t - τm(t))), and gy′(t) = g(x(t),x(t- τ1(t)),…,x(t- τm(t)),y(t),y(t- τ1(t)),…,y(t- τm(t))), where 0 < ε <<1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.
Stability of the accelerated expansion in nonlinear electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Sharif, M.; Mumtaz, Saadia [University of the Punjab, Department of Mathematics, Lahore (Pakistan)
2017-02-15
This paper is devoted to the phase space analysis of an isotropic and homogeneous model of the universe by taking a noninteracting mixture of the electromagnetic and viscous radiating fluids whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. We establish an autonomous system of equations by introducing normalized dimensionless variables. In order to analyze the stability of the system, we find corresponding critical points for different values of the parameters. We also evaluate the power-law scale factor whose behavior indicates different phases of the universe in this model. It is concluded that the bulk viscosity as well as electromagnetic field enhances the stability of the accelerated expansion of the isotropic and homogeneous model of the universe. (orig.)
Analytical model and MD simulation of nonlinear Richtmyer-Meshkov instability
Nishihara, Katsunobu; Abe, Motomi; Fukuda, Yuko; Zhakhovskii, Vasilii; Matsuoka, Chihiro
2001-10-01
We present two topics, an analytical model and moelrcular dynamic (MD) simulations of the Richtmyer-Meshokov instability (RMI). We have developled a selfconsistent analytical model that describes a nonlinear evolution of a vortex sheet in the two-dimensional RMI. The model consists of two kinematic boundary conditions, a modified Birkhoff-Rott equation and an equation for time evolution of circulation at the interface with a finite Atwood number. It is shown that the created vortcity on the interface has strong inhomogeneity, that causes locally streching and compression of the sheet. We discuss the dependence of the Atwood number on the nonlinear dynamics of the sheet. MD approache has been applied for converging shocks and RMI in a dense Lennard-Jones fluid in cylindrical geometry. MD method has fundamental advantages over hydrodymanic simulations such as no limitation of resolution in turbulent state. The appearance of Mach stems in the rippled shocks and turbulent mixing in RMI have been observed when the reflected shock passes through the unstable surface again. We discuss the mode number and Mach number dependence on the mixing.
Landscape stability and instability in an experimental mountain
Reinhardt, L.; Ellis, M.
2008-12-01
We have designed a series of physical experiments to explore the interrelationships between drainage network organization and topographic development in high-relief landscapes. Our experiments reveal striking internal variability in catchment-scale sediment efflux and drainage network evolution under constant rainfall and rates of base-level fall. We capture this internal dynamic using a unique set of measurement systems that allow us to relate the 3D evolution of topography to sediment flux from the model-orogen. We also observed remarkable stability off the main catchment drainage divides, suggesting that catchment structure is more robust than recent studies propose. We infer that a transition in the mix of dominant processes at the scale of a catchment generates the observed scale dependant autogenic dynamics. Our experimental apparatus is an erosion box in which two opposing panels slide downwards, so simulating base-level fall across emerging topography. Rainfall is generated by an ultra-fine misting apparatus.
Strong stabilization of the Rayleigh-Taylor instability by material strength at Mbar pressures
Energy Technology Data Exchange (ETDEWEB)
Park, H S; Lorenz, K T; Cavallo, R M; Pollaine, S M; Prisbrey, S T; Rudd, R E; Becker, R C; Bernier, J V; Remington, B A
2009-11-19
Experimental results showing significant reductions from classical in the Rayleigh-Taylor (RT) instability growth rate due to high pressure effective lattice viscosity are presented. Using a laser created ramped drive, vanadium samples are compressed and accelerated quasi-isentropically at {approx}1 Mbar pressures, while maintaining the sample in the solid-state. Comparisons with simulations and theory indicate that the high pressure, high strain rate conditions trigger a phonon drag mechanism, resulting in the observed high effective lattice viscosity and strong stabilization of the RT instability.
Tian, Qing; Wu, Lei; Zhang, Jie-Fang; Malomed, Boris A; Mihalache, D; Liu, W M
2011-01-01
We put forward a generic transformation which helps to find exact soliton solutions of the nonlinear Schrödinger equation with a spatiotemporal modulation of the nonlinearity and external potentials. As an example, we construct exact solitons for the defocusing nonlinearity and harmonic potential. When the soliton's eigenvalue is fixed, the number of exact solutions is determined by energy levels of the linear harmonic oscillator. In addition to the stable fundamental solitons, stable higher-order modes, describing array of dark solitons nested in a finite-width background, are constructed too. We also show how to control the instability domain of the nonstationary solitons.
MD1831: Single Bunch Instabilities with Q" and Non-Linear Corrections
Carver, Lee Robert; De Maria, Riccardo; Li, Kevin Shing Bruce; Amorim, David; Biancacci, Nicolo; Buffat, Xavier; Maclean, Ewen Hamish; Metral, Elias; Lasocha, Kacper; Lefevre, Thibaut; Levens, Tom; Salvant, Benoit; CERN. Geneva. ATS Department
2017-01-01
During MD1751, it was observed that both a full single beam and 964 non-colliding bunches in Beam 1 (B1) and Beam 2 (B2) were both stable at the End of Squeeze (EOS) for 0A in the Landau Octupoles. At ß* = 40cm there is also a significant Q" arising from the lattice, as well as uncorrected non-linearities in the Insertion Regions (IRs). Each of these effects could be capable of fully stabilising the beam. This MD made first use of a Q" knob through variation of the Main Sextupoles (MS) by stabilising a single bunch at Flat Top, before showing at EOS that the non-linearities were the main contributors to the beam stability.
Thermodynamic instability of nonlinearly charged black holes in gravity's rainbow
Energy Technology Data Exchange (ETDEWEB)
Hendi, S.H. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Panahiyan, S. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Shahid Beheshti University, Physics Department, Tehran (Iran, Islamic Republic of); Panah, B.E.; Momennia, M. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)
2016-03-15
Motivated by the violation of Lorentz invariance in quantum gravity, we study black hole solutions in gravity's rainbow in the context of Einstein gravity coupled with various models of nonlinear electrodynamics. We regard an energy dependent spacetime and obtain the related metric functions and electric fields. We show that there is an essential singularity at the origin which is covered by an event horizon. We also compute the conserved and thermodynamical quantities and examine the validity of the first law of thermodynamics in the presence of rainbow functions. Finally, we investigate the thermal stability conditions for these black hole solutions in the context of canonical ensemble. We show that the thermodynamical structure of the solutions depends on the choices of nonlinearity parameters, charge, and energy functions. (orig.)
Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes
Hendi, Seyed Hossein; Panah, Behzad Eslam
2015-01-01
In this paper we consider three dimensional BTZ black holes with three models of nonlinear electrodynamics as source. Calculating heat capacity, we study the stability and phase transitions of these black holes. We show that Maxwell, logarithmic and exponential theories yield only type one phase transition which is related to the root(s) of heat capacity. Whereas for correction form of nonlinear electrodynamics, heat capacity contains two roots and one divergence point. Next, we use geometrical approach for studying classical thermodynamical behavior of the system. We show that Weinhold and Ruppeiner metrics fail to provide fruitful results and the consequences of the Quevedo approach are not completely matched to the heat capacity results. Then, we employ a new metric for solving this problem. We show that this approach is successful and all divergencies of its Ricci scalar and phase transition points coincide. We also show that there is no phase transition for uncharged BTZ black holes.
Anderson, Miles; Coen, Stéphane; Erkintalo, Miro; Murdoch, Stuart G
2016-01-01
Localized dissipative structures (LDS) have been predicted to display a rich array of instabilities, yet systematic experimental studies have remained scarce. We have used a synchronously-driven optical fiber ring resonator to experimentally study LDS instabilities in the strong-driving regime of the AC-driven nonlinear Schr\\"odinger equation (also known as the Lugiato-Lefever model). Through continuous variation of a single control parameter, we have observed a string of theoretically predicted instability modes, including irregular oscillations and chaotic collapses. Beyond a critical point, we observe behaviour reminiscent of a phase transition: LDSs trigger localized domains of spatiotemporal chaos that invade the surrounding homogeneous state. Our findings directly confirm a number of theoretical predictions, and they highlight that complex LDS instabilities can play a role in experimental systems.
Linear stability and instability patterns in ion-sputtered silicon
Energy Technology Data Exchange (ETDEWEB)
Madi, Charbel S; Bola George, H; Aziz, Michael J [Harvard School of Engineering and Applied Sciences, Cambridge, MA 02138 (United States)
2009-06-03
We study the patterns formed on Ar{sup +} ion-sputtered Si surfaces at room temperature as a function of the control parameters ion energy and incidence angle. We observe the sensitivity of pattern formation to artifacts such as surface contamination and report the procedures we developed to control them. We identify regions in control parameter space where holes, parallel mode ripples and perpendicular mode ripples form, and identify a region where the flat surface is stable. In the vicinity of the boundaries between the stable and pattern-forming regions, called bifurcations, we follow the time dependence from exponential amplification to saturation and examine the amplification rate and the wavelength in the exponential amplification regime. The resulting power laws are consistent with the theory of nonequilibrium pattern formation for a type I (constant wavelength) bifurcation at low angles and for a type II (diverging wavelength) bifurcation at high angles. We discuss the failure of all sputter rippling models to adequately describe these aspects of the simplest experimental system studied, consisting of an elemental, isotropic amorphous surface in the simplest evolution regime of linear stability.
Global stabilizer of a general class of feedback nonlinear systems and its exponential convergence
Institute of Scientific and Technical Information of China (English)
Runing MA; Jundi DIAN
2005-01-01
We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent. Our stabilizer consists of a nested saturation function, which is a nonlinear combination of satrration functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above.
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.
Master stability functions reveal diffusion-driven instabilities in multi-layer networks
Brechtel, Andreas; Ritterskamp, Daniel; Drossel, Barbara; Gross, Thilo
2016-01-01
Many systems in science and technology can be described as multilayer networks, which are known to exhibit phenomena such as catastrophic failure cascades and pattern-forming instabilities. A particular class of multilayer networks describes systems where different interacting copies of a local network exist in different spatial locations, including for instance regulatory and metabolic networks of identical cells and interacting habitats of ecological populations. Here, we show that such systems can be analyzed by a master stability function (MSF) approach, which reveals conditions for diffusion-driven instabilities (DDIs). We demonstrate the methodology on the example of state-of-the-art meta-foodweb models, where it reveals diffusion-driven instabilities that lead to localized dynamics and spatial patterns. This type of approach can be applied to a variety of systems from nature, science and engineering to aid the understanding and design of complex self-organizing systems.
Carver, Lee Robert; Biancacci, Nicolo; Buffat, Xavier; Iadarola, Giovanni; Lasocha, Kacper; Li, Kevin Shing Bruce; Levens, Tom; Metral, Elias; Salvant, Benoit; Tambasco, Claudia; CERN. Geneva. ATS Department
2017-01-01
Instabilities were being routinely observed in B1V during ADJUST. The timing of the instabilities has been localised to shortly after the TOTEM bump has been implemented. The result is emittance blowup which can negatively effect the luminosity output of the fill. This MD aimed to rule out possible sources of the instability (i.e. beam-beam effects or electron cloud) by only taking one single beam to 6.5TeV and going through the full machine cycle. After the implementation of the TOTEM bump, a reduction of the octupole current was performed in order to determine if there was a discrepancy in the threshold between simulations and measurement. As a precursor, the results of the End of Fill MD: Validation of Single Bunch Stability Threshold will also be described.
DEFF Research Database (Denmark)
Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus
2004-01-01
We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...
A note on nonlinear aspects of large-scale atmospheric instabilities
Energy Technology Data Exchange (ETDEWEB)
Wiin-Nielsen, A [The Royal Danish Academy of Sciences and Letters, Copenhagen (Denmark)
2001-04-01
A barotropic model with momentum transport, a simple baroclinic model with transports of heat only and a baroclinic model with both momentum and heat transports are used to illustrate the instabilities and the nonlinear longer term behavior of barotropic, baroclinic and mixed barotropic-baroclinic processes in models without forcing and frictional dissipation. While the instabilities of such models are well known thorough analytical studies of the linear perturbation equations, it is obvious that these studies give no information on the long term behavior which can be studied only by nonlinear equations. Numerical integration of low order nonlinear equations will be used to illustrate the long term behavior of the two models. The mains aspects of the observed atmospheric energy processes maybe reproduce by the most general low-order model used in this study give no information on the long term behavior, which can be studied only by nonlinear equations. Numerical integrations of low order nonlinear equations will be used to illustrate the long term behavior of the two models. The main aspects of the observed atmospheric energy processes may be reproduce by the most general low-order model used in this study. This model contains meridional transports of sensible heat and momentum by the Eddies which are included in the model. The reproduce the atmospheric energy diagram based on observational studies it is necessary to include heating and frictional dissipations. The latter two processes will be excluded in the present study in order to obtain the long term behavior is observed with rather large time scales. The most periodic variations are obtained from initial states with moderate values of the zonal parameters. [Spanish] Para ilustrar las inestabilidades y el comportamiento a largo plazo de procesos barotropicos-baroclinicos, mezclados en modelos sin disipaciones de friccion y forzamiento, se usan: un simple modelo baroclinico con transporte de momentum, un modelo
AMABILI, M.; PELLICANO, F.; PAÏDOUSSIS, M. P.
1999-08-01
The study presented is an investigation of the non-linear dynamics and stability of simply supported, circular cylindrical shells containing inviscid incompressible fluid flow. Non-linearities due to large-amplitude shell motion are considered by using the non-linear Donnell's shallow shell theory, with account taken of the effect of viscous structural damping. Linear potential flow theory is applied to describe the fluid-structure interaction. The system is discretiszd by Galerkin's method, and is investigated by using a model involving seven degrees of freedom, allowing for travelling wave response of the shell and shell axisymmetric contraction. Two different boundary conditions are applied to the fluid flow beyond the shell, corresponding to: (i) infinite baffles (rigid extensions of the shell), and (ii) connection with a flexible wall of infinite extent in the longitudinal direction, permitting solution by separation of variables; they give two different kinds of dynamical behaviour of the system, as a consequence of the fact that axisymmetric contraction, responsible for the softening non-linear dynamical behaviour of shells, is not allowed if the fluid flow beyond the shell is constrained by rigid baffles. Results show that the system loses stability by divergence.
Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, Lyapunov function method isused to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
Institute of Scientific and Technical Information of China (English)
Xianqiong Zhong; Anping Xiang
2007-01-01
@@ The synthetic effects of group-velocity mismatch and cubic-quintic nonlinearity on cross-phase modulation induced modulation instability in loss single-mode optical fibers have been numerically investigated. The results show that the quintic nonlinearity plays a role similar to the case of neglecting the group-velocity mismatch in modifying the modulation instability, namely, the positive and negative quintic nonlinearities can still enhance and weaken the modulation instability, respectively. The group-velocity mismatch can considerably change the gain spectrum of modulation instability in terms of its shape, peak value, and position. In the normal dispersion regime, with the increase of the group-velocity mismatch parameter,the gain spectrum widens and then narrows, shifts to higher frequencies, and the peak value gets higher before approaching a saturable value. In the abnormal dispersion regime, two separated spectra may occur when the group-velocity mismatch is taken into account. With the increase of the group-velocity mismatch parameter, the peak value of the gain spectrum gets higher and shorter before tending to a saturable value for the first and second spectral regimes, respectively.
Nonlinear interaction of instability waves and vortex-pairing noise in axisymmetric subsonic jets
Yang, Hai-Hua; Zhou, Lin; Zhang, Xing-Chen; Wan, Zhen-Hua; Sun, De-Jun
2016-10-01
A direct simulation with selected inflow forcing is performed for an accurate description of the jet flow field and far-field noise. The effects of the Mach number and heating on the acoustic field are studied in detail. The beam patterns and acoustic intensities are both varied as the change of the Mach number and temperature. The decomposition of the source terms of the Lilley-Goldstein (L-G) equation shows that the momentum and thermodynamic components lead to distinctly different beam patterns. Significant cancellation is found between the momentum and thermodynamic components at low polar angles for the isothermal jet and large polar angles for the hot jet. The cancellation leads to the minimum values of the far-field sound. Based on linear parabolized stability equation solutions, the nonlinear interaction model for sound prediction is built in combination with the L-G equation. The dominant beam patterns and their original locations predicted by the nonlinear model are in good agreement with the direct simulation results, and the predictions of sound pressure level (SPL) by the nonlinear model are relatively reasonable.
Mustsevaya, J. V.; Mustsevoy, V. V.
1998-01-01
Linear analysis of vortex sheet stability in the rotating gaseous disk or shallow water layer shows that presence of a central reflecting surface changes system stability significantly. An effect of absence of vortex sheet stabilization has been found as compressibility exceeds Landau criterion. The properties of multimode short-scale instability of acoustical resonance type are investigated and probability of its influence upon experiments on the rotating shallow water is discussed.
Mustsevaya, J V
1998-01-01
Linear analysis of vortex sheet stability in the rotating gaseous disk or shallow water layer shows that presence of a central reflecting surface changes system stability significantly. An effect of absence of vortex sheet stabilization has been found as compressibility exceeds Landau criterion. The properties of multimode short-scale instability of acoustical resonance type are investigated and probability of its influence upon experiments on the rotating shallow water is discussed.
Energy Technology Data Exchange (ETDEWEB)
Gerwin, R.
1976-10-01
A criterion due to N. Krall for magnetic shear stabilization of the Lower-Hybrid Drift Instability is applied to model profiles of the Reverse-Field Screw Pinch configuration. Conditions that can virtually eliminate this instability are found numerically, for gentle density profiles. However, shear-stabilization proves to be ineffective for sharper (but still reasonable-looking) profiles. If such profiles have to be lived with, it becomes necessary to rely either on finite-beta stabilization or on the fact that this instability possesses a threshold related to ion gyro-resonance.
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...
Analysis of Stability and Bifurcation in Nonlinear Mechanics with Dissipation
Directory of Open Access Journals (Sweden)
Claude Stolz
2011-01-01
Full Text Available The analysis of stability and bifurcation is studied in nonlinear mechanics with dissipative mechanisms: plasticity, damage, fracture. The description is based on introduction of a set of internal variables. This framework allows a systematic description of the material behaviour via two potentials: the free energy and the potential of dissipation. In the framework of standard generalized materials the internal state evolution is governed by a variational inequality which depends on the mechanism of dissipation. This inequality is obtained through energetic considerations in an unified description based upon energy and driving forces associated to the dissipative process. This formulation provides criterion for existence and uniqueness of the system evolution. Examples are presented for plasticity, fracture and for damaged materials.
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.
Multivariable nonlinear control of STATCOM for synchronous generator stabilization
Energy Technology Data Exchange (ETDEWEB)
Sahoo, N.C. [Multimedia Univ., Melaka (Malaysia). Faculty of Engineering and Technology; Panigrahi, B.K.; Panda, G. [Multimedia Univ., Selangor (Malaysia); Dash, P.K. [National Inst. of Technology, Rourkela (India)
2004-01-01
A static synchronous compensator (STATCOM) is a typical flexible ac transmission system device playing a vital role as a stability aid for small and large transient disturbances in an interconnected power system. This article deals with design and evaluation of a feedback linearizing nonlinear controller for STATCOM installed in a single-machine infinite-bus power system. In addition to the coordinated control of ac and dc bus voltages, the proposed controller also provides good damping to the electromechanical oscillation of the synchronous generator under transient disturbances. The efficiency of the control strategy is evaluated by computer simulation studies. The comparative study of these results with the conventional cascade control structure establishes the elegance of the proposed control scheme. (author)
STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR NONLINEAR SYSTEMS OF PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yue-xin Yu; Shou-fu Li
2005-01-01
This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k, l)-algebraically stable Runge-Kutta methods are suggested. Global and asymptotic stability conditions for the presented methods are derived.
STABILIZATION OF NONLINEAR TIME-VARYING SYSTEMS: A CONTROL LYAPUNOV FUNCTION APPROACH
Institute of Scientific and Technical Information of China (English)
Zhongping JIANG; Yuandan LIN; Yuan WANG
2009-01-01
This paper presents a control Lyapunov function approach to the global stabilization problem for general nonlinear and time-varying systems. Explicit stabilizing feedback control laws are proposed based on the method of control Lyapunov functions and Sontag's universal formula.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
Energy Technology Data Exchange (ETDEWEB)
Casner, A., E-mail: alexis.casner@cea.fr; Masse, L.; Liberatore, S.; Loiseau, P.; Masson-Laborde, P. E.; Jacquet, L. [CEA, DAM, DIF, F-91297 Arpajon (France); Martinez, D.; Moore, A. S.; Seugling, R.; Felker, S.; Haan, S. W.; Remington, B. A.; Smalyuk, V. A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Farrell, M.; Giraldez, E.; Nikroo, A. [General Atomics, San Diego, California 92121 (United States)
2015-05-15
Academic tests in physical regimes not encountered in Inertial Confinement Fusion will help to build a better understanding of hydrodynamic instabilities and constitute the scientifically grounded validation complementary to fully integrated experiments. Under the National Ignition Facility (NIF) Discovery Science program, recent indirect drive experiments have been carried out to study the ablative Rayleigh-Taylor Instability (RTI) in transition from weakly nonlinear to highly nonlinear regime [A. Casner et al., Phys. Plasmas 19, 082708 (2012)]. In these experiments, a modulated package is accelerated by a 175 eV radiative temperature plateau created by a room temperature gas-filled platform irradiated by 60 NIF laser beams. The unique capabilities of the NIF are harnessed to accelerate this planar sample over much larger distances (≃1.4 mm) and longer time periods (≃12 ns) than previously achieved. This extended acceleration could eventually allow entering into a turbulent-like regime not precluded by the theory for the RTI at the ablation front. Simultaneous measurements of the foil trajectory and the subsequent RTI growth are performed and compared with radiative hydrodynamics simulations. We present RTI growth measurements for two-dimensional single-mode and broadband multimode modulations. The dependence of RTI growth on initial conditions and ablative stabilization is emphasized, and we demonstrate for the first time in indirect-drive a bubble-competition, bubble-merger regime for the RTI at ablation front.
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
Liu, Yunqiao; Calvisi, Michael L.; Wang, Qianxi
2017-04-01
Encapsulated microbubbles (EMBs) are widely used in medical ultrasound imaging as contrast-enhanced agents. However, the potential damaging effects of violent collapsing EMBs to cells and tissues in clinical settings have remained a concern. Dual-frequency ultrasound is a promising technique for improving the efficacy and safety of sonography. The system modeled consists of the external liquid, membrane and internal gases of an EMB. The microbubble dynamics are simulated using a simple nonlinear interactive theory, considering the compressibility of the internal gas, viscosity of the liquid flow and viscoelasticity of the membrane. The radial oscillation and interfacial stability of an EMB under single- and dual-frequency excitations are compared. The simulation results show that the dual-frequency technique produces larger backscatter pressure at higher harmonics of the primary driving frequency—this enriched acoustic spectrum can enhance blood-tissue contrast and improve the quality of sonographic images. The results further show that the acoustic pressure threshold associated with the onset of shape instability is greater for dual-frequency driving. This suggests that the dual-frequency technique stabilizes the encapsulated bubble, thereby improving the efficacy and safety of contrast-enhanced agents.
An Enhanced Asymptotic Expansion for the Stability of Nonlinear Elastic Structures
DEFF Research Database (Denmark)
Christensen, Claus Dencker; Byskov, Esben
2010-01-01
A new, enhanced asymptotic expansion applicable to stability of structures made of nonlinear elastic materials is established. The method utilizes “hyperbolic” terms instead of the conventional polynomial terms, covers full kinematic nonlinearity and is applied to nonlinear elastic Euler columns ...
Stability of dithered non-linear systems with backlash or hysteresis
Desoer, C. A.; Shahruz, S. M.
1986-01-01
A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.
Energy Technology Data Exchange (ETDEWEB)
Jain, Neeraj; Büchner, Jörg [Max Planck/Princeton Center for Plasma Physics, Göttingen (Germany); Max Planck Institute for Solar System Research, Justus-Von-Liebig-Weg-3, Göttingen (Germany)
2014-07-15
Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =d{sub e}=c/ω{sub pe}), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheets (half thickness ∼5 d{sub e}), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Energy Technology Data Exchange (ETDEWEB)
Guo, Shimin, E-mail: gsm861@126.com [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands); Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn [School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049 (China); Center for Computational Geosciences, Xi’an Jiaotong University, Xi’an, 710049 (China); Sun, Anbang [Research Group MAC, Centrum Wiskunde and Informatica, Amsterdam, 1098XG (Netherlands)
2013-05-15
The nonlinear propagation of planar and nonplanar (cylindrical and spherical) ion-acoustic waves in an unmagnetized electron–positron–ion–dust plasma with two-electron temperature distributions is investigated in the context of the nonextensive statistics. Using the reductive perturbation method, a modified nonlinear Schrödinger equation is derived for the potential wave amplitude. The effects of plasma parameters on the modulational instability of ion-acoustic waves are discussed in detail for planar as well as for cylindrical and spherical geometries. In addition, for the planar case, we analyze how the plasma parameters influence the nonlinear structures of the first- and second-order ion-acoustic rogue waves within the modulational instability region. The present results may be helpful in providing a good fit between the theoretical analysis and real applications in future spatial observations and laboratory plasma experiments. -- Highlights: ► Modulational instability of ion-acoustic waves in a new plasma model is discussed. ► Tsallis’s statistics is considered in the model. ► The second-order ion-acoustic rogue wave is studied for the first time.
Combustion instability of pilot flame in a pilot bluff body stabilized combustor
Institute of Scientific and Technical Information of China (English)
Fu Xiao; Yang Fujiang; Guo Zhihui
2015-01-01
Combustion instability of pilot flame has been investigated in a model pilot bluff body stabilized combustor by running the pilot flame only. The primary objectives are to investigate the pilot flame dynamics and to provide bases for the study of the interaction mechanisms between the pilot flame and the main flame. Dynamic pressures are measured by dynamic pressure transduc-ers. A high speed camera with CH*bandpass filter is used to capture the pilot flame dynamics. The proper orthogonal decomposition (POD) is used to further analyze the high speed images. With the increase of the pilot fuel mass flow rate, the pilot flame changes from stable to unstable state grad-ually. The combustion instability frequency is 136 Hz when the pilot flame is unstable. Numerical simulation results show that the equivalence ratios in both the shear layer and the recirculation zone increase as the pilot fuel mass flow rate increases. The mechanism of the instability of the pilot flame can be attributed to the coupling between the second order acoustic mode and the unsteady heat release due to symmetric vortex shedding. These results illustrate that the pilot fuel mass flow rate has significant influences on the dynamic stability of the pilot flame.
Combustion instability of pilot flame in a pilot bluff body stabilized combustor
Directory of Open Access Journals (Sweden)
Fu Xiao
2015-12-01
Full Text Available Combustion instability of pilot flame has been investigated in a model pilot bluff body stabilized combustor by running the pilot flame only. The primary objectives are to investigate the pilot flame dynamics and to provide bases for the study of the interaction mechanisms between the pilot flame and the main flame. Dynamic pressures are measured by dynamic pressure transducers. A high speed camera with CH∗ bandpass filter is used to capture the pilot flame dynamics. The proper orthogonal decomposition (POD is used to further analyze the high speed images. With the increase of the pilot fuel mass flow rate, the pilot flame changes from stable to unstable state gradually. The combustion instability frequency is 136 Hz when the pilot flame is unstable. Numerical simulation results show that the equivalence ratios in both the shear layer and the recirculation zone increase as the pilot fuel mass flow rate increases. The mechanism of the instability of the pilot flame can be attributed to the coupling between the second order acoustic mode and the unsteady heat release due to symmetric vortex shedding. These results illustrate that the pilot fuel mass flow rate has significant influences on the dynamic stability of the pilot flame.
Lee, Nam G.; You, Joshua (Sung) H.; Kim, Tae H.; Choi, Bong S.
2015-01-01
Context: The exact neuromechanical nature and relative contribution of the abdominal drawing-in maneuver (ADIM) to postural instability warrants further investigation in uninjured and injured populations. Objective: To determine the effects of the ADIM on static core and unipedal postural stability in nonathletes with core instability. Design: Controlled laboratory study. Setting: University research laboratory. Patients or Other Participants: A total of 19 nonathletes (4 women: age = 22.3 ± 1.3 years, height = 164.0 ± 1.7 cm, mass = 56.0 ± 4.6 kg; 15 men: age = 24.6 ± 2.8 years, height = 172.6 ± 4.7 cm, mass = 66.8 ± 7.6 kg) with core instability. Intervention(s): Participants received ADIM training with visual feedback 20 minutes each day for 7 days each week over a 2-week period. Main Outcome Measures(s): Core instability was determined using a prone formal test and measured by a pressure biofeedback unit. Unipedal postural stability was determined by measuring the center-of-pressure sway and associated changes in the abdominal muscle-thickness ratios. Electromyographic activity was measured concurrently in the external oblique, erector spinae, gluteus medius, vastus medialis oblique, tibialis anterior, and medial gastrocnemius muscles. Results: All participants initially were unable to complete the formal test. However, after the 2-week ADIM training period, all participants were able to reduce the pressure biofeedback unit by a range of 4 to 10 mm Hg from an initial 70 mm Hg and maintain it at 60 to 66 mm Hg with minimal activation of the external oblique (t18 = 3.691, P = .002) and erector spinae (t18 = 2.823, P = .01) muscles. Monitoring of the pressure biofeedback unit and other muscle activations confirmed that the correct muscle contraction defining the ADIM was accomplished. This core stabilization was well maintained in the unipedal-stance position, as evidenced by a decrease in the center-of-pressure sway measures (t18 range, 3.953–5.775, P
Lee, Nam G; You, Joshua Sung H; Kim, Tae H; Choi, Bong S
2015-02-01
The exact neuromechanical nature and relative contribution of the abdominal drawing-in maneuver (ADIM) to postural instability warrants further investigation in uninjured and injured populations. To determine the effects of the ADIM on static core and unipedal postural stability in nonathletes with core instability. Controlled laboratory study. University research laboratory. A total of 19 nonathletes (4 women: age = 22.3 ± 1.3 years, height = 164.0 ± 1.7 cm, mass = 56.0 ± 4.6 kg; 15 men: age = 24.6 ± 2.8 years, height = 172.6 ± 4.7 cm, mass = 66.8 ± 7.6 kg) with core instability. Participants received ADIM training with visual feedback 20 minutes each day for 7 days each week over a 2-week period. Core instability was determined using a prone formal test and measured by a pressure biofeedback unit. Unipedal postural stability was determined by measuring the center-of-pressure sway and associated changes in the abdominal muscle-thickness ratios. Electromyographic activity was measured concurrently in the external oblique, erector spinae, gluteus medius, vastus medialis oblique, tibialis anterior, and medial gastrocnemius muscles. All participants initially were unable to complete the formal test. However, after the 2-week ADIM training period, all participants were able to reduce the pressure biofeedback unit by a range of 4 to 10 mm Hg from an initial 70 mm Hg and maintain it at 60 to 66 mm Hg with minimal activation of the external oblique (t(18) = 3.691, P = .002) and erector spinae (t(18) = 2.823, P = .01) muscles. Monitoring of the pressure biofeedback unit and other muscle activations confirmed that the correct muscle contraction defining the ADIM was accomplished. This core stabilization was well maintained in the unipedal-stance position, as evidenced by a decrease in the center-of-pressure sway measures (t(18) range, 3.953-5.775, P core and postural stability in nonathletes with core instability.
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.
Delay-dependent robust stabilization for a class of neutral systems with nonlinear perturbations
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This note deals with the problem of stabilization/stability for neutral systems with nonlinear perturbations.A new stabilization/stability scheme is presented.Using improved Lyapunov functionals.less conservative stabilization/stability conditions are derived for such systems based on linear matrix inequalities(LMI).Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature.
Stabilization of the Rayleigh-Taylor instability in quantum magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Wang, L. F.; Ye, W. H.; He, X. T. [HEDPS and CAPT, Peking University, Beijing 100871 (China); Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China); Yang, B. L. [Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China); Graduate School, China Academy of Engineering Physics, Beijing 100088 (China)
2012-07-15
In this research, stabilization of the Rayleigh-Taylor instability (RTI) due to density gradients, magnetic fields, and quantum effects, in an ideal incompressible plasma, is studied analytically and numerically. A second-order ordinary differential equation (ODE) for the RTI including quantum corrections, with a continuous density profile, in a uniform external magnetic field, is obtained. Analytic expressions of the linear growth rate of the RTI, considering modifications of density gradients, magnetic fields, and quantum effects, are presented. Numerical approaches are performed to solve the second-order ODE. The analytical model proposed here agrees with the numerical calculation. It is found that the density gradients, the magnetic fields, and the quantum effects, respectively, have a stabilizing effect on the RTI (reduce the linear growth of the RTI). The RTI can be completely quenched by the magnetic field stabilization and/or the quantum effect stabilization in proper circumstances leading to a cutoff wavelength. The quantum effect stabilization plays a central role in systems with large Atwood number and small normalized density gradient scale length. The presence of external transverse magnetic fields beside the quantum effects will bring about more stability on the RTI. The stabilization of the linear growth of the RTI, for parameters closely related to inertial confinement fusion and white dwarfs, is discussed. Results could potentially be valuable for the RTI treatment to analyze the mixing in supernovas and other RTI-driven objects.
Weakly nonlinear stability of vicsous vortices in three-dimensional boundary layers
Bassom, Andrew P.; Otto, S. R.
1993-01-01
Attention is given to the weakly nonlinear stability of essentially viscous vortices in 3D boundary layers. These modes are unstable in the absence of crossflow, but the imposition of small crossflow has a stabilizing effect. Bassom and Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wave number combinations, and the weakly nonlinear stability properties of these disturbances are described. It is shown that the effect of crossflow is to stabilize the nonlinear modes, and the present calculations allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting.
Remarkable stability of an instability-prone lentiviral vector plasmid in Escherichia coli Stbl3.
Al-Allaf, Faisal A; Tolmachov, Oleg E; Zambetti, Lia Paola; Tchetchelnitski, Viktoria; Mehmet, Huseyin
2013-02-01
Large-scale production of plasmid DNA to prepare therapeutic gene vectors or DNA-based vaccines requires a suitable bacterial host, which can stably maintain the plasmid DNA during industrial cultivation. Plasmid loss during bacterial cell divisions and structural changes in the plasmid DNA can dramatically reduce the yield of the desired recombinant plasmid DNA. While generating an HIV-based gene vector containing a bicistronic expression cassette 5'-Olig2cDNA-IRES-dsRed2-3', we encountered plasmid DNA instability, which occurred in homologous recombination deficient recA1 Escherichia coli strain Stbl2 specifically during large-scale bacterial cultivation. Unexpectedly, the new recombinant plasmid was structurally changed or completely lost in 0.5 L liquid cultures but not in the preceding 5 mL cultures. Neither the employment of an array of alternative recA1 E. coli plasmid hosts, nor the lowering of the culture incubation temperature prevented the instability. However, after the introduction of this instability-prone plasmid into the recA13E. coli strain Stbl3, the transformed bacteria grew without being overrun by plasmid-free cells, reduction in the plasmid DNA yield or structural changes in plasmid DNA. Thus, E. coli strain Stbl3 conferred structural and maintenance stability to the otherwise instability-prone lentivirus-based recombinant plasmid, suggesting that this strain can be used for the faithful maintenance of similar stability-compromised plasmids in large-scale bacterial cultivations. In contrast to Stbl2, which is derived wholly from the wild type isolate E. coli K12, E. coli Stbl3 is a hybrid strain of mixed E. coli K12 and E. coli B parentage. Therefore, we speculate that genetic determinants for the benevolent properties of E. coli Stbl3 for safe plasmid propagation originate from its E. coli B ancestor.
Nath, Sujit K
2016-01-01
We investigate the evolution of hydromagnetic perturbations in a small section of accretion disks. It is known that molecular viscosity is negligible in accretion disks. Hence, it has been argued that Magnetorotational Instability (MRI) is responsible for transporting matter in the presence of weak magnetic field. However, there are some shortcomings, which question effectiveness of MRI. Now the question arises, whether other hydromagnetic effects, e.g. transient growth (TG), can play an important role to bring nonlinearity in the system, even at weak magnetic fields. Otherwise, whether MRI or TG, which is primarily responsible to reveal nonlinearity to make the flow turbulent? Our results prove explicitly that the flows with high Reynolds number (Re), which is the case of realistic astrophysical accretion disks, exhibit nonlinearity by best TG of perturbation modes faster than that by best modes producing MRI. For a fixed wavevector, MRI dominates over transient effects, only at low Re, lower than its value ...
Institute of Scientific and Technical Information of China (English)
LI Shoufu
2005-01-01
A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.
Nonlinear Stability of a SIRS Epidemic Model with Convex Incidence Rate
Buonomo, B.; Rionero, S.
2010-09-01
We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be convex respect to the infective class. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability of the endemic equilibrium are also obtained. Our procedure allows to enlarge the class of incidence rates ensuring the Lyapunov nonlinear stability of the endemic equilibrium for SIRS models.
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.
Sakly, Anis; Kermani, Marwen
2015-07-01
This paper is concerned with the problems of stability analysis and stabilization with a state feedback controller through pole placement for a class of both continuous and discrete-time switched nonlinear systems. These systems are modeled by differential or difference equations. Then, a transformation under the arrow form is employed. Note that, the main contribution in this work is twofold: firstly, based on the construction of an appropriated common Lyapunov function, as well the use of the vector norms notion, the recourse to the Kotelyanski lemma, the M-matrix proprieties, the aggregation techniques and the application of the Borne-Gentina criterion, new sufficient stability conditions under arbitrary switching for the autonomous system are deduced. Secondly, this result is extended for designing a state feedback controller by using pole assignment control, which guarantee that the corresponding closed-loop system is globally asymptotically stable under arbitrary switching. The main novelties features of these obtained results are the explicitness and the simplicity in their application. Moreover, they allow us to avoid the search of a common Lyapunov function which is a difficult matter. Finally, as validation to stabilize a shunt DC motor under variable mechanical loads is performed to demonstrate the effectiveness of the proposed results.
Nonlinear and Variable Structure Excitation Controller for Power System Stability
Institute of Scientific and Technical Information of China (English)
Wang Ben; Ronnie Belmans
2006-01-01
A new nonlinear variable structure excitation controller is proposed. Its design combines the differential geometry theory and the variable structure controlling theory. The mathematical model in the form of "an affine nonlinear system" is set up for the control of a large-scale power system. The static and dynamic performances of the nonlinear variable structure controller are simulated. The response of system with the controller proposed is compared to that of the nonlinear optimal controller when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure excitation controller gives more satisfactorily static and dynamic performance and better robustness.
Robust stability of discrete-time nonlinear system with time-delay
Institute of Scientific and Technical Information of China (English)
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
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...
Nonlinear tides in a homogeneous rotating planet or star: global modes and elliptical instability
Barker, Adrian J; Ogilvie, Gordon I
2016-01-01
We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders $\\ell\\leq 5$, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when $\\frac{n}{\\Omega}\\lesssim -1$, where $n$ and $\\Omega$ are the orbital and spin angular freque...
ON THE PARTIAL EQUIASYMPTOTIC STABILITY OF NONLINEAR TIME-VARYING DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
JianJigui; JiangMinghui; ShenYanjun
2005-01-01
In this paper, the problem of partial equiasymptotic stability for nonlinear time-varying differential equations are analyzed. A sufficient condition of partial stability and a set of sufficient conditions of partial equiasymptotic stability are given. Some of these conditions allow the derivative of Lyapunov function to be positive. Finally, several numerical examples are also given to illustrate the main results.
Directory of Open Access Journals (Sweden)
Meng-Meng Jiang
2016-01-01
Full Text Available Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.
Remick, Kevin; Dane Quinn, D.; Michael McFarland, D.; Bergman, Lawrence; Vakakis, Alexander
2016-05-01
The authors investigate a vibration-based energy harvesting system utilizing essential (nonlinearizable) nonlinearities and electromagnetic coupling elements. The system consists of a grounded, weakly damped linear oscillator (primary system) subjected to a single impulsive load. This primary system is coupled to a lightweight, damped oscillating attachment (denoted as nonlinear energy sink, NES) via a neodymium magnet and an inductance coil, and a piano wire, which generates an essential geometric cubic stiffness nonlinearity. Under impulsive input, the transient damped dynamics of this system exhibit transient resonance captures (TRCs) causing intentional large-amplitude and high-frequency instabilities in the response of the NES. These TRCs result in strong energy transfer from the directly excited primary system to the light-weight attachment. The energy is harvested by the electromagnetic elements in the coupling and, in the present case, dissipated in a resistive element in the electrical circuit. The primary goal of this work is to numerically, analytically, and experimentally demonstrate the efficacy of employing this type of intentional high-frequency dynamic instability to achieve enhanced vibration energy harvesting under impulsive excitation.
Directory of Open Access Journals (Sweden)
B.S. Bhadauria
2014-02-01
Full Text Available The present paper deals with a weak nonlinear stability problem of magneto-convection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to an imposed time-periodic boundary temperature (ITBT along with internal heating effects. In the case of (ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent oscillatory part. The temperature of both walls is modulated in this case. The disturbance is expanded in terms of power series of amplitude of convection, which is assumed to be small. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Using Ginzburg-Landau equation, the effect of modulations on heat transport is analyzed. Effect of various parameters on the heat transport is also discussed. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.
Bykov, Andrei M; Osipov, Sergei M; Vladimirov, Andrey E
2014-01-01
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvenic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of particles, from thermal (~eV) injected at the viscous subshock, to the escape of the highest energy CRs (~PeV) from the shock precursor, are calculated consistently with the shock structure, precursor heating, magnetic field amplification (MFA), and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the d...
Adams, Colin S; Hsu, Scott C
2014-01-01
We present time-resolved observations of Rayleigh-Taylor-instability growth at the interface between an unmagnetized plasma jet colliding with a stagnated, magnetized plasma. The observed instability growth time ($\\sim 10$ $\\mu$s) is consistent with the estimated linear Rayleigh-Taylor growth rate calculated using experimentally inferred values of density ($\\sim 10^{14}$ cm$^{-3}$) and acceleration ($10^9$ m/s$^2$). The observed instability wavelengths ($\\gtrsim 1$ cm) are consistent with stabilization of short wavelengths by a magnetic field of the experimentally measured magnitude ($\\sim 15$ G) and direction. Comparisons of data with idealized magnetohydrodynamic simulations including a physical viscosity model suggest that the observed instability evolution is consistent with both magnetic and viscous stabilization.
Institute of Scientific and Technical Information of China (English)
Shu-jun Liu; Ji-feng Zhang; Zhong-ping Jiang
2008-01-01
In this paper, the property of practical input-to-state stability and its application to stability of cascaded nonlinear systems are investigated in the stochastic framework. Firstly, the notion of (practical)stochastic input-to-state stability with respect to a stochastic input is introduced, and then by the method of changing supply functions, (a) an (practical) SISS-Lyapunov function for the overall system is obtained from the corresponding Lyapunov functions for cascaded (practical) SISS subsystems.
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.
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Directory of Open Access Journals (Sweden)
Qiang Yang
2016-01-01
Full Text Available Based on adaptive nonlinear damping, a novel decentralized robust adaptive output feedback stabilization comprising a decentralized robust adaptive output feedback controller and a decentralized robust adaptive observer is proposed for a large-scale interconnected nonlinear system with general uncertainties, such as unknown nonlinear parameters, bounded disturbances, unknown nonlinearities, unmodeled dynamics, and unknown interconnections, which are nonlinear function of not only states and outputs but also unmodeled dynamics coming from other subsystems. In each subsystem, the proposed stabilization only has two adaptive parameters, and it is not needed to generate an additional dynamic signal or estimate the unknown parameters. Under certain assumptions, the proposed scheme guarantees that all the dynamic signals in the interconnected nonlinear system are bounded. Furthermore, the system states and estimate errors can approach arbitrarily small values by choosing the design parameters appropriately large. Finally, simulation results illustrated the effectiveness of the proposed scheme.
Theory and analysis of nonlinear dynamics and stability in storage rings: A working group summary
Energy Technology Data Exchange (ETDEWEB)
Chattopadhyay, S.; Audy, P.; Courant, E.D.; Forest, E.; Guignard, G.; Hagel, J.; Heifets, S.; Keil, E.; Kheifets, S.; Mais, H.; Moshammer, H.; Pellegrini, C.; Pilat, F.; Suzuki, T.; Turchetti, G.; Warnock, R.L.
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.
ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.
Ji, Shanming; Yin, Jingxue; Cao, Yang
2016-11-01
In this paper, we consider the periodic problem for semilinear heat equation and pseudo-parabolic equation with logarithmic source. After establishing the existence of positive periodic solutions, we discuss the instability of such solutions.
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; 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 bet
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.
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...
Institute of Scientific and Technical Information of China (English)
Wan-sheng WANG; Shou-fu LI; Run-sheng YANG
2012-01-01
A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.
Global stabilization of nonlinear systems based on vector control lyapunov functions
Karafyllis, Iasson
2012-01-01
This paper studies the use of vector Lyapunov functions for the design of globally stabilizing feedback laws for nonlinear systems. Recent results on vector Lyapunov functions are utilized. The main result of the paper shows that the existence of a vector control Lyapunov function is a necessary and sufficient condition for the existence of a smooth globally stabilizing feedback. Applications to nonlinear systems are provided: simple and easily checkable sufficient conditions are proposed to guarantee the existence of a smooth globally stabilizing feedback law. The obtained results are applied to the problem of the stabilization of an equilibrium point of a reaction network taking place in a continuous stirred tank reactor.
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
2011-01-01
International audience; In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization~: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show ...
P-th moment and almost sure stability of stochastic switched nonlinear systems.
Gu, Haibo; Gao, Caixia
2016-01-01
This paper mainly tends to utilize [Formula: see text]-type function to investigate p-th moment and almost sure stability for a class of stochastic switched nonlinear systems. Based on the multiple Lyapunov functions approach, some sufficient conditions are derived to check the stability criteria of stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effectiveness of the proposed results.
Improved Stability Analysis of Nonlinear Networked Control Systems over Multiple Communication Links
Delavar, Rahim; Tavassoli, Babak; Beheshti, Mohammad Taghi Hamidi
2015-01-01
In this paper, we consider a nonlinear networked control system (NCS) in which controllers, sensors and actuators are connected via several communication links. In each link, networking effects such as the transmission delay, packet loss, sampling jitter and data packet miss-ordering are captured by time-varying delays. Stability analysis is carried out based on the Lyapunov Krasovskii method to obtain a condition for stability of the nonlinear NCS in the form of linear matrix inequality (LMI...
Roberts, Dustyn; Khan, Humera; Kim, Joo H; Slover, James; Walker, Peter S
2013-10-01
There is no universally accepted definition of human joint stability, particularly in nonperiodic general activities of daily living. Instability has proven to be a difficult parameter to define and quantify, since both spatial and temporal measures need to be considered to fully characterize joint stability. In this preliminary study, acceleration-based parameters were proposed to characterize the joint stability. Several time-statistical parameters of acceleration and jerk were defined as potential stability measures, since anomalous acceleration or jerk could be a symptom of poor control or stability. An inertial measurement unit attached at the level of the tibial tubercle of controls and patients following total knee arthroplasty was used to determine linear acceleration of the knee joint during several activities of daily living. The resulting accelerations and jerks were compared with patient-reported instability as determined through a standard questionnaire. Several parameters based on accelerations and jerks in the anterior/posterior direction during the step-up/step-down activity were significantly different between patients and controls and correlated with patient reports of instability in that activity. The range of the positive to negative peak acceleration and infinity norm of acceleration, in the anterior/posterior direction during the step-up/step-down activity, proved to be the best indicators of instability. As time derivatives of displacement, these acceleration-based parameters represent spatial and temporal information and are an important step forward in developing a definition and objective quantification of human joint stability that can complement the subjective patient report.
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.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Zhang, Li; Zhang, Fan; Ruan, Shigui
2017-03-01
We study a diffusive predator-prey model describing the interactions of small fishes and their resource base (small invertebrates) in the fluctuating freshwater marsh landscapes of the Florida Everglades. The spatial model is described by a reaction-diffusion system with Beddington-DeAngelis functional response. Uniform bound, local and global asymptotic stability of the steady state of the PDE model under the no-flux boundary conditions are discussed in details. Sufficient conditions on the Turing (diffusion-driven) instability which induces spatial patterns in the model are derived via linear analysis. Existence of one-dimensional and two-dimensional spatial Turing patterns, including rhombic and hexagonal patterns, are established by weakly nonlinear analyses. These results provide theoretical explanations and numerical simulations of spatial dynamical behaviors of the wetland ecosystems of the Florida Everglades.
Passive control of thermoacoustic instabilities in swirl-stabilized combustion at elevated pressures
Directory of Open Access Journals (Sweden)
L Justin Williams
2016-09-01
Full Text Available In this study, a porous insert is placed at the dump plane of a swirl-stabilized lean premixed combustor to passively suppress thermoacoustic instabilities. The diffuser-shaped annular ring of porous inert material influences the turbulent flow field directly, including recirculation zones and vortical and/or shear layer structures to passively control the acoustic performance of the combustor. The porous inert material is made of silicon carbide–hafnium carbide coated, high-strength, high-temperature-resistant open-cell foam materials. In this study, the porous insert concept is investigated at above-ambient operating pressures to demonstrate its suitability for practical combustion applications. Experiments are conducted in quartz and metal combustors, without and with the porous insert while varying operating pressure, equivalence ratio, and reactant flow rate. Measurements show that the porous insert, and consequent changes in the combustor flow field, decrease the sound pressure levels at the frequency of combustion instability at all operating conditions investigated in this study. The porous insert also decreases the broadband combustion noise, i.e. the measured sound pressure levels over a wide frequency range.
Indian Academy of Sciences (India)
P K Karmakar
2011-06-01
The pulsational mode of gravitational collapse (PMGC) in a hydrostatically bounded dust molecular cloud is responsible for the evolution of tremendous amount of energy during star formation. The source of free energy for this gravito-electrostatic instability lies in the associated self-gravity of the dispersed phase of relatively huge dust grains of solid matter over the gaseous phase of background plasma. The nonlinear stability of the same PMGC in an inﬁnite dusty plasma model (plane geometry approximation for large wavelength ﬂuctuation in the absence of curvature effects) is studied in a hydrostatic kind of homogeneous equilibrium conﬁguration. By the standard reductive perturbation technique, a Korteweg–de Vries (KdV) equation for investigating the nonlinear evolution of the lowest order perturbed self-gravitational potential is developed in a time-stationary (steady-state) form, which is studied analytically as well as numerically. Different nonlinear structures (soliton-like and soliton chain-like) are found to exist in different situations. Astrophysical situations, relevant to it, are brieﬂy discussed.
Static feedback stabilization of nonlinear systems with single sensor and single actuator.
Wang, Jiqiang; Hu, Zhongzhi; Ye, Zhifeng
2014-01-01
This paper considers a single sensor and single actuator approach to the static feedback stabilization of nonlinear systems. This is essentially a remote control problem that is present in many engineering applications. The proposed method solves this problem that is less expensive to implement and more reliable in practice. Significant results are obtained on the design of controllers for stabilizing the nonlinear systems. Important issues on control implementation are also discussed. The proposed design method is validated through its application to nonlinear control of aircraft engines.
Saleem, H.; Ali Shan, S.; Haque, Q.
2016-11-01
It is shown that the inhomogeneous field-aligned flow of heavier ions into the stationary plasma of the upper ionosphere produces very low frequency (of the order of a few Hz) electrostatic unstable ion acoustic waves (IAWs). This instability is an oscillatory instability unlike D'Angelo's purely growing mode. The growth rate of the ion acoustic wave (IAW) corresponding to heavier ions is due to shear flow and is larger than the ion Landau damping. However, the ion acoustic waves corresponding to non-flowing lighter ions are Landau damped. It is found that even if D'Angelo's instability condition is satisfied, the unstable mode develops its real frequency in this coupled system. Hence, the shear flow of one type of ions in a bi-ion plasma system produces ion acoustic wave activity. If the density non-uniformity is taken into account, then the drift wave becomes unstable. The coupled nonlinear equations for stationary ions "a," flowing ions "b," and inertialess electrons are also solved using the small amplitude limit. The solutions predict the existence of the order of a few kilometers electric field structures in the form of solitons and vortices, which is in agreement with the satellite observations.
Stability and instability of Ellis and phantom wormholes: Are there ghosts?
Nandi, Kamal K; Izmailov, Ramil; Tamang, Amarjit; Evans, James C
2016-01-01
It is concluded in the literature that Ellis wormhole is unstable under small perturbations and would decay either to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to Schwarzschild black hole \\textit{only} when the Ellis solution parameter $\\gamma $ assumes a complex value $-i$. We shall then reexamine stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequantal statistical simulation about photon motion in the real optical medium to an effective medium reformulation of motions obtained via Hamilton's optical-mechanical analogy in a gravity field. A crucial component of Tangherlini's idea is the observed increase of momentum of the photons entering a real medium. We show that this fact has a heuristic parallel in the effective medium\\ version of the Pound-Rebka exper...
Cherif, Alhaji; Barley, Kamal
2010-12-29
Quantification of historical sociological processes have recently gained attention among theoreticians in the effort of providing a solid theoretical understanding of the behaviors and regularities present in socio-political dynamics. Here we present a reliability theory of polity processes with emphases on individual political dynamics of African countries. We found that the structural properties of polity failure rates successfully capture the risk of political vulnerability and instabilities in which , , , and of the countries with monotonically increasing, unimodal, U-shaped and monotonically decreasing polity failure rates, respectively, have high level of state fragility indices. The quasi-U-shape relationship between average polity duration and regime types corroborates historical precedents and explains the stability of the autocracies and democracies.
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.
Arkharov, A. M.; Lavrov, N. A.; Romanovskii, V. R.
2014-06-01
The current instability is studied in high-temperature superconducting current-carrying elements with I- V characteristics described by power or exponential equations. Stability analysis of the macroscopic states is carried out in terms of a stationary zero-dimensional model. In linear temperature approximation criteria are derived that allow one to find the maximum allowable values of the induced current, induced electric field intensity, and overheating of the superconductor. A condition is formulated for the complete thermal stabilization of the superconducting composite with regard to the nonlinearity of its I- V characteristic. It is shown that both subcritical and supercritical stable states may arise. In the latter case, the current and electric field intensity are higher than the preset critical parameters of the superconductor. Conditions for these states depending on the properties of the matrix, superconductor's critical current, fill factor, and nonlinearity of the I- V characteristic are discussed. The obtained results considerably augment the class of allowable states for high-temperature superconductors: it is demonstrated that there exist stable resistive conditions from which superconductors cannot pass to the normal state even if the parameters of these conditions are supercritical.
Trauth, Martin H; Bergner, Andreas G N; Foerster, Verena; Junginger, Annett; Maslin, Mark A; Schaebitz, Frank
2015-10-01
Episodes of environmental stability and instability may be equally important for African hominin speciation, dispersal, and cultural innovation. Three examples of a change from stable to unstable environmental conditions are presented on three different time scales: (1) the Mid Holocene (MH) wet-dry transition in the Chew Bahir basin (Southern Ethiopian Rift; between 11 ka and 4 ka), (2) the MIS 5-4 transition in the Naivasha basin (Central Kenya Rift; between 160 ka and 50 ka), and (3) the Early Mid Pleistocene Transition (EMPT) in the Olorgesailie basin (Southern Kenya Rift; between 1.25 Ma and 0.4 Ma). A probabilistic age modeling technique is used to determine the timing of these transitions, taking into account possible abrupt changes in the sedimentation rate including episodes of no deposition (hiatuses). Interestingly, the stable-unstable conditions identified in the three records are always associated with an orbitally-induced decrease of insolation: the descending portion of the 800 kyr cycle during the EMPT, declining eccentricity after the 115 ka maximum at the MIS 5-4 transition, and after ∼ 10 ka. This observation contributes to an evidence-based discussion of the possible mechanisms causing the switching between environmental stability and instability in Eastern Africa at three different orbital time scales (10,000 to 1,000,000 years) during the Cenozoic. This in turn may lead to great insights into the environmental changes occurring at the same time as hominin speciation, brain expansion, dispersal out of Africa, and cultural innovations and may provide key evidence to build new hypotheses regarding the causes of early human evolution. Copyright © 2015 Elsevier Ltd. All rights reserved.
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.
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
A Technique to Eliminate External Transport Barriers and Stabilize Fiscal Instabilities
Heeter, Robert F.
1997-11-01
The case is made for a coordinated national effort to diffuse plasma science knowledge to the public. Like earlier "fiscal instabilities" in plasma research, the 1995-7 magnetic fusion budget disruption can be attributed to a lack of public awareness about the value of science research, as reflected in the attitude of Congress. Magnetic fusion researchers now create "internal transport barriers" to reduce plasma heat loss, but observations also reveal a problematic "external transport barrier" in all of plasma science - the inadequate diffusion of knowledge beyond the scientists. Public funding creates scientific knowledge for the public good, and now the public cares - and deserves to know - what it pays for. Eliminating the external transport barrier should suppress the fiscal instability: theory predicts that funding should stabilize - or even increase - if the value of plasma science is understood by the bulk of Congress' members before they're elected, rather than just a small population of patrons energetically lobbied in office. If the public understands the value of plasma research, Congress will too. But plasmas are poorly represented in both contemporary classrooms and public perception. To reach the "Lawson Criterion" for ignition of public understanding, we should reach out to the public and to educators nationwide. Education and outreach activities are, and ought to be, part of the professional life of a plasma scientist. Our current activities consist largely of teaching our own classes, writing papers, lobbying Congress, giving lab tours, making Web pages, and promoting education locally; these have been useful, but insufficient. Now we must do better. To stabilize fiscal instabilities for good, we should restructure not only our research programs, but our sense of what it means to be a scientist. We should coordinate our education and outreach activities on a national scale, maximizing impact while minimizing cost in time, labor, and money. To this
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
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
RESEARCH OF THE PERIODIC MOTION AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS
Institute of Scientific and Technical Information of China (English)
刘俊
2002-01-01
The periodic motion and stability for a class of two-degree-of freedom nonlinear oscillating systems are studied by using the method of Liapunov function.The sufficient conditions which guarantee the existence, uniqueness and asymptotic stability of the periodic solutions are obtained.
Non-smooth finite-time stabilization for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear for small velocities asymptotically stabilizes the system.
THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM
Institute of Scientific and Technical Information of China (English)
方聪娜; 王全义
2004-01-01
In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.
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.
Energy Technology Data Exchange (ETDEWEB)
Qin, S.Q.; Jiao, J.J.; Tang, C.A.; Li, Z.G. [Chinese Academy of Sciences, Beijing (China)
2006-12-15
This paper studies the unstable mechanisms of the mechanical system that is composed of the stiff hosts (roof and floor) and the coal pillar using catastrophe theory. It is assumed that the roof is an elastic beam and the coal pillar is a strain-softening medium which can be described by the Weibull's distribution theory of strength. It is found that the instability leading to coal bump depends mainly on the system's stiffness ratio k, which is defined as the ratio of the flexural stiffness of the beam to the absolute value of the stiffness at the turning point of the constitutive curve of the coal pillar, and the homogeneity index m or shape parameter of the Weibull's distribution for the coal pillar. The applicability of the cusp catastrophe is demonstrated by applying the equations to the Mentougou coal mine. A non-linear dynamical model, which is derived by considering the time-dependent property of the coal pillar, is used to study the physical prediction of coal bumps. An algorithm of inversion for determining the parameters of the nonlinear dynamical model is suggested for seeking the precursory abnormality from the observed series of roof settlement. A case study of the Muchengjian coal mine is conducted and its nonlinear dynamical model is established from the observation series using the algorithm of inversion. An important finding is that the catastrophic characteristic index D (i.e., the bifurcation set of the cusp catastrophe model) drastically increases to a high peak value and then quickly drops close to instability. From the viewpoint of damage mechanics of coal pillar, a dynamical model of acoustic emission (AE) is established for modeling the AE activities in the evolutionary process of the system. It is revealed that the values of m and the evolutionary path (D = 0 or D not equal 0) of the system have a great impact on the AE activity patterns and characters.
Institute of Scientific and Technical Information of China (English)
SUN LiYing; WANG YuZhen
2009-01-01
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonlan function method.Firstly,based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback,two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation,and a sufficient condition for two closed-loop systems to be impulse-free is given.The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique,based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems.Secondly,the case of more than two nonlinear descriptor systems is investigated,and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization,respectively.Finally,an illustrative example is studied by using the results proposed in this paper,and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
Modeling and stability analysis of the nonlinear reactive sputtering process
Directory of Open Access Journals (Sweden)
György Katalin
2011-12-01
Full Text Available The model of the reactive sputtering process has been determined from the dynamic equilibrium of the reactive gas inside the chamber and the dynamic equilibrium of the sputtered metal atoms which form the compound with the reactive gas atoms on the surface of the substrate. The analytically obtained dynamical model is a system of nonlinear differential equations which can result in a histeresis-type input/output nonlinearity. The reactive sputtering process has been simulated by integrating these differential equations. Linearization has been applied for classical analysis of the sputtering process and control system design.
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.
Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set n,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.
Feedback diagonal canonical form and its application to stabilization of nonlinear systems
Institute of Scientific and Technical Information of China (English)
CHENG Daizhan; HU Qingxi; QIN Huashu
2005-01-01
This paper considers the problem of stabilization of a class of nonlinear systems, which are possibly of non-minimum phase. A new feedback-equivalent canonical form, called diagonal normal form, of linear control systems is proposed. Using it, the corresponding normal form of affine nonlinear control systems is obtained. Based on this new normal form and the design technique of center manifold, a new constructing method for stabilizing control is presented. Certain examples are included to demonstrate the design strategy of stabilizers.
Multi-shocks generation and collapsing instabilities induced by competing nonlinearities
Crosta, Matteo
2012-01-01
We investigate dispersive shock dynamics in materials with competing cubic-quintic nonlinearities. Whitham theory of modulation, hydrodynamic analysis and numerics demonstrate a rich physical scenario, ranging from multi-shock generation to collapse.
Wave instabilities in nonlinear Schrödinger systems with non vanishing background
Trillo, Stefano
2014-01-01
We investigate wave collapse in the generalized nonlinear Schrödinger (NLS) equation and in the presence of a non vanishing background. Through the use of virial identities, we establish a new criterion for blow-up.
Institute of Scientific and Technical Information of China (English)
Jian Guangde; Huang Lin; Qiu Xiaoming
2005-01-01
The assembling stabilizing effect of the finite Larmor radius (FLR) and the sheared axial flow (SAF) on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible finite Larmor radius magnetohydrodynamic (MHD) equations. The finite Larmor radius effects are introduced in the momentum equation with the sheared axial flow through an anisotropic ion stress tensor. In this paper a linear mode equation is derived that is valid for arbitrary kL, where k is the wave number and L is the plasma shell thickness. Numerical solutions are presented. The results indicate that the short-wavelength modes of the RayleighTaylor instability are easily stabilized by the individual effect of the finite Larmor radius or the sheared axial flow. The assembling effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability, and the unstable region can be compressed considerably.
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......) techniques with matrix-based methods for formulations in both one and two horizontal dimensions. The matrix-based method is also extended to show the local de-stabilizing effects of the nonlinear terms, as well as the stabilizing effects of numerical dissipation. A comparison of the relative stability...... moderately non-normal, suggesting that the eigenvalues are likely suitable for analysis purposes. Numerical experiments demonstrate excellent agreement with the linear analysis, and good qualitative agreement with the local nonlinear analysis. The various methods of analysis combine to provide significant...
Spectral and modulational stability of periodic wavetrains for the nonlinear Klein-Gordon equation
Jones, Christopher K. R. T.; Marangell, Robert; Miller, Peter D.; Plaza, Ramón G.
2014-12-01
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation utt-uxx+V‧(u)=0, where u is a scalar-valued function of x and t, and the potential V(u) is of class C2 and periodic. Stability is considered both from the point of view of spectral analysis of the linearized problem (spectral stability analysis) and from the point of view of wave modulation theory (the strongly nonlinear theory due to Whitham as well as the weakly nonlinear theory of wave packets). The aim is to develop and present new spectral stability results for periodic traveling waves, and to make a solid connection between these results and predictions of the (formal) modulation theory, which has been developed by others but which we review for completeness.
Yang, Jianke
2012-01-01
Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. It is shown that the smooth solution branch switches stability at the bifurcation point. In addition, the two bifurcated solution branches and the smooth branch have the opposite (same) stability when their power slopes have the same (opposite) sign. One unusual feature on the stability of these pitchfork bifurcations is that the smooth and bifurcated solution branches can be both stable or both unstable, which contrasts such bifurcations in finite-dimensional dynamical systems where the smooth and bifurcated branches generally have opposite stability. For the special case of positive solitary waves, stronger and more explicit stab...
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Institute of Scientific and Technical Information of China (English)
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
Stability of planar diffusion wave for nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
It is known that the one-dimensional nonlinear heat equation ut = f(u)x1x1,f'(u) 0,u(±∞,t) = u±,u+ = u_ has a unique self-similar solution u(x1/1+t).In multi-dimensional space,u(x1/1+t) is called a planar diffusion wave.In the first part of the present paper,it is shown that under some smallness conditions,such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation:ut-△f(u) = 0,x ∈ Rn.The optimal time decay rate is obtained.In the second part of this paper,it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping:utt + utt+ △f(u) = 0,x ∈ Rn.The time decay rate is also obtained.The proofs are given by an elementary energy method.
STABILITY OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION VIA FIXED POINT
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
In this paper,a nonlinear neutral differential equation is considered.By a fixed point theory,we give some conditions to ensure that the zero solution to the equation is asymptotically stable.Some existing results are improved and generalized.
DEFF Research Database (Denmark)
Boesen, Morten P; Jensen, Tim Toftgaard; Husted, Henrik
2004-01-01
A case of a fractured polyethylene stabilizing insert causing secondary knee instability in a Dual-articular total knee arthroplasty (TKA) is presented. A 65-year-old woman who underwent surgery with a Dual-articular TKA 4 years earlier had a well-functioning prosthesis until a fall, after which ...
Goldweber, Asha; Bradshaw, Catherine P.; Goodman, Kimberly; Monahan, Kathryn; Cooley-Strickland, Michele
2011-01-01
There is compelling evidence for the role of social information processing (SIP) in aggressive behavior. However, less is known about factors that influence stability versus instability in patterns of SIP over time. Latent transition analysis was used to identify SIP patterns over one year and examine how community violence exposure, aggressive…
DEFF Research Database (Denmark)
Boesen, Morten P; Jensen, Tim Toftgaard; Husted, Henrik
2004-01-01
A case of a fractured polyethylene stabilizing insert causing secondary knee instability in a Dual-articular total knee arthroplasty (TKA) is presented. A 65-year-old woman who underwent surgery with a Dual-articular TKA 4 years earlier had a well-functioning prosthesis until a fall, after which......-articular knee....
Robust Stability Analysis of Nonlinear Switched Systems with Filippov Solutions
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafal
2012-01-01
. Based on the theory of differential inclusions, a Lyapunov stability theorem is brought forward. These results are also extended to autonomous switched systems subject to polytopic uncertainty. Furthermore, the proposed stability theorems are reformulated using the sum of squares decomposition method...... which provides sufficient means to construct the corresponding Lyapunov functions via available semi-definite programming techniques....
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...
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
Mordukhovich, B. S.; Outrata, J. (Jiří)
2013-01-01
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian–Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. I...
PARTIAL STABILIZATION OF A CLASS OF CONTINUOUS NONLINEAR CONTROL SYSTEMS WITH SEPARATED VARIABLES
Institute of Scientific and Technical Information of China (English)
Jigui JIAN; Xiaoxin LIAO
2005-01-01
In this paper, the partial stabilization problem for a class of nonlinear continuous control systems with separated variables is investigated. Several stabilizing controllers are constructed based on the partial stability theory of Lyapunov and the property of M-matrix, and some of these stabilizing controllers are only related to partial state variables. The controllers constructed here are shown to guarantee partial asymptotic stability of the closed-loop systems and these sufficient conditions may give some instructions to actual engineering application. A example is also given to illustrate the design method.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Directory of Open Access Journals (Sweden)
Y. Javadian
2008-01-01
Full Text Available AbstractIntroduction: Lumbar segmental instability is one of the subgroups of non specific chronic low back pain and it seems that 30-40% of patients with LBP suffer from lumbar segmental instability. Pain intensity, functional disability and reduced muscle endurance are common in such patients. The aim of this study was to evaluate the effects of stabilization exercise on pain, functional disability and muscle endurance in patients suspected to lumbar segmental instability Material & methods: Following ethical approval, a randomized clinical trial was carried out on 30 patients suspected to lumbar segmental instability ranging from 18-45 years old. They were randomly divided into two groups; the first group underwent routine exercise only while the second group performed routine exercise plus stabilization training for 8 weeks. Outcome measure included pain intensity, functional disability, and flexion and extension range of motion and flexor, extensor and side support muscle endurance which were evaluated before and after treatment. Data were analyzed using paired t test and independent t test.Results: Muscle endurance and flexion range of motion increased in both groups although the increase was higher in stabilization training group (p=0.00. Pain intensity and functional disability significantly decreased in both groups (p=0.00, but decreasing of pain intensity and functional disability were more in stabilization training group (p=0.00. Conclusion: Stabilization training is more effective than routine exercise in improvement of pain intensity, functional disability, muscle endurance and range of motion in patients suspected to lumbar segmental instability. J Mazand Univ Med Sci 2008; 18(65: 63-73 (Persian
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.
Stabilization and Stochastic Control of a Class of Nonlinear Systems.
1980-10-01
0 is infinite. Thus it is not sufficient that our composite control be only a stabilizing control . To qualify as a candidate for near-optimality uc...completes the proof. 8. Near Optimality The question can now be posed whether uc, being a stabilizing control which produces a bounded cost, is also...procedure when jjc is a small but unknown parameter. For u to be a meaningful feedback control of the system (2.1), it c must first of all be a stabilizing
Energy Technology Data Exchange (ETDEWEB)
Brunner, S. [Centre de Recherches en Physique des Plasmas, Association Euratom-Confédération Suisse, Ecole Polytechnique Fédérale de Lausanne, Lausanne, (Switzerland); Berger, R. L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Cohen, B. I. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Hausammann, L. [Centre de Recherches en Physique des Plasmas, Association Euratom-Confédération Suisse, Ecole Polytechnique Fédérale de Lausanne, Lausanne, (Switzerland); Valeo, E. J. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2014-10-01
Kinetic Vlasov simulations of one-dimensional finite amplitude Electron Plasma Waves are performed in a multi-wavelength long system. A systematic study of the most unstable linear sideband mode, in particular its growth rate γ and quasi- wavenumber δk, is carried out by scanning the amplitude and wavenumber of the initial wave. Simulation results are successfully compared against numerical and analytical solutions to the reduced model by Kruer et al. [Phys. Rev. Lett. 23, 838 (1969)] for the Trapped Particle Instability (TPI). A model recently suggested by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)], which in addition to the TPI accounts for the so-called Negative Mass Instability because of a more detailed representation of the trapped particle dynamics, is also studied and compared with simulations.
Stability Analysis of Nonlinear Vibrations of a Deploying Flexible Beam
Institute of Scientific and Technical Information of China (English)
JunfengLI; ZhaolinWANG
1996-01-01
Consider a rigid-flexible coupled system which consists of a central rigid body deploying a flexible appendage,The appendage is modeled as a finite deflection beam having linear constitutive equations.By taking the energy integral as Lyapunov function,it is proved that nonlinear transverse vibrations of the beam undergoing uniform extension or retrieval are stable when there are not controlling moment in the central rigid body and driving force on the beam,according to the partial stablity theorem.
Identifying the active flow regions that drive linear and nonlinear instabilities
Marquet, Olivier
2015-01-01
A new framework for the analysis of unstable oscillator flows is explored. In linear settings, temporally growing perturbations in a non-parallel flow represent unstable eigenmodes of the linear flow operator. In nonlinear settings, self-sustained periodic oscillations of finite amplitude are commonly described as nonlinear global modes. In both cases the flow dynamics may be qualified as being endogenous, as opposed to the exogenous behaviour of amplifier flows driven by external forcing. This paper introduces the endogeneity concept, a specific definition of the sensitivity of the global frequency and growth rate with respect to variations of the flow operator. The endogeneity, defined both in linear and nonlinear settings, characterizes the contribution of localized flow regions to the global eigendynamics. It is calculated in a simple manner as the local point-wise inner product between the time derivative of the direct flow state and an adjoint mode. This study demonstrates for two canonical examples, th...
Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines
Institute of Scientific and Technical Information of China (English)
Eric Tala-Tebue; Aurelien Kenfack-Jiotsa; Marius Hervé Tatchou-Ntemfack; Timoléon Crépin Kofané
2013-01-01
In this work,we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines.Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch.Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing.On one hand,the difference between the two lines induced the fission for only one mode of propagation.This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton,leading to a possible increasing of the bit rate.On the other hand,the dissymmetry of the two lines converts the network into a good amplifier for the w_ mode which corresponds to the regime admitting low frequencies.
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.
Stabilization of nonlinear systems with parametric uncertainty using variable structure techniques
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A. [Oak Ridge National Lab., TN (United States); Oezguener, Ue. [Ohio State Univ., Columbus, OH (United States). Dept. of Electrical Engineering
1995-07-01
The authors present a result on the robust stabilization of a class of nonlinear systems exhibiting parametric uncertainty. They consider feedback linearizable nonlinear systems with a vector of unknown constant parameters perturbed about a known value. A Taylor series of the system about the nominal parameter vector coupled with a feedback linearizing control law yields a linear system plus nonlinear perturbations. Via a structure matching condition, a variable structure control law is shown to exponentially stabilize the full system. The novelty of the result is that the linearizing coordinates are completely known since they are defined about the nominal parameter vector, and fewer restrictions are imposed on the nonlinear perturbations than elsewhere in the literature.
Shvarts, D.; Oron, D.; Kartoon, D.; Rikanati, A.; Sadot, O.; Srebro, Y.; Yedvab, Y.; Ofer, D.; Levin, A.; Sarid, E.; Ben-Dor, G.; Erez, L.; Erez, G.; Yosef-Hai, A.; Alon, U.; Arazi, L.
2016-10-01
The late-time nonlinear evolution of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated using a statistical mechanics model based on single-mode and bubble-competition physics at all Atwood numbers (A) and full numerical simulations in two and three dimensions. It is shown that the RT mixing zone bubble and spike fronts evolve as h ~ α · A · gt2 with different values of a for the bubble and spike fronts. The RM mixing zone fronts evolve as h ~ tθ with different values of θ for bubbles and spikes. Similar analysis yields a linear growth with time of the Kelvin-Helmholtz mixing zone. The dependence of the RT and RM scaling parameters on A and the dimensionality will be discussed. The 3D predictions are found to be in good agreement with recent Linear Electric Motor (LEM) experiments.
Stability of switched nonlinear systems via extensions of LaSalle's invariance principle
Institute of Scientific and Technical Information of China (English)
WANG JinHuan; CHENG DaiZhan
2009-01-01
This paper studies the extension of LaSalle's invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle's invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.
Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?
Gadelha, H.
2010-05-12
Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.
Energy Technology Data Exchange (ETDEWEB)
Carbajal, L., E-mail: L.Carbajal-Gomez@warwick.ac.uk; Cook, J. W. S. [Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Dendy, R. O. [EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon OX14 3DB, Oxfordshire (United Kingdom); Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Chapman, S. C. [Centre for Fusion, Space and Astrophysics, Department of Physics, The University of Warwick, Coventry CV4 7AL (United Kingdom); Department of Mathematics and Statistics, University of Tromsø, N-9037, Tromsø (Norway); Max Planck Institute for the Physics of Complex Systems, D-01187, Dresden (Germany)
2014-01-15
The magnetoacoustic cyclotron instability (MCI) probably underlies observations of ion cyclotron emission (ICE) from energetic ion populations in tokamak plasmas, including fusion-born alpha-particles in JET and TFTR [Dendy et al., Nucl. Fusion 35, 1733 (1995)]. ICE is a potential diagnostic for lost alpha-particles in ITER; furthermore, the MCI is representative of a class of collective instabilities, which may result in the partial channelling of the free energy of energetic ions into radiation, and away from collisional heating of the plasma. Deep understanding of the MCI is thus of substantial practical interest for fusion, and the hybrid approximation for the plasma, where ions are treated as particles and electrons as a neutralising massless fluid, offers an attractive way forward. The hybrid simulations presented here access MCI physics that arises on timescales longer than can be addressed by fully kinetic particle-in-cell simulations and by analytical linear theory, which the present simulations largely corroborate. Our results go further than previous studies by entering into the nonlinear stage of the MCI, which shows novel features. These include stronger drive at low cyclotron harmonics, the re-energisation of the alpha-particle population, self-modulation of the phase shift between the electrostatic and electromagnetic components, and coupling between low and high frequency modes of the excited electromagnetic field.
Indian Academy of Sciences (India)
P A Subha; C P Jisha; V C Kuriakose
2007-08-01
The nonlinear Schrödinger equation which governs the dynamics of two-dimensional spatial solitons in Kerr media with periodically varying diffraction and nonlinearity has been analyzed in this paper using variational approach and numerical studies. Analytical expressions for soliton parameters have been derived using variational analysis. Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.
Institute of Scientific and Technical Information of China (English)
周少波; 薛明皋
2014-01-01
The paper develops exponential stability of the analytic solution and convergence in probability of the numerical method for highly nonlinear hybrid stochastic pantograph equation. The classical linear growth condition is replaced by polynomial growth conditions, under which there exists a unique global solution and the solution is almost surely exponen-tially stable. On the basis of a series of lemmas, the paper establishes a new criterion on convergence in probability of the Euler-Maruyama approximate solution. The criterion is very general so that many highly nonlinear stochastic pantograph equations can obey these conditions. A highly nonlinear example is provided to illustrate the main theory.
Komech, A I; Stuart, D
2008-01-01
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\\"odinger equation coupled to a nonlinear oscillator; mathematically the system under study is a nonlinear Schr\\"odinger equation, whose nonlinear term includes a Dirac delta. The coupled system is invariant with respect to the phase rotation group U(1). This article, which extends the results of a previous one, provides a proof of asymptotic stability of solitary wave solutions in the case that the linearization contains a single discrete oscillatory mode satisfying a non-degeneracy assumption of the type known as the Fermi Golden Rule.
Characterization of the shape stability for nonlinear elliptic problems
Bucur, Dorin
We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γ-convergence. If the dimension N of the space satisfies N-1
Prediction of Nonlinear Evolution Character of Energetic-Particle-Driven Instabilities
Duarte, Vinicius; Gorelenkov, Nikolai; Heidbrink, William; Kramer, Gerrit; Nazikian, Raffi; Pace, David; Podesta, Mario; Tobias, Benjamin; Van Zeeland, Michael
2016-01-01
A general criterion is proposed and found to successfully predict the emergence of chirping oscillations of unstable Alfv\\'enic eigenmodes in tokamak plasma experiments. The model includes realistic eigenfunction structure, detailed phase-space dependences of the instability drive, stochastic scattering and the Coulomb drag. The stochastic scattering combines the effects of collisional pitch angle scattering and micro-turbulence spatial diffusion. The latter mechanism is essential to accurately identify the transition between the fixed-frequency mode behavior and rapid chirping in tokamaks and to resolve the disparity with respect to chirping observation in spherical and conventional tokamaks.
Stability of Gain Scheduling Control for Aircraft with Highly Nonlinear Behavior
Directory of Open Access Journals (Sweden)
Fany Mendez-Vergara
2014-01-01
Full Text Available The main goal of this work is to study the stability properties of an aircraft with nonlinear behavior, controlled using a gain scheduled approach. An output feedback is proposed which is able to guarantee asymptotical stability of the task-coordinates origin and safety of the operation in the entire flight envelope. The results are derived using theory of hybrid and singular perturbed systems. It is demonstrated that both body velocity and orientation asymptotic tracking can be obtained in spite of nonlinearities and uncertainty. The results are illustrated using numerical simulations in F16 jet.
On Robust Stability of a Class of Uncertain Nonlinear Systems with Time-Varying Delay
Institute of Scientific and Technical Information of China (English)
NIAN Xiao-hong
2002-01-01
The problem of robust stability of a class of uncertain nonlinear dynamical systems with time-delay is considered. Based on the assumption that the nominal system is stable, some sufficient conditions onrobust stability of uncertain nonlinear dynamical systems with time-delay are derived. Some analytical methods and a type of Lyapunov functional are used to investigate such sufficient conditions. The results obtained in this paper are applicable to perturbed time-delay systems with unbounded time-varying delay.Some previous results are improved and a numerical example is given to demonstrate the validity of our results.
Nonlinear model predictive control with guaraneed stability based on pesudolinear neural networks
Institute of Scientific and Technical Information of China (English)
WANG Yongji; WANG Hong
2004-01-01
A nonlinear model predictive control problem based on pseudo-linear neural network (PNN) is discussed, in which the second order on-line optimization method is adopted. The recursive computation of Jacobian matrix is investigated. The stability of the closed loop model predictive control system is analyzed based on Lyapunov theory to obtain the sufficient condition for the asymptotical stability of the neural predictive control system. A simulation was carried out for an exothermic first-order reaction in a continuous stirred tank reactor. It is demonstrated that the proposed control strategy is applicable to some of nonlinear systems.
STABILITY AND BIFURCATION BEHAVIORS ANALYSIS IN A NONLINEAR HARMFUL ALGAL DYNAMICAL MODEL
Institute of Scientific and Technical Information of China (English)
WANG Hong-li; FENG Jian-feng; SHEN Fei; SUN Jing
2005-01-01
A food chain made up of two typical algae and a zooplankton was considered. Based on ecological eutrophication, interaction of the algal and the prey of the zooplankton, a nutrient nonlinear dynamic system was constructed. Using the methods of the modern nonlinear dynamics, the bifurcation behaviors and stability of the model equations by changing the control parameter r were discussed. The value of r for bifurcation point was calculated, and the stability of the limit cycle was also discussed. The result shows that through quasi-periodicity bifurcation the system is lost in chaos.
Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.
Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji
2014-05-01
This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The nonlinear dynamical behaviors of artificial neural network (ANN) and their application to science and engineering were summarized. The mechanism of two kinds of dynamical processes, i.e. weight dynamics and activation dynamics in neural networks, and the stability of computing in structural analysis and design were stated briefly. It was successfully applied to nonlinear neural network to evaluate the stability of underground stope structure in a gold mine. With the application of BP network, it is proven that the neuro-computing is a practical and advanced tool for solving large-scale underground rock engineering problems.
Practical stabilization of a class of uncertain time-varying nonlinear delay systems
Institute of Scientific and Technical Information of China (English)
Bassem Ben HAMED; Mohamed Ali HAMMAMI
2009-01-01
In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
Institute of Scientific and Technical Information of China (English)
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
Nonlinear Image Restoration in Confocal Microscopy : Stability under Noise
Roerdink, J.B.T.M.
1995-01-01
In this paper we study the noise stability of iterative algorithms developed for attenuation correction in Fluorescence Confocal Microscopy using FT methods. In each iteration the convolution of the previous estimate is computed. It turns out that the estimators are robust to noise perturbation.
Nonlinear Image Restoration in Confocal Microscopy : Stability under Noise
Roerdink, J.B.T.M.
1995-01-01
In this paper we study the noise stability of iterative algorithms developed for attenuation correction in Fluorescence Confocal Microscopy using FT methods. In each iteration the convolution of the previous estimate is computed. It turns out that the estimators are robust to noise perturbation.
Shear instabilities in metallic nanoparticles: hydrogen-stabilized structure of Pt37 on carbon.
Wang, Lin-Lin; Johnson, D D
2007-03-28
Using density functional theory calculations, we have studied the morphology of a Pt37 nanoparticle supported on carbon with and without hydrogen (H) passivation that arises with postprocessing of nanoparticles before characterization. Upon heating in an anneal cycle, we find that without H (e.g., in a helium atmosphere or evacuation at high temperature), the morphology change of a truncated cuboctahedral Pt37 is driven by the shearing of (100) to (111) facets to lower the surface energy, a remnant shear instability that drives surface reconstruction in semi-infinite Pt(100). With H passivation from a postprocessing anneal, we show that the sheared structure automatically reverts to the observed truncated cuboctahedral structure and the average first nearest-neighbor Pt-Pt bond length increases by 3%, agreeing well with experiment. We explain the stabilization of the truncated cuboctahedral structure due to H passivation via adsorption energetics of hydrogen on Pt(100) and (111) facets, specifically, the preference for H adsorption at bridge sites on (100) facets, which should be considered in a realistic model for H adsorption on Pt nanoparticles. We find that dramatic morphological change of a nanoparticle can occur even with small changes to first-shell Pt-Pt coordination number. The implications of our findings when comparing to experimental data are discussed.
Zocco, A.; Plunk, G. G.; Xanthopoulos, P.; Helander, P.
2016-08-01
The effects of a non-axisymmetric (3D) equilibrium magnetic field on the linear ion-temperature-gradient (ITG) driven mode are investigated. We consider the strongly driven, toroidal branch of the instability in a global (on the magnetic surface) setting. Previous studies have focused on particular features of non-axisymmetric systems, such as strong local shear or magnetic ripple, that introduce inhomogeneity in the coordinate along the magnetic field. In contrast, here we include non-axisymmetry explicitly via the dependence of the magnetic drift on the field line label α, i.e., across the magnetic field, but within the magnetic flux surface. We consider the limit where this variation occurs on a scale much larger than that of the ITG mode, and also the case where these scales are similar. Close to axisymmetry, we find that an averaging effect of the magnetic drift on the flux surface causes global (on the surface) stabilization, as compared to the most unstable local mode. In the absence of scale separation, we find destabilization is also possible, but only if a particular resonance occurs between the magnetic drift and the mode, and finite Larmor radius effects are neglected. We discuss the relative importance of surface global effects and known radially global effects.
Directory of Open Access Journals (Sweden)
R. Mantovani
2002-01-01
Full Text Available This paper presents the analysis of symmetric circulations of a rotating baroclinic flow, forced by a steady thermal wind and dissipated by Laplacian friction. The analysis is performed with numerical time-integration. Symmetric flows, vertically bound by horizontal walls and subject to either periodic or vertical wall lateral boundary conditions, are investigated in the region of parameter-space where unstable small amplitude modes evolve into stable stationary nonlinear solutions. The distribution of solutions in parameter-space is analysed up to the threshold of chaotic behaviour and the physical nature of the nonlinear interaction operating on the finite amplitude unstable modes is investigated. In particular, analysis of time-dependent energy-conversions allows understanding of the physical mechanisms operating from the initial phase of linear instability to the finite amplitude stable state. Vertical shear of the basic flow is shown to play a direct role in injecting energy into symmetric flow since the stage of linear growth. Dissipation proves essential not only in limiting the energy of linearly unstable modes, but also in selecting their dominant space-scales in the finite amplitude stage.
Misra, A P
2010-01-01
We consider the nonlinear propagation of electrostatic wave packets in an ultra-relativistic (UR) degenerate dense electron-ion plasma, whose dynamics is governed by the nonlocal two-dimensional nonlinear Schroedinger-like equations. The coupled set of equations are then used to study the modulational instability (MI) of a uniform wave train to an infinitesimal perturbation of multi-dimensional form. The condition for the MI is obtained, and it is shown that the nondimensional parameter, $\\beta\\propto\\lambda_C n_0^{1/3}$ (where $\\lambda_C$ is the reduced Compton wavelength and $n_0$ is the particle number density), associated with the UR pressure of degenerate electrons, shifts the stable (unstable) regions at $n_{0}\\sim10^{30}$ cm$^{-3}$ to unstable (stable) ones at higher densities, i.e. $n_{0}\\gtrsim7\\times10^{33}$. It is also found that higher the values of $n_{0}$, the lower is the growth rate of MI with cut-offs at lower wave numbers of modulation. Furthermore, the dynamical evolution of the wave packet...
Nonlinear r-Modes in Neutron Stars Instability of an unstable mode
Gressman, P T; Suen, W M; Stergioulas, N; Friedman, J L; Gressman, Philip; Lin, Lap-Ming; Suen, Wai-Mo; Friedman, John L.
2002-01-01
We study the dynamical evolution of a large amplitude r-mode by numerical simulations. R-modes in neutron stars are unstable growing modes, driven by gravitational radiation reaction. In these simulations, r-modes of amplitude unity or above are destroyed by a catastrophic decay: A large amplitude r-mode gradually leaks energy into other fluid modes, which in turn act nonlinearly with the r-mode, leading to the onset of the rapid decay. As a result the r-mode suddenly breaks down into a differentially rotating configuration. The catastrophic decay does not appear to be related to shock waves at the star's surface. The limit it imposes on the r-mode amplitude is significantly smaller than that suggested by previous fully nonlinear numerical simulations.
On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations
Friedlander, Susan
2011-01-01
We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is well-posed. In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo effect in the sense of an exponentially growing magnetic field.
Heidari, Mohammad; Heidari, Ali; Homaei, Hadi
2014-01-01
The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS.
Directory of Open Access Journals (Sweden)
DARIUSZ ELIGIUSZ STASZCZAK
2015-03-01
Full Text Available This paper analyses reasons of the instability of the world monetary system. The author considers this problem from historical and contemporary perspectives. According to presented point of view banknotes and electronic money which replaced gold and silver coins in popular circulation are the most important reason of the instability. There are also proven positive and negative consequences of money instability. Reforms of the world monetary system need agreement within the global collective hegemony of state-powers and transnational corporations.
STABILITY, BIFURCATIONS AND CHAOS IN UNEMPLOYMENT NON-LINEAR DYNAMICS
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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
Global asymptotic stability of a class of nonlinear systems with parametric uncertainty
Institute of Scientific and Technical Information of China (English)
Cai Xiushan; Lǜ Ganyun; Zhang Changfiang; He Xiuhui
2009-01-01
Stability of a class of nonlinear systems with parametric uncertainty is dealt with. This kind of systems can be viewed as feedback interconnection systems. By constructing the Lyapunov function for one of the feedback interconnection systems, the Lyapunov function for this kind of systems is obtained. Sufficient conditions of global asymptotic stability for this class of systems axe deduced. The simulation shows the effectiveness of the method.
A NEW APPROACH TO THE NONLINEAR STABILITY OF PARALLEL SHEAR FLOWS
Institute of Scientific and Technical Information of China (English)
XU Lan-xi; HUANG Yong-nian
2005-01-01
Lyapunov's second method was used to study the nonlinear stability of parallel shear flows for stress-free boundaries. By introducing an energy functional, it was shown that the plane Couette and plane Poiseuille flows are conditionally and asymptotically stable for all Reynolds numbers. In particular, to two-dimensional perturbations, by defining new energy functionals the unconditional stability of the basic flows was proved.
Adaptive Stabilization for a Class of Dynamical Systems with Nonlinear Delayed State Perturbations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The problem of adaptive stabilization for a class of systems with nonlinear delayed state perturbations is considered. The bound of the perturbations is assumed to be unknown, by using the adaptive control method, an adaptive controller is designed. Based on the Lyapunov- Karasovskii functional, it is shown that the dynamical system can be stabilized by the adaptive controller. The effectiveness of the proposed controller is demonstrated by some simulations.
Emission characteristics and combustion instabilities in an oxy-fuel swirl-stabilized combustor
Institute of Scientific and Technical Information of China (English)
Guo-neng LI; Hao ZHOU; Ke-fa CEN
2008-01-01
This paper presents an experimental study on the emission characteristics and combustion instabilities of oxy-fuel combustions in a swirl-stabilized combustor.Different oxygen concentrations(Xoxy=25%-45%,where Xoxy is oxygen concentra-tion by volume),equivalence ratios(=0.75～1.15)and combustion powers(CP=1.08～2.02kW)were investigated in the oxy-fuel (CH4/CO2/O2)combustions,and reference cases(Xoxy=25%～35%,Cha/N2/O2 flames)were covered.The results show that the oxygen concentration in the oxidant stream significantly affects the combustion delay in the oxy-fuel flames,and the equivalence ratio has a slight effect,whereas the combustion power shows no impact.The temperature levels of the oxy-fuel flames inside the combustion chamber are much higher(up to 38.7%)than those of the reference cases.Carbon monoxide was vastly producedwhen Xoxy>35% or >0.95 in the oxy-fuel flames,while no nitric oxide was found in the exhaust gases because no N2 participates in the combustion process.The combustion instability of the oxy-fuel combustion is very different from those of the reference cases with similar oxygen content.Oxy-fuel combustions excite strong oscillations in all cases studied Xoxy=25%～45%.However,no pressure fluctuations were detected in the reference cases when Xoxy>28.6% accomplished by heavily sooting flames which were not found in the oxy-fuel combustions.Spectrum analysis shows that the frequency of dynamic pressure oscillations exhibits randomness in the range of 50～250 Hz,therefore resulting in a very small resultant amplitude.Temporal oscillations are very strong with amplitudes larger than 200 Pa,even short time fast Fourier transform(FFT)analysis(0.08 s)shows that the pressure amplitude can be larger than 40 Pa.
Taamallah, Soufien
2014-06-16
In this paper, we conduct an experimental investigation of a confined premixed swirl-stabilized dump combustor similar to those found in modern gas turbines. We operate the combustor with premixed methane-air in the lean range of equivalence ratio ϕ ∈ [0.5–0.75]. First, we observe different dynamic modes in the lean operating range, as the equivalence ratio is raised, confirming observations made previously in a similar combustor geometry but with a different fuel [1]. Next we examine the correspondence between dynamic mode transitions and changes in the mean flame configuration or macrostructure. We show that each dynamic mode is associated with a specific flame macrostructure. By modifying the combustor length without changing the underlying flow, the resonant frequencies of the geometry are altered allowing for decoupling the heat release fluctuations and the acoustic field, in a certain range of equivalence ratio. Mean flame configurations in the modified (short) combustor and for the same range of equivalence ratio are examined. It is found that not only the same sequence of flame configurations is observed in both combustors (long and short) but also that the set of equivalence ratio where transitions in the flame configuration occur is closely related to the onset of thermo-acoustic instabilities. For both combustor lengths, the flame structure changes at similar equivalence ratio whether thermo-acoustic coupling is allowed or not, suggesting that the flame configuration holds the key to understanding the onset of self-excited thermo-acoustic instability in this range. Finally, we focus on the flame configuration transition that was correlated with the onset of the first dynamically unstable mode ϕ ∈ [0.61–0.64]. Our analysis of this transition in the short, uncoupled combustor shows that it is associated with an intermittent appearance of a flame in the outer recirculation zone (ORZ). The spectral analysis of this “ORZ flame flickering”
Jain, Neeraj
2016-01-01
The dissipation mechanism by which the magnetic field reconnects in the presence of an external (guide) magnetic field in the direction of the main current is not well understood. In thin electron current sheets (ECS) (thickness ~ an electron inertial length) formed in collisionless magnetic reconnection, electron shear flow instabilities (ESFI) are potential candidates for providing an anomalous dissipation mechanism which can break the frozen-in condition of the magnetic field affecting the structure and rate of reconnection. We investigate the evolution of ESFI in guide field magnetic reconnection. The properties of the resulting plasma turbulence and their dependence on the strength of the guide field are studied. Utilizing 3-D electron-magnetohydrodynamic simulations of ECS we show that, unlike the case of ECS self-consistently embedded in anti-parallel magnetic fields, the evolution of thin ECS in the presence of a guide field (equal to the asymptotic value of the reconnecting magnetic field or larger) ...
Non-linear aspects of Görtler instability in boundary layers with pressure gradient
Rogenski, J. K.; de Souza, L. F.; Floryan, J. M.
2016-12-01
The laminar flow over a concave surface may undergo transition to a turbulent state driven by secondary instabilities initiated by the longitudinal vortices known as Görtler vortices. These vortices distort the boundary layer structure by modifying the streamwise velocity component in both spanwise and wall-normal directions. Numerical simulations have been conducted to identify the role of the external pressure gradients in the development and saturation of the vortices. The results show that flows with adverse pressure gradients reach saturation upstream from the saturation location for neutral and favorable pressure gradients. In the transition region, the mean spanwise shear stress is about three times larger than in the flow without the vortices.
A simplified nonlinear model of the Marangoni instability in gas absorption
Skurygin, E. F.; Poroyko, T. A.
2016-04-01
The process of gas absorption into initially motionless liquid layer is investigated. The convective instability caused by the temperature dependence of the surface tension. The critical time of transition of the process to unstable convective regime, as well as the intensity of mass transfer in a surface convection are estimated numerically. The mathematical model includes the equations of convective diffusion, thermal conduction and fluid motion. The problem was solved numerically in the two-dimensional formulation. In the coordinate along the interface the concentration of the absorbed substance is represented by three terms of the trigonometric Fourier series. A difference approximation of equations with an exponentially changing grid in the direction normal to the interface is used. The simulations results agree with the well-known experimental data on the absorption of carbon dioxide in water.
Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems
Institute of Scientific and Technical Information of China (English)
Zhihong HUANG; Y. V. VENKATESH; Cheng XIANG; Tong Heng LEE
2014-01-01
The paper deals with the L2-stability analysis of multi-input-multi-output (MIMO) systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin-earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general L2-stability conditions in the frequency domain. These conditions have the following features:i) They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block. ii) For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.
Effects of nonlinear strength parameters on stability of 3D soil slopes
Institute of Scientific and Technical Information of China (English)
高玉峰; 吴迪; 张飞; 秦红玉; 朱德胜
2016-01-01
Actual slope stability problems have three-dimensional (3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.
Directory of Open Access Journals (Sweden)
Changchuan Xie
2016-01-01
Full Text Available VFAs (very flexible aircraft have begun to attract significant attention because of their good flight performances and significant application potentials; however, they also bring some challenges to researchers due to their unusual lightweight designs and large elastic deformations. A framework for the geometrically nonlinear aeroelastic stability analysis of very flexible wings is constructed in this paper to illustrate the unique aeroelastic characteristics and convenient use of these designs in engineering analysis. The nonlinear aeroelastic analysis model includes the geometrically nonlinear structure finite elements and steady and unsteady nonplanar aerodynamic computations (i.e., the nonplanar vortex lattice method and nonplanar doublet-lattice method. Fully nonlinear methods are used to analyse static aeroelastic features, and linearized structural dynamic equations are established at the structural nonlinear equilibrium state to estimate the stability of the system through the quasimode of the stressed and deformed structure. The exact flutter boundary is searched via an iterative procedure. A wind tunnel test is conducted to validate this theoretical analysis framework, and reasonable agreement is obtained. Both the analysis and test results indicate that the geometric nonlinearity of very flexible wings presents significantly different aeroelastic characteristics under different load cases with large deformations.
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
Energy Technology Data Exchange (ETDEWEB)
Tare, U. A.; Mody, F. K.; Mese, A. I. [Haliburton Energy Services, TX (United States)
2002-07-01
In order to develop a real-time wellbore (in)stability modelling capability, experimental work was carried out to investigate the role of the chemical potential of drilling fluids on transient pore pressure and time-dependent rock property alterations of shale formations. Time-dependent alterations in the pore pressure, acoustic and rock properties of formations subjected to compressive tri-axial test were recorded during the experiments involving the Pore Pressure Transmission (PPT) test. Based on the transient pore pressure of shale exposed to the test fluid presented here, the 20 per cent calcium chloride showed a very low membrane efficiency of 4.45 per cent. The need for a thorough understanding of the drilling fluid/shale interaction prior to applying any chemical potential wellbore (in)stability model to real-time drilling operations was emphasized. 9 refs., 5 figs.
Institute of Scientific and Technical Information of China (English)
TO Shi-hao; YUAN Yong; LI Nai-liang; DOU Feng-jin; WANG Fang-tian
2008-01-01
Analyzed the support instable mode of sliding, tripping, and so on, and believedthe key point of the support stability control of fully mechanized coal caving face with steepcoal seams was to maintain that the seam true angle was less than the hydraulic supportinstability critical angle. Through the layout of oblique face, the improvement of supportsetting load, the control of mining height and nonskid platform, the group support systemof end face, the advance optimization of conveyor and support, and the other control tech-nical measures, the true angle of the seam is reduced and the instable critical angle of thesupport is increased, the hydraulic support stability of fully mechanized coal caving facewith steep coal seams is effectively controlled.
Nonlinear ion dynamics in Hall thruster plasma source by ion transit-time instability
Lim, Youbong; Choe, Wonho; Mazouffre, Stéphane; Park, Jae Sun; Kim, Holak; Seon, Jongho; Garrigues, L.
2017-03-01
High-energy tail formation in an ion energy distribution function (IEDF) is explained in a Hall thruster plasma with the stationary crossed electric and magnetic fields whose discharge current is oscillated at the ion transit-time scale with a frequency of 360 kHz. Among ions in different charge states, singly charged Xe ions (Xe+) have an IEDF that is significantly broadened and shifted toward the high-energy side, which contributes to tail formation in the entire IEDF. Analytical and numerical investigations confirm that the IEDF tail is due to nonlinear ion dynamics in the ion transit-time oscillation.
Barker, Blake; Noble, Pascal; Rodrigues, L Miguel; Zumbrun, Kevin
2012-01-01
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by demonstrating that spectrally stable waves are nonlinearly stable when subject to small localized (integrable) perturbations. Our analysis is based upon detailed estimates of the linearized solution operator, which are complicated by the fact that the (necessarily essential) spectrum of the associated linearization intersects the imaginary axis at the origin. We carry out a numerical Evans function study of the spectral problem and find bands of spectrally stable periodic traveling waves, in close agreement with previous numerical studies of Frisch-She-Thual, Bar-Nepomnyashchy, Chang-Demekhin-Kopelevich, and others carried out by other techniques. We also compare predictions of the associated Whitham modulation equations, which formally describe the dynamics of weak large s...
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.
Rodríguez, Hugo; Schaft, Arjan J. van der; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the “control by interconnection” method provides a simple and elegant procedure for stab
On Stability of Flat Band Modes in a Rhombic Nonlinear Optical Waveguide Array
Maimistov, Andrey I
2016-01-01
The quasi-one-dimensional rhombic array of the waveguides is considered. In the nonlinear case the system of equations describing coupled waves in the waveguides has the solutions that represent the superposition of the flat band modes. The property of stability of these solutions is considered. It was found that the flat band solution is unstable until the power threshold be attained.
Rodríguez, Hugo; Schaft, van der Arjan J.; Ortega, Romeo
2001-01-01
Energy-shaping techniques have been successfully used for stabilization of nonlinear finite dimensional systems for 20 years now. In particular, for systems described by Port-Controlled Hamiltonian (PCH) models, the "control by interconnection" method provides a simple and elegant procedure for stab
Explicit Conditions for Stability of Nonlinear Scalar Delay Impulsive Difference Equation
Directory of Open Access Journals (Sweden)
Bo Zheng
2010-01-01
Full Text Available Sufficient conditions are obtained for the uniform stability and global attractivity of the zero solution of nonlinear scalar delay impulsive difference equation, which extend and improve the known results in the literature. An example is also worked out to verify that the global attractivity condition is a sharp condition.
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.
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...
Minimal data rate stabilization of nonlinear systems over networks with large delays
Persis, Claudio De
2007-01-01
We consider the problem of designing encoders, decoders and controllers which stabilize feedforward nonlinear systems over a communication network with finite bandwidth and large delay. The control scheme guarantees minimal data-rate semi-global asymptotic and local exponential stabilizatioln of the
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...
Asymptotic stability for a class of boundary control systems with non-linear damping
Zwart, Heiko J.; Ramirez, Hector; Le Gorrec, Yann
2016-01-01
The asymptotic stability of boundary controlled port-Hamiltonian systems defined on a 1D spatial domain interconnected to a class of non-linear boundary damping is addressed. It is shown that if the port-Hamiltonian system is approximately observable, then any boundary damping which behaves linear
Nonlinear Stability for the Periodic and Non-Periodic Zakharov System
Angulo, Jaime
2010-01-01
We prove the existence of a smooth curve of periodic traveling wave solutions for the Zakharov system. We also show that this type of solutions are nonlinear stable by the periodic flow generated for the system mentioned before. An improvement of the work of Ya Ping is made, we prove the stability of the solitary wave solutions associated to the Zakharov system.
A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Niu Yuanling; Zhang Chengjian; Duan Jinqiao
2011-01-01
A type of complex systems under both random influence and memory effects is considered.The systems are modeled by a class of nonlinear stochastic delay-integrodifferential equations.A delay-dependent stability criterion for such equations is derived under the condition that the time lags are small enough.Numerical simulations are presented to illustrate the theoretical result.
At the edge of nuclear stability nonlinear quantum amplifiers, pt. 2
Csoto, A; Schlattl, H; Csoto, Attila; Oberhummer, Heinz; Schlattl, Helmut
2000-01-01
We show that nuclei lying at the edge of stability can behave as nonlinear quantum amplifiers. A tiny change in the nucleon-nucleon interaction can trigger a much bigger change in the binding energy of these systems, relative to the few-cluster breakup threshold.
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 solitons under competing nonlinearities by external potentials
Zegadlo, Krzysztof B; Malomed, Boris A; Karpierz, Miroslaw A; Trippenbach, Marek
2014-01-01
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 (BEC) 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 (VA and TFA), 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 com...
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.
Directory of Open Access Journals (Sweden)
Florian Hartig
Full Text Available 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
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
Non-linear ultimate strength and stability limit state analysis of a wind turbine blade
DEFF Research Database (Denmark)
Rosemeier, Malo; Berring, Peter; Branner, Kim
2016-01-01
flap-wise loading has been compared with a linear response to determine the blade's resistance in the ultimate strength and stability limit states. The linear analysis revealed an unrealistic failure mechanism and failure mode. Further, it did not capture the highly non-linear response of the blade...... of an imperfection. The more realistic non-linear approaches yielded more optimistic results than the mandatory linear bifurcation analysis. Consequently, the investigated blade designed after the lesser requirements was sufficient. Using the non-linear approaches, considering inter-fibre failure as the critical...... failure mode, yielded still a significant safety margin for the designer (7–28%). The non-linear response was significantly dependent on the scaling of the imperfection. Eurocode's method of applying an imperfection appeared more realistic than the GL method. Since the considered blade withstood 135...
Nonlinear control for global stabilization of multiple-integrator system by bounded controls
Institute of Scientific and Technical Information of China (English)
Bin ZHOU; Guangren DUAN; Liu ZHANG
2008-01-01
The global stabilization problem of the multiple-integrator system by bounded controls is considered.A nonlinear feedback law consisting of nested saturation functions is proposed.This type of nonlinear feedback law that is a modification and generalization of the result given in[1] needs only[(n+1)/2](n is the dimensions of the system)saturation elements,which is fewer than that which the other nonlinear laws need.Funhermore.the poles of the closedloop system Can be placed on any location on the left real axis when none of the saturafion elements in the control laws is saturated.This type of nonlinear control law exhibits a simpler structure and call significantly improve the transient performances of the closed-loop system,and is very superior to the other existing methods.Simulation on a fourth-order system is used to validate the proposed method.
Budroni, M. A.
2015-12-01
Cross diffusion, whereby a flux of a given species entrains the diffusive transport of another species, can trigger buoyancy-driven hydrodynamic instabilities at the interface of initially stable stratifications. Starting from a simple three-component case, we introduce a theoretical framework to classify cross-diffusion-induced hydrodynamic phenomena in two-layer stratifications under the action of the gravitational field. A cross-diffusion-convection (CDC) model is derived by coupling the fickian diffusion formalism to Stokes equations. In order to isolate the effect of cross-diffusion in the convective destabilization of a double-layer system, we impose a starting concentration jump of one species in the bottom layer while the other one is homogeneously distributed over the spatial domain. This initial configuration avoids the concurrence of classic Rayleigh-Taylor or differential-diffusion convective instabilities, and it also allows us to activate selectively the cross-diffusion feedback by which the heterogeneously distributed species influences the diffusive transport of the other species. We identify two types of hydrodynamic modes [the negative cross-diffusion-driven convection (NCC) and the positive cross-diffusion-driven convection (PCC)], corresponding to the sign of this operational cross-diffusion term. By studying the space-time density profiles along the gravitational axis we obtain analytical conditions for the onset of convection in terms of two important parameters only: the operational cross-diffusivity and the buoyancy ratio, giving the relative contribution of the two species to the global density. The general classification of the NCC and PCC scenarios in such parameter space is supported by numerical simulations of the fully nonlinear CDC problem. The resulting convective patterns compare favorably with recent experimental results found in microemulsion systems.
UNCONDITIONAL NONLINEAR EXPONENTIAL STABILITY OF THE MOTIONLESS CONDUCTION-DIFFUSION SOLUTION
Institute of Scientific and Technical Information of China (English)
许兰喜
2000-01-01
Nonlinear stability of the motionless state of a heterogeneous fluid with constant temperature-gradient and concentration-gradient is studied for both cases of stress-free and rigid boundary conditions. By introducing new energy functionals we have shown that for τ = PC/PT _＜ 1, α = C/R ＞ 1 the motionless state is always stable and for τ＜ 1, α ＜ 1 the sufficient and necessary conditions for stability coincide, where PC, PT, C and R are the Schmidt number, Prandtl number,Rayleigh number for solute and heat, respectively. Moreover, the criteria guarantees the exponential stability.
Directory of Open Access Journals (Sweden)
Kanit Mukdasai
2012-01-01
Full Text Available This paper investigates the problem of robust exponential stability for linear parameter-dependent (LPD systems with discrete and distributed time-varying delays and nonlinear perturbations. Parameter dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, and linear matrix inequality are proposed to analyze the stability. On the basis of the estimation and by utilizing free-weighting matrices, new delay-dependent exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
Yang, Li-Ping; Ding, Shun-Liang; Litak, Grzegorz; Song, En-Zhe; Ma, Xiu-Zhen
2015-01-01
The cycling combustion instabilities in a diesel engine have been analyzed based on chaos theory. The objective was to investigate the dynamical characteristics of combustion in diesel engine. In this study, experiments were performed under the entire operating range of a diesel engine (the engine speed was changed from 600 to 1400 rpm and the engine load rate was from 0% to 100%), and acquired real-time series of in-cylinder combustion pressure using a piezoelectric transducer installed on the cylinder head. Several methods were applied to identify and quantitatively analyze the combustion process complexity in the diesel engine including delay-coordinate embedding, recurrence plot (RP), Recurrence Quantification Analysis, correlation dimension (CD), and the largest Lyapunov exponent (LLE) estimation. The results show that the combustion process exhibits some determinism. If LLE is positive, then the combustion system has a fractal dimension and CD is no more than 1.6 and within the diesel engine operating range. We have concluded that the combustion system of diesel engine is a low-dimensional chaotic system and the maximum values of CD and LLE occur at the lowest engine speed and load. This means that combustion system is more complex and sensitive to initial conditions and that poor combustion quality leads to the decrease of fuel economy and the increase of exhaust emissions.