A spectral characterization of nonlinear normal modes
Cirillo, G. I.; Mauroy, A.; Renson, L.; Kerschen, G.; Sepulchre, R.
2016-09-01
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity.
Numerical computation of nonlinear normal modes in mechanical engineering
Renson, L.; Kerschen, G.; Cochelin, B.
2016-03-01
This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures.
Nonlinear normal modes and their application in structural dynamics
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.
Relationships between nonlinear normal modes and response to random inputs
Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.
2017-02-01
The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
Hoffmann, Alexandre; Grudinin, Sergei
2017-01-01
International audience; We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velo...
Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes
2016-04-20
Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F...AFRL-RV-PS- AFRL-RV-PS- TR-2015-0182 TR-2015-0182 CHARACTERIZATION OF NON-LINEARIZED SPACECRAFT RELATIVE MOTION USING NONLINEAR NORMAL MODES Eric...STATEMENT. THOMAS LOVELL PAUL HAUSGEN, Ph.D. Program Manager Technical Advisor, Spacecraft Component Technology JOHN BEAUCHEMIN Chief Engineer
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2016-01-01
/softening behavior of nonlinear mechanical systems. The iterative optimization procedure consists of calculation of nonlinear normal modes, solving an adjoint equation system for sensitivity analysis and an update of design variables using a mathematical programming tool. We demonstrate the method with examples......Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...
Development of numerical algorithms for practical computation of nonlinear normal modes
2008-01-01
When resorting to numerical algorithms, we show that nonlinear normal mode (NNM) computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed method relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. In addition, sensitivity analysis is used to reduce the computational burden of the algorithm. A simplified discrete model of a...
Pump induced normal mode splittings in phase conjugation in a Kerr nonlinear waveguide
Indian Academy of Sciences (India)
S Dutta Gupta
2000-03-01
Phase conjugation in a Kerr nonlinear waveguide is studied with counter-propagating normally incident pumps and a probe beam at an arbitrary angle of incidence. Detailed numerical results for the specular and phase conjugated reﬂectivities are obtained with full account of pump depletion. For sufﬁcient strengths of the pump a normal mode splitting is demonstrated in both the specular and the phase conjugated reﬂectivities of the probe wave. The splitting is explained in terms of a simple model under undepleted pump approximation.
Nonlinear normal modes of a two degree of freedom oscillator with a bilateral elastic stop
Moussi, El Hadi; Cochelin, Bruno; Nistor, I
2013-01-01
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to obtain the Nonlinear Normal Mode (NNM), the harmonic balance method with a large number of harmonics, combined with the asymptotic numerical method, is used to solve the regularized problem. These methods are present in the software "package" MANLAB. The results are validated from periodic orbits obtained analytically in the time domain by direct integration of the non regular problem. The two NNMs starting respectively from the two linear normal modes of the associated underlying linear system are discussed. The energy-frequency plot is used to present a global vision of the behavior of the modes. The dynamics of the modes are also analyzed comparing each periodic orbits and modal lines. The first NNM shows an elaborate dynamics with the occurrence of multiple impacts per p...
Large net-normal dispersion Er-doped fibre laser mode-locked with a nonlinear amplifying loop mirror
Bowen, Patrick; Broderick, Neil G R
2016-01-01
We report on an environmentally stable, all-PM-fibre, Er-doped, mode-locked laser with a central wavelength of 1550 nm. Significantly, the laser possesses large net-normal dispersion such that its dynamics are comparable to that of an all-normal dispersion fibre laser at 1 {\\mu}m with an analogous architecture. The laser is mode-locked with a nonlinear amplifying loop mirror to produce pulses that are externally compressible to 500 fs. Experimental results are in good agreement with numerical simulations.
A New Non-linear Technique for Measurement of Splitting Functions of Normal Modes of the Earth
Pachhai, S.; Masters, G.; Tkalcic, H.
2014-12-01
Normal modes are the vibrating patterns of the Earth in response to the large earthquakes. Normal mode spectra are split due to Earth's rotation, ellipticity, and heterogeneity. The normal mode splitting is visualized through splitting functions, which represent the local radial average of Earth's structure seen by a mode of vibration. The analysis of the splitting of normal modes can provide unique information about the lateral variation of the Earth's elastic properties that cannot be directly imaged in body wave tomographic images. The non-linear iterative spectral fitting of the observed complex spectra and autoregressive linear inversion have been widely utilized to compute the Earth's 3-D structure. However, the non-linear inversion requires a model of the earthquake source and the retrieved 3-D structure is sensitive to the initial constraints. In contrast, the autoregressive linear inversion does not require the source model. However, this method requires many events to achieve full convergence. In addition, significant disagreement exists between different studies because of the non-uniqueness of the problem and limitations of different methods. We thus apply the neighbourhood algorithm (NA) to measure splitting functions. The NA is an efficient model space search technique and works in two steps: In the first step, the algorithm finds all the models compatible with given data while the posterior probability density of the model parameters are obtained in the second step. The NA can address the problem of non-uniqueness by taking advantage of random sampling of the full model space. The parameter trade-offs are conveniently visualized using joint marginal distributions. In addition, structure coefficients uncertainties can be extracted from the posterior probability distribution. After demonstrating the feasibility of NA with synthetic examples, we compute the splitting functions for the mode 13S2 (sensitive to the inner core) from several large
Institute of Scientific and Technical Information of China (English)
李欣业; 陈予恕; 吴志强
2002-01-01
The nonlinear normal modes (NNMs) associated with integrnal resonance can be classified into two kinds: uncoupled and coupled.The bifurcation problem of the coupled NNM of systems with 1: 2: 5 dual internal resonance is in two variables.The singular analysis of it is presented after separating the two variables by taking advantage of Maple algebra, and some new bifurcation patterns are found.Different from the NNMs of systems with single internal resonance, the number of the NNMs of systems with dual internal resonance may be more or less than the number of the degrees of freedom.At last, it is pointed out that bifurcation problems in two variables can be conveniently solved by separating variables as well as using coupling equations.
Xiao, Xiaosheng; Hua, Yi
2016-10-01
All-normal-dispersion (ANDi) mode-locked Yb-doped fiber laser is a promising seed source for supercontinuum (SC) generation, due to its compact structure and broadband output. The influences of output ports of the ANDi laser mode-locked by nonlinear polarization rotation (NPR), on the generated SC are investigated. Two output ports of ANDi laser are considered, one of which is the conventional nonlinear polarization rotation (NPR) port and the other is extracted from a coupler after the NPR port. It is found that, the SC originated from the coupler port is much broader than that from the NPR port, which is validated by lots of experiments with different output parameters. Furthermore, the conclusion is verified and generalized to general ANDi lasers by numerical simulations, because the output pulse from coupler port could be cleaner than that from NPR port. Besides, there are no significant differences in the phase coherence and temporal stability between the SCs generated from both ports. Hence for the SC generation based on ANDi laser, it is preferred to use the pulse of coupler port (i.e. pulse after NPR port) serving as the seed source.
Seismic base isolation by nonlinear mode localization
Energy Technology Data Exchange (ETDEWEB)
Wang, Y. [University of Illinois, Department of Civil and Environmental Engineering, Urbana, IL (United States); Washington University, Department of Civil and Environmental Engineering, St. Louis, MO (United States); McFarland, D.M. [University of Illinois, Department of Aerospace Engineering, Urbana, IL (United States); Vakakis, A.F. [National Technical University of Athens, Division of Mechanics (Greece); Bergman, L.A. [University of Illinois, Department of Mechanical and Industrial Engineering, Urbana, IL (United States)
2005-03-01
In this paper, the performance of a nonlinear base-isolation system, comprised of a nonlinearly sprung subfoundation tuned in a 1:1 internal resonance to a flexible mode of the linear primary structure to be isolated, is examined. The application of nonlinear localization to seismic isolation distinguishes this study from other base-isolation studies in the literature. Under the condition of third-order smooth stiffness nonlinearity, it is shown that a localized nonlinear normal mode (NNM) is induced in the system, which confines energy to the subfoundation and away from the primary or main structure. This is followed by a numerical analysis wherein the smooth nonlinearity is replaced by clearance nonlinearity, and the system is excited by ground motions representing near-field seismic events. The performance of the nonlinear system is compared with that of the corresponding linear system through simulation, and the sensitivity of the isolation system to several design parameters is analyzed. These simulations confirm the existence of the localized NNM, and show that the introduction of simple clearance nonlinearity significantly reduces the seismic energy transmitted to the main structure, resulting in significant attenuation in the response. (orig.)
Nonlinear dynamics by mode superposition
Energy Technology Data Exchange (ETDEWEB)
Nickell, R.E.
1976-01-01
A mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward-difference operators. The initial natural frequencies and mode shapes are found by inverse power iteration with the trial vectors for successively higher modes being swept by Gram-Schmidt orthonormalization at each iteration. The subsequent modal spectrum for nonlinear states is based upon the tangent stiffness of the structure and is calculated by a subspace iteration procedure that involves matrix multiplication only, using the most recently computed spectrum as an initial estimate. Then, a precise time integration algorithm that has no artificial damping or phase velocity error for linear problems is applied to the uncoupled modal equations of motion. Squared-frequency extrapolation is examined for nonlinear problems as a means by which these qualities of accuracy and precision can be maintained when the state of the system (and, thus, the modal spectrum) is changing rapidly. The results indicate that a number of important advantages accrue to nonlinear mode superposition: (a) there is no significant difference in total solution time between mode superposition and implicit direct integration analyses for problems having narrow matric half-bandwidth (in fact, as bandwidth increases, mode superposition becomes more economical), (b) solution accuracy is under better control since the analyst has ready access to modal participation factors and the ratios of time step size to modal period, and (c) physical understanding of nonlinear dynamic response is improved since the analyst is able to observe the changes in the modal spectrum as deformation proceeds.
Phase mixing and nonlinearity in geodesic acoustic modes
Energy Technology Data Exchange (ETDEWEB)
Hung, C. P.; Hassam, A. B. [University of Maryland at College Park, College Park, Maryland 20742 (United States)
2013-09-15
Phase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIII-D tokamak.
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...
Discrete-time nonlinear sliding mode controller
African Journals Online (AJOL)
user
: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
The effective degeneracy of protein normal modes.
Na, Hyuntae; Song, Guang
2016-05-12
Normal modes are frequently computed and used to portray protein dynamics and interpret protein conformational changes. In this work, we investigate the nature of normal modes and find that the normal modes of proteins, especially those at the low frequency range (0-600 cm(-1)), are highly susceptible to degeneracy. Two or more modes are degenerate if they have the same frequency and consequently any orthogonal transformation of them also is a valid representation of the mode subspace. Thus, degenerate modes can no longer characterize unique directions of motions as regular modes do. Though the normal modes of proteins are usually of different frequencies, the difference in frequency between neighboring modes is so small that, under even slight structural uncertainty that unavoidably exists in structure determination, it can easily vanish and as a result, a mode becomes effectively degenerate with its neighboring modes. This can be easily observed in that some modes seem to disappear and their matching modes cannot be found when the structure used to compute the modes is modified only slightly. We term this degeneracy the effective degeneracy of normal modes. This work is built upon our recent discovery that the vibrational spectrum of globular proteins is universal. The high density of modes observed in the vibrational frequency spectra of proteins renders their normal modes highly susceptible to degeneracy, under even the smallest structural uncertainty. Indeed, we find the degree of degeneracy of modes is proportional to the density of modes in the vibrational spectrum. This means that for modes at the same frequency, degeneracy is more severe for larger proteins. Degeneracy exists also in the modes of coarse-grained models, but to a much lesser extent than those of all-atom models. In closing, we discuss the implications of the effective degeneracy of normal modes: how it may significantly affect the ways in which normal modes are used in various normal modes
Localized modes in nonlinear binary kagome ribbons
Belicev, P. P.; Gligoric, G.; Radosavljevic, A; Maluckov, A.; Stepic, M.; Vicencio, R. A.; Johansson, Magnus
2015-01-01
The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the "binarism." Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in t...
Nonlinear magnetohydrodynamics of edge localized mode precursors
Energy Technology Data Exchange (ETDEWEB)
Guo, Z. B., E-mail: guozhipku@gmail.com [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China); WCI Center for Fusion Theory, NFRI, Gwahangno 113, Yusung-gu, Daejeon 305-333 (Korea, Republic of); Wang, Lu [SEEE, Huazhong University of Science and Technology, Wuhan, Hubei 430074 (China); Wang, X. G. [State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing (China)
2015-02-15
A possible origin of edge-localized-mode (ELM) precursors based on nonlinear ideal peeling-ballooning mode is reported. Via nonlinear variational principle, a nonlinear evolution equation of the radial displacement is derived and solved, analytically. Besides an explosive growth in the initial nonlinear phase, it is found that the local displacement evolves into an oscillating state in the developed nonlinear phase. The nonlinear frequency of the ELM precursors scales as ω{sub pre}∼x{sup 1/3}ξ{sup ^}{sub ψ,in}{sup 2/3}n, with x position in radial direction, ξ{sup ^}{sub ψ,in} strength of initial perturbation, and n toroidal mode number.
Nonlinear modes of clarinet-like musical instruments
Noreland, Daniel; Vergez, Christophe; Bouc, Robert
2009-01-01
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second order ordinary differential equations is obtained. The equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed. The system is treated using an amplitude-phase formulation for nonlinear modes, where the frequency and damping functions, as well as the invariant manifolds in the phase space, are unknowns to be determined. The formulation gives, without explicit integration of the underlying ordinary differential equation, access to the transient, the limit cycle, its period and stability. The process is illustrated for a model reduced to three normal modes of the air column.
Nonlinear modes of clarinet-like musical instruments
Noreland, Daniel; Bellizzi, Sergio; Vergez, Christophe; Bouc, Robert
2009-07-01
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second-order ordinary differential equations is obtained. The equations are coupled through the nonlinear relation describing the volume flow of air through the reed channel in response to the pressure difference across the reed. The system is treated using an amplitude-phase formulation for nonlinear modes, where the frequency and damping functions, as well as the invariant manifolds in the phase space, are unknowns to be determined. The formulation gives, without explicit integration of the underlying ordinary differential equation, access to the transient, the limit cycle, its period and stability. The process is illustrated for a model reduced to three normal modes of the air column.
Perturbations of normally solvable nonlinear operators, I
Directory of Open Access Journals (Sweden)
William O. Ray
1985-01-01
Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.
Mode matching for optimal plasmonic nonlinear generation
O'Brien, Kevin; Suchowski, Haim; Rho, Jun Suk; Kante, Boubacar; Yin, Xiaobo; Zhang, Xiang
2013-03-01
Nanostructures and metamaterials have attracted interest in the nonlinear optics community due to the possibility of engineering their nonlinear responses; however, the underlying physics to describe nonlinear light generation in nanostructures and the design rules to maximize the emission are still under debate. We study the geometry dependence of the second harmonic and third harmonic emission from gold nanostructures, by designing arrays of nanostructures whose geometry varies from bars to split ring resonators. We fix the length (and volume) of the nanostructure on one axis, and change the morphology from a split ring resonator on the other axis. We observed that the optimal second harmonic generation does not occur at the morphology indicated by a nonlinear oscillator model with parameters derived from the far field transmission and is not maximized by a spectral overlap of the plasmonic modes; however, we find a near field overlap integral and mode matching considerations accurately predict the optimal geometry.
Nonlinear Bogolyubov-Valatin transformations: 2 modes
Scharnhorst, K
2010-01-01
Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes which can be implemented by means of unitary SU(2^n = 4) transformations is isomorphic to SO(6;R)/Z_2. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in ter...
Lagrangian Space Nonlinear $E$-mode clustering
Yu, Hao-Ran; Zhu, Hong-Ming
2016-01-01
We study the nonlinear $E$-mode clustering in Lagrangian space by using large scale structure (LSS) $N$-body simulations and use the displacement field information in Lagrangian space to recover the primordial linear density field. We find that, compared to Eulerian nonlinear density fields, the $E$-mode displacement fields in Lagrangian space improves the cross-correlation scale $k$ with initial density field by factor of 6 $\\sim$ 7, containing 2 orders of magnitude more primordial information. This illustrates ability of potential density reconstruction algorithms, to improve the baryonic acoustic oscillation (BAO) measurements from current and future large scale structure surveys.
Mean flow generation mechanism by inertial waves and normal modes
Will, Andreas; Ghasemi, Abouzar
2016-04-01
The mean flow generation mechanism by nonlinearity of the inertial normal modes and inertial wave beams in a rotating annular cavity with longitudinally librating walls in stable regime is discussed. Inertial normal modes (standing waves) are excited when libration frequency matches eigenfrequencies of the system. Inertial wave beams are produced by Ekman pumping and suction in a rotating cylinder and form periodic orbits or periodic ray trajectories at selected frequencies. Inertial wave beams emerge as concentrated shear layers in a librating annular cavity, while normal modes appear as global recirculation cells. Both (inertial wave beam and mode) are helical and thus intrinsically non-linear flow structures. No second mode or wave is necessary for non-linearity. We considered the low order normal modes (1,1), (2,1) and (2,2) which are expected to be excited in the planetary objects and investigate the mean flow generation mechanism using two independent solutions: 1) analytical solution (Borcia 2012) and 2) the wave component of the flow (ω0 component) obtained from the direct numerical simulation (DNS). It is well known that a retrograde bulk mean flow is generated by the Ekman boundary layer and E1/4-Stewartson layer close to the outer cylinder side wall due to libration. At and around the normal mode resonant frequencies we found additionally a prograde azimuthal mean flow (Inertial Normal Mode Mean Flow: INMMF) in the bulk of the fluid. The fluid in the bulk is in geostrophic balance in the absence of the inertial normal modes. However, when INMMF is excited, we found that the geostrophic balance does not hold in the region occupied by INMMF. We hypothesize that INMMF is generated by the nonlinearity of the normal modes or by second order effects. Expanding the velocity {V}(u_r,u_θ,u_z) and pressure (p) in a power series in ɛ (libration amplitude), the Navier-Stokes equations are segregated into the linear and nonlinear parts at orders ɛ1 and ɛ^2
Localized modes in nonlinear binary kagome ribbons.
Beličev, P P; Gligorić, G; Radosavljević, A; Maluckov, A; Stepić, M; Vicencio, R A; Johansson, M
2015-11-01
The localized mode propagation in binary nonlinear kagome ribbons is investigated with the premise to ensure controlled light propagation through photonic lattice media. Particularity of the linear system characterized by the dispersionless flat band in the spectrum is the opening of new minigaps due to the "binarism." Together with the presence of nonlinearity, this determines the guiding mode types and properties. Nonlinearity destabilizes the staggered rings found to be nondiffracting in the linear system, but can give rise to dynamically stable ringlike solutions of several types: unstaggered rings, low-power staggered rings, hour-glass-like solutions, and vortex rings with high power. The type of solutions, i.e., the energy and angular momentum circulation through the nonlinear lattice, can be controlled by suitable initial excitation of the ribbon. In addition, by controlling the system "binarism" various localized modes can be generated and guided through the system, owing to the opening of the minigaps in the spectrum. All these findings offer diverse technical possibilities, especially with respect to the high-speed optical communications and high-power lasers.
Localized modes in nonlinear photonic kagome nanoribbons
Energy Technology Data Exchange (ETDEWEB)
Molina, Mario I., E-mail: mmolina@uchile.cl [Departamento de Física, MSI – Nucleus for Advanced Optics, and Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2012-10-01
We examine localization of light in nonlinear (Kerr) kagome lattices in the shape of narrow strips of varying width. For the narrowest ribbon, the band structure features a flat band leading to linear dynamical trapping of an initially localized excitation. We also find a geometry-induced bistability of the nonlinear modes as the width of the strip is changed. A crossover from one to two dimensions localization behavior is observed as the width is increased, attaining two-dimensional behavior for relatively narrow ribbons.
Magnetic normal modes in nano-particles
Energy Technology Data Exchange (ETDEWEB)
Grimsditch, M. [Materials Science Division, Argonne National Laboratory, Argonne, IL 60439 (United States)]. E-mail: grimsditch@anl.gov; Giovannini, L. [Dipartimento di Fisica, Universita di Ferrara and Istituto Nazionale per la Fisica della Materia, Via del Paradiso 12, I-44100 Ferrara (Italy); Montoncello, F. [Dipartimento di Fisica, Universita di Ferrara and Istituto Nazionale per la Fisica della Materia, Via del Paradiso 12, I-44100 Ferrara (Italy); Nizzoli, F. [Dipartimento di Fisica, Universita di Ferrara and Istituto Nazionale per la Fisica della Materia, Via del Paradiso 12, I-44100 Ferrara (Italy); Leaf, G. [Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439 (United States); Kaper, H. [Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439 (United States); Karpeev, D. [Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439 (United States)
2004-12-31
We have recently developed two methods to calculate the magnetic normal modes of a magnetic nano-particle. One of the methods is based on a conventional micromagnetic approach in which the time evolution of the magnetization of each cell is monitored. After filtering in frequency domain, the magnetic normal modes can be reconstructed. The second method is based on solving the same micromagneitc system in a dynamical matrix formulation. The results of the two methods, applied to a rectangular parallelepiped of Fe, will be presented and compared.
Normal modes of confined cold ionic systems
Energy Technology Data Exchange (ETDEWEB)
Schiffer, J.P.; Dubin, D.H. [Univ. of California, San Diego, CA (United States)
1995-08-01
The normal modes of a cloud of confined ions forming a strongly-correlated plasma were investigated. The results of molecular-dynamics simulations were compared to predictions of a cold fluid mode. Mode frequencies are observed to shift slightly compared to the cold fluid predictions, and the modes are also observed to damp in time. Simulations also reveal a set of torsional oscillations which have no counterpart in cold fluid theory. The frequency shift, damping, and torsional effects are compared to a model that treats trapped plasmas as a visco-elastic spheroid. It may be possible to measure high-frequency bulk and shear moduli of a strongly-correlated plasma from mode excitation experiments on trapped non-neutral plasmas. An example of the results of the calculation is presented.
Nonlinear Bogolyubov-Valatin transformations: Two modes
Scharnhorst, K.; van Holten, J.-W.
2011-11-01
Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes, which can be implemented by means of unitary SU(2n=4) transformations, is isomorphic to SO(6;R)/Z2. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions H. From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin- {1}/{2} and single-spin- {3}/{2} systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin- {1}/{2} and single-spin- {3}/{2} Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of SU(4) and SO(6;R) matrices (of respective sizes 4×4 and 6×6) and their mutual relation.
Mode-locking in nonlinear rotordynamics
van der Heijden, G. H. M.
1995-05-01
We present a computer-assisted study of the dynamics of two nonlinearly coupled driven oscillators with rotational symmetry which arise in rotordynamics (the nonlinearity coming from bearing clearance). The nonlinearity causes a splitting of the twofold degenerate natural frequency of the associated linear model, leading to three interacting frequencies in the system. Partial mode-locking then yields a biinfinite series of attracting invariant 2-tori carrying (quasi-) periodic motion. Due to the resonance nature, the (quasi-) periodic solutions become periodic in a corotating coordinate system. They can be viewed as entrainments of periodic solutions of the associated linear problem. One presumably infinite family is generated by (scaled) driving frequencies ω = 1+2/ n, n = 1,2,3,...; another one is generated by frequencies ω = m, m = 4,5,6,... Both integers n and m can be related to discrete symmetry properties of the particular periodic solutions. Under a perturbation that breaks the rotational symmetry, more complicated behavior is possible. In particular, a second rational relation between the frequencies can be established, resulting in fully mode-locked periodic motion.
Normal modes and mode transformation of pure electron vortex beams
Thirunavukkarasu, G.; Mousley, M.; Babiker, M.; Yuan, J.
2017-02-01
Electron vortex beams constitute the first class of matter vortex beams which are currently routinely produced in the laboratory. Here, we briefly review the progress of this nascent field and put forward a natural quantum basis set which we show is suitable for the description of electron vortex beams. The normal modes are truncated Bessel beams (TBBs) defined in the aperture plane or the Fourier transform of the transverse structure of the TBBs (FT-TBBs) in the focal plane of a lens with the said aperture. As these modes are eigenfunctions of the axial orbital angular momentum operator, they can provide a complete description of the two-dimensional transverse distribution of the wave function of any electron vortex beam in such a system, in analogy with the prominent role Laguerre-Gaussian (LG) beams played in the description of optical vortex beams. The characteristics of the normal modes of TBBs and FT-TBBs are described, including the quantized orbital angular momentum (in terms of the winding number l) and the radial index p>0. We present the experimental realization of such beams using computer-generated holograms. The mode analysis can be carried out using astigmatic transformation optics, demonstrating close analogy with the astigmatic mode transformation between LG and Hermite-Gaussian beams. This article is part of the themed issue 'Optical orbital angular momentum'.
Thermally induced nonlinear mode coupling in high power fiber amplifiers
DEFF Research Database (Denmark)
Johansen, Mette Marie; Hansen, Kristian Rymann; Alkeskjold, Thomas T.;
2013-01-01
Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W.......Thermally induced nonlinear mode coupling leads to transverse mode instability (TMI) in high power fiber amplifiers. A numerical model including altering mode profiles from thermal effects and waveguide perturbations predicts a TMI threshold of ~200W....
Breatherlike impurity modes in discrete nonlinear lattices
DEFF Research Database (Denmark)
Hennig, D.; Rasmussen, Kim; Tsironis, G. P.
1995-01-01
We investigate the properties of a disordered generalized discrete nonlinear Schrodinger equation, containing both diagonal and nondiagonal nonlinear terms. The equation models a Linear host lattice doped with nonlinear impurities. We find different types of impurity states that form itinerant...
Nonlinear r-modes in rapidly rotating relativistic stars.
Stergioulas, N; Font, J A
2001-02-12
The r-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications, provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3D general-relativistic hydrodynamical evolutions. We find that (1) on dynamical time scales, there is no strong nonlinear coupling of r-modes to other modes at amplitudes of order one-the maximum r-mode amplitude is of order unity. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes. (3) The kinematical drift associated with r-modes appears to be present in our simulations, but confirmation requires more precise initial data.
Optimal second order sliding mode control for nonlinear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-07-01
In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.
New approach to the normal mode method in underwater acoustics
Institute of Scientific and Technical Information of China (English)
王宁; 刘进忠
2002-01-01
A new approach to the numerical solution of normal mode problems in underwater acoustics is presented, in whichthe corresponding normal mode problem is transformed to the problem of solving a dynamic system. Three applica-tions are considered: (1) the broad band normal mode problem; (2) the range-dependent problem with perturbationproportional to the range parameter; and (3) the evolution of the normal mode with environmental parameters. Anumerical simulation for a broad band problem is performed, and the calculated eigenvalues have good agreement withthose obtained by the standard normal mode code KRAKAN.
DVI Film Flow Instability Based on the Normal Mode Analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Jae Young; Euh, Dong Jin [Handong Global Univ., Pohang (Korea, Republic of)
2013-10-15
In the present paper, as the first step of nonlinear studies, the appearance of the third order spatial differentiation of the film thickness in the wave propagation equation is to be derived. The two-fluid model in the adiabatic condition is employed and normal mode analysis. Interfacial pressure forces between steam and water need to be modeled for this purpose. n the present study, we developed a theoretical basis to study nonlinear wave phenomena on the DVI film flow which highly affect the DVI penetration and liquid droplets entrainment out. We set the hyperbolicity breaking condition by providing the interfacial pressure difference considering the curvature of the reactor vessel. The interfacial pressure difference could generate nonlinear wave such as the horseshoe wave which has been believed as a main source of film break up to produce huge amount of droplets to be entrained out. As a safety injection method, the direct vessel injection has been intensively developed in Korea and employed in the APR1400. The developing efforts were made from the determination of the number, location and size of DVI nozzles to the experimental demonstrations. Experimental facilities with various scales have shown its complicated phenomena due to highly nonlinear interaction between the steam and injected water flow. The injected DVI water forms a film type flow but very unstable due to the unsteady energetic steam flow which find the exits around the shell of the downcomer of the reactor vessel. This steam and liquid film interaction leads to the instability on the surface of the film flow and the waves are highly nonlinear to form undercutting, roll over, and finally droplet releasing. The entrained droplets causes a difficulty in the analysis to estimate the water penetrated into the reactor core to cool the nuclear fuels heated up. Unfortunately, these instabilities on the interface of the DVI liquid film have not been studied appropriately and the conservative
Discrete dissipative localized modes in nonlinear magnetic metamaterials.
Rosanov, Nikolay N; Vysotina, Nina V; Shatsev, Anatoly N; Shadrivov, Ilya V; Powell, David A; Kivshar, Yuri S
2011-12-19
We analyze the existence, stability, and propagation of dissipative discrete localized modes in one- and two-dimensional nonlinear lattices composed of weakly coupled split-ring resonators (SRRs) excited by an external electromagnetic field. We employ the near-field interaction approach for describing quasi-static electric and magnetic interaction between the resonators, and demonstrate the crucial importance of the electric coupling, which can completely reverse the sign of the overall interaction between the resonators. We derive the effective nonlinear model and analyze the properties of nonlinear localized modes excited in one-and two-dimensional lattices. In particular, we study nonlinear magnetic domain walls (the so-called switching waves) separating two different states of nonlinear magnetization, and reveal the bistable dependence of the domain wall velocity on the external field. Then, we study two-dimensional localized modes in nonlinear lattices of SRRs and demonstrate that larger domains may experience modulational instability and splitting.
Nonlinear and Non Normal Regression Models in Physiological Research
1984-01-01
Applications of nonlinear and non normal regression models are in increasing order for appropriate interpretation of complex phenomenon of biomedical sciences. This paper reviews critically some applications of these models physiological research.
Nonlinear dynamics exploration through normal forms
Kahn, Peter B
2014-01-01
Geared toward advanced undergraduates and graduate students, this exposition covers the method of normal forms and its application to ordinary differential equations through perturbation analysis. In addition to its emphasis on the freedom inherent in the normal form expansion, the text features numerous examples of equations, the kind of which are encountered in many areas of science and engineering. The treatment begins with an introduction to the basic concepts underlying the normal forms. Coverage then shifts to an investigation of systems with one degree of freedom that model oscillations
Spiralling solitons and multipole localized modes in nonlocal nonlinear media
DEFF Research Database (Denmark)
Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan
2007-01-01
We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form.......We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different...
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
The Symmetricity of Normal Modes in Symmetric Complexes
Song, Guang
2016-01-01
In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel theoretical result of this work is that, for a ring structure with $m$ subunits, the symmetricity of the normal modes falls into $m$ groups of equal size, with normal modes in each group having the same symmetricity. The normal modes in each group can be computed separately, using a much smaller amount of memory and time (up to $m^3$ less), thus making it applicable to larger complexes. We show that normal modes with perfect symmetry or anti-symmetry have no degeneracy while the rest of the modes have a degeneracy of two. We show also how symmetry in normal modes correlates with symmetry in structure. While a broken symmetry in structure generally leads to a loss of symmetricity in symmetric normal modes, the symmetricity of some symmetric normal modes is preserved even when s...
Fuzzy Sliding Mode Control for Discrete Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
F.Qiao.Q.M.Zhu; A.Winfield; C.Melhuish
2003-01-01
Sliding mode control is introduced into classical model free fuzzy logic control for discrete time nonlinear systems with uncertainty to the design of a novel fuzzy sliding mode control to meet the requirement of necessary and sufficient reaching conditions of sliding mode control. The simulation results show that the proposed controller outperforms the original fuzzy sliding mode controller and the classical fuzzy logic controller in stability, convergence and robustness.
Three-dimensional modes of a symmetric nonlinear plane waveguide
Akhmediev, N. N.; Nabiev, R. F.; Popov, Yu. M.
1989-01-01
The three-dimensional problem of a symmetric nonlinear plane waveguide, which consist of a linear medium layer surrounded by nonlinear media, is investigated. The stationary solution of this problem is a mode whose field is falling to zero at infinity in all directions perpendicular to the propagation direction. The even, odd and assymetrical solutions of the problem are obtained.
Gang, Zhou
2008-01-01
Nonlinear Schrodinger / Gross-Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground state manifold, discrete neutral modes (``excited states'') and dispersive radiation. Systems with symmetry, in spatial dimensions larger than one, typically have degenerate neutral modes. Thus, we study the large time dynamics of systems with degenerate neutral modes. This requires a new normal form (nonlinear matrix Fermi Golden Rule) governing the system's large time asymptotic relaxation to the ground state (soliton) manifold.
Parametric localized modes in quadratic nonlinear photonic structures
DEFF Research Database (Denmark)
Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole;
2001-01-01
We analyze two-color spatially localized nonlinear modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi2) nonlinear interfaces embedded in a linear layered structure-a quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear...... interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi2 equations) and find, numerically and analytically, the spatially localized solutions-discrete gap solitons. For a single nonlinear interface...... in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities to and differences from quadratic solitons in homogeneous media....
Passive harmonic mode locked all-normal-dispersion Yb-doped fibre lasers
Institute of Scientific and Technical Information of China (English)
Kong Ling-Jie; Xiao Xiao-Sheng; Yang Chang-Xi
2011-01-01
Passive harmonic mode-locking of dissipative solitons is demonstrated in all-normal dispersion Yb-doped fibre lasers. A difference equation model of the mode-locked fibre lasers is adopted to simulate the intra-cavity nonlinear dynamics. Hysteresis phenomena around the mode-locking threshold, and the effect of introducing linear phase bias are discussed. The passive harmonic mode-locking as one kind of multipulsing operations is revealed. Moreover, the simulation shows the bistability between multipulsing and single-pulse or period multiplication.
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.
A Bloch mode expansion approach for analyzing quasi-normal modes in open nanophotonic structures
DEFF Research Database (Denmark)
de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper;
2014-01-01
to conventional techniques. The quasi-normal modes are determined by constructing a cavity roundtrip matrix and iterating the complex mode wavelength towards a unity eigenvalue. We demonstrate the method by deter- mining quasi-normal modes of cavities in two-dimensional photonic crystals side-coupled to W1...
Perturbative calculation of quasi-normal modes
Siopsis, G
2005-01-01
I discuss a systematic method of analytically calculating the asymptotic form of quasi-normal frequencies. In the case of a four-dimensional Schwarzschild black hole, I expand around the zeroth-order approximation to the wave equation proposed by Motl and Neitzke. In the case of a five-dimensional AdS black hole, I discuss a perturbative solution of the Heun equation. The analytical results are in agreement with the results from numerical analysis.
Instantaneous Normal Modes and the Protein Glass Transition
Energy Technology Data Exchange (ETDEWEB)
Schultz, Roland [University of Tennessee, Knoxville (UTK); Krishnan, Marimuthu [ORNL; Daidone, Isabella [University of Heidelberg; Smith, Jeremy C [ORNL
2009-01-01
In the instantaneous normal mode method, normal mode analysis is performed at instantaneous configurations of a condensed-phase system, leading to modes with negative eigenvalues. These negative modes provide a means of characterizing local anharmonicities of the potential energy surface. Here, we apply instantaneous normal mode to analyze temperature-dependent diffusive dynamics in molecular dynamics simulations of a small protein (a scorpion toxin). Those characteristics of the negative modes are determined that correlate with the dynamical (or glass) transition behavior of the protein, as manifested as an increase in the gradient with T of the average atomic mean-square displacement at 220 K. The number of negative eigenvalues shows no transition with temperature. Further, although filtering the negative modes to retain only those with eigenvectors corresponding to double-well potentials does reveal a transition in the hydration water, again, no transition in the protein is seen. However, additional filtering of the protein double-well modes, so as to retain only those that, on energy minimization, escape to different regions of configurational space, finally leads to clear protein dynamical transition behavior. Partial minimization of instantaneous configurations is also found to remove nondiffusive imaginary modes. In summary, examination of the form of negative instantaneous normal modes is shown to furnish a physical picture of local diffusive dynamics accompanying the protein glass transition.
Normal mode calculations of trigonal selenium
DEFF Research Database (Denmark)
Hansen, Flemming Yssing; McMurry, H. L.
1980-01-01
symmetry. The intrachain force field is projected from a valence type field including a bond stretch, angle bend, and dihedral torsion. With these coordinates we obtain the strong dispersion of the upper optic modes as observed by neutron scattering, where other models have failed and give flat bands......The phonon dispersion relations for trigonal selenium have been calculated on the basis of a short range potential field model. Electrostatic long range forces have not been included. The force field is defined in terms of symmetrized coordinates which reflect partly the symmetry of the space group....... In this way we have eliminated the ambiguity in the choice of valence coordinates, which has been a problem in previous models which used valence type interactions. Calculated sound velocities and elastic moduli are also given. The Journal of Chemical Physics is copyrighted by The American Institute...
Intrinsic localized modes and nonlinear impurity modes in curved Fermi-Pasta-Ulam chain
Indian Academy of Sciences (India)
Ranja Sarkar; Bishwajyoti Dey
2008-06-01
We explore the nature of intrinsic localized modes (ILMs) in a curved FermiPasta-Ulam (FPU) chain and the effects of geometry and second-neighbor interaction on the localization and movability properties of such modes. We determine analytically the structure of the localized modes induced by an isotopic light-mass impurity in this chain. We further demonstrate that a nonlinear impurity mode may be treated as a bound state of an ILM with the impurity.
Nonlinear saturation of trapped electron modes via perpendicular particle diffusion.
Merz, F; Jenko, F
2008-01-25
In magnetized fusion plasmas, trapped electron mode (TEM) turbulence constitutes, together with ion temperature gradient (ITG) turbulence, the dominant source of anomalous transport on ion scales. While ITG modes are known to saturate via nonlinear zonal flow generation, this mechanism is shown to be of little importance for TEM turbulence in the parameter regime explored here. Instead, a careful analysis of the statistical properties of the ExB nonlinearity in the context of gyrokinetic turbulence simulations reveals that perpendicular particle diffusion is the dominant saturation mechanism. These findings allow for the construction of a rather realistic quasilinear model of TEM induced transport.
Terminal Sliding Modes In Nonlinear Control Systems
Venkataraman, Subramanian T.; Gulati, Sandeep
1993-01-01
Control systems of proposed type called "terminal controllers" offers increased precision and stability of robotic operations in presence of unknown and/or changing parameters. Systems include special computer hardware and software implementing novel control laws involving terminal sliding modes of motion: closed-loop combination of robot and terminal controller converge, in finite time, to point of stable equilibrium in abstract space of velocity and/or position coordinates applicable to particular control problem.
Nonlinear Mirror Modes in Space Plasmas
Sulem, P -L
2011-01-01
Since the first observations by Kaufmann et al.\\ (1970), special attention has been paid to static pressure-balanced structures in the form of magnetic holes or humps observed in regions of the solar wind and of planetary magnetosheaths where the $\\beta$ parameter is relatively large and the ion perpendicular temperature exceeds the parallel one. Although alternative interpretations have been proposed, these structures are usually viewed as associated with the mirror instability discovered in 1957 by Vedenov and Sagdeev. After reviewing observational results provided by satellite missions, high-resolution numerical simulations of the Vlasov--Maxwell equations together with asymptotic and phenomenological models of the nonlinear dynamics near the instability threshold are discussed. The constraining effect of the mirror instability on the temperature anisotropy associated with a dominant perpendicular ion heating observed in the solar wind is reported, and recent simulations of this phenomenon based on an elab...
WEBnm@: a web application for normal mode analyses of proteins
Directory of Open Access Journals (Sweden)
Reuter Nathalie
2005-03-01
Full Text Available Abstract Background Normal mode analysis (NMA has become the method of choice to investigate the slowest motions in macromolecular systems. NMA is especially useful for large biomolecular assemblies, such as transmembrane channels or virus capsids. NMA relies on the hypothesis that the vibrational normal modes having the lowest frequencies (also named soft modes describe the largest movements in a protein and are the ones that are functionally relevant. Results We developed a web-based server to perform normal modes calculations and different types of analyses. Starting from a structure file provided by the user in the PDB format, the server calculates the normal modes and subsequently offers the user a series of automated calculations; normalized squared atomic displacements, vector field representation and animation of the first six vibrational modes. Each analysis is performed independently from the others and results can be visualized using only a web browser. No additional plug-in or software is required. For users who would like to analyze the results with their favorite software, raw results can also be downloaded. The application is available on http://www.bioinfo.no/tools/normalmodes. We present here the underlying theory, the application architecture and an illustration of its features using a large transmembrane protein as an example. Conclusion We built an efficient and modular web application for normal mode analysis of proteins. Non specialists can easily and rapidly evaluate the degree of flexibility of multi-domain protein assemblies and characterize the large amplitude movements of their domains.
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...
Quasi-normal modes of superfluid neutron stars
Gualtieri, L; Gusakov, M E; Chugunov, A I
2014-01-01
We study non-radial oscillations of neutron stars with superfluid baryons, in a general relativistic framework, including finite temperature effects. Using a perturbative approach, we derive the equations describing stellar oscillations, which we solve by numerical integration, employing different models of nucleon superfluidity, and determining frequencies and gravitational damping times of the quasi-normal modes. As expected by previous results, we find two classes of modes, associated to superfluid and non-superfluid degrees of freedom, respectively. We study the temperature dependence of the modes, finding that at specific values of the temperature, the frequencies of the two classes of quasi-normal modes show avoided crossings, and their damping times become comparable. We also show that, when the temperature is not close to the avoided crossings, the frequencies of the modes can be accurately computed by neglecting the coupling between normal and superfluid degrees of freedom. Our results have potential...
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode (SM) based identifier to deal wit h the parameter identification problem for a class of parameter uncertain nonlin ear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonline ar system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
The nonlinear evolution of modes on unstable stratified shear layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1993-06-01
The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.
Nonlinear plastic modes in disordered solids.
Gartner, Luka; Lerner, Edan
2016-01-01
We propose a theoretical framework within which a robust micromechanical definition of precursors to plastic instabilities, often termed soft spots, naturally emerges. They are shown to be collective displacements (modes) z[over ̂] that correspond to local minima of a barrier function b(z[over ̂]), which depends solely on inherent structure information. We demonstrate how some heuristic searches for local minima of b(z[over ̂]) can a priori detect the locus and geometry of imminent plastic instabilities with remarkable accuracy, at strains as large as γ_{c}-γ∼10^{-2} away from the instability strain γ_{c}. Our findings suggest that the a priori detection of the entire field of soft spots can be effectively carried out by a systematic investigation of the landscape of b(z[over ̂]).
Edge localized mode rotation and the nonlinear dynamics of filaments
Energy Technology Data Exchange (ETDEWEB)
Morales, J. A.; Bécoulet, M.; Garbet, X.; Dif-Pradalier, G.; Huijsmans, G. T. A.; Fil, A.; Nardon, E.; Passeron, C.; Latu, G. [CEA, IRFM, 13108 St. Paul-Lez-Durance (France); Orain, F.; Hoelzl, M. [Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching (Germany); Pamela, S. [CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom); Cahyna, P. [Institute of Plasma Physics ASCR, Za Slovankou 1782/3, 182 00 Prague 8 (Czech Republic)
2016-04-15
Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.
Edge localized mode rotation and the nonlinear dynamics of filaments
Morales, J. A.; Bécoulet, M.; Garbet, X.; Orain, F.; Dif-Pradalier, G.; Hoelzl, M.; Pamela, S.; Huijsmans, G. T. A.; Cahyna, P.; Fil, A.; Nardon, E.; Passeron, C.; Latu, G.
2016-04-01
Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.
Assessing the Comprehensive Seismic Earth Model using normal mode data
Koelemeijer, Paula; Afanasiev, Michael; Fichtner, Andreas; Gokhberg, Alexey
2016-04-01
Advances in computational resources and numerical methods allow the simulation of realistic seismic wave propagation through complex media, while ensuring that the complete wave field is correctly represented in synthetic seismograms. This full waveform inversion is widely applied on regional and continental scales, where particularly dense data sampled can be achieved leading to an increased resolution in the obtained model images. On a global scale, however, full waveform tomography is still and will continue to be limited to longer length scales due to the large computational costs. Normal mode tomography provides an alternative fast full waveform approach for imaging seismic structures in a global way. Normal modes are not limited by the poor station-earthquake distribution and provide sensitivity to density structure. Using normal modes, a more robust long wavelength background model can be obtained, leading to more accurate absolute velocity models for tectonic and mineral physics interpretations. In addition, it is vital to combine all seismic data types across accessible periods to obtain a more complete, consistent and interpretable image of the Earth's interior. Here, we aim to combine the globally sensitive long period normal modes with shorter period full waveform modelling within the multi-scale framework of the Comprehensive Seismic Earth Model (CSEM). The multi-scale inversion framework of the CSEM allows exploitation of the full waveform capacity on both sides of the seismic spectrum. As the CSEM includes high-resolution subregions with velocity variations at much shorter wavelengths than normal modes could constrain, the question arises whether these small-scale variations are noticeable in normal mode data, and which modes respond in particular. We report here on experiments in which we address these questions. We separately investigate the effects of small-scale variations in shear-wave velocity and compressional wave velocity compared to the
Optical surface modes in the presence of nonlinearity and disorder
Molina, M I; Tsironis, G P
2011-01-01
We investigate numerically the effect of the competition of disorder, nonlinearity, and boundaries on the Anderson localization of light waves in finite-size, one-dimensional waveguide arrays. Using the discrete Anderson - nonlinear Schr\\"odinger equation, the propagation of the mode amplitudes up to some finite distance is monitored. The analysis is based on the calculated localization length and the participation number, two standard measures for the statistical description of Anderson localization. For relatively weak disorder and nonlinearity, a higher disorder strength is required to achieve the same degree of localization at the edge than in the interior of the array, in agreement with recent experimental observations in the linear regime. However, for relatively strong disorder and/or nonlinearity, this behavior is reversed and it is now easier to localize an excitation at the edge than in the interior.
Fuzzy fractional order sliding mode controller for nonlinear systems
Delavari, H.; Ghaderi, R.; Ranjbar, A.; Momani, S.
2010-04-01
In this paper, an intelligent robust fractional surface sliding mode control for a nonlinear system is studied. At first a sliding PD surface is designed and then, a fractional form of these networks PDα, is proposed. Fast reaching velocity into the switching hyperplane in the hitting phase and little chattering phenomena in the sliding phase is desired. To reduce the chattering phenomenon in sliding mode control (SMC), a fuzzy logic controller is used to replace the discontinuity in the signum function at the reaching phase in the sliding mode control. For the problem of determining and optimizing the parameters of fuzzy sliding mode controller (FSMC), genetic algorithm (GA) is used. Finally, the performance and the significance of the controlled system two case studies (robot manipulator and coupled tanks) are investigated under variation in system parameters and also in presence of an external disturbance. The simulation results signify performance of genetic-based fuzzy fractional sliding mode controller.
Kerr-lens Mode Locking Without Nonlinear Astigmatism
Yefet, Shi; Pe'er, Avi
2013-01-01
We demonstrate a Kerr-lens mode locked folded cavity using a planar (non-Brewster) Ti:sapphire crystal as a gain and Kerr medium, thus cancelling the nonlinear astigmatism caused by a Brewster cut Kerr medium. Our method uses a novel cavity folding in which the intra-cavity laser beam propagates in two perpendicular planes such that the astigmatism of one mirror is compensated by the other mirror, enabling the introduction of an astigmatic free, planar-cut gain medium. We demonstrate that this configuration is inherently free of nonlinear astigmatism, which in standard cavity folding needs a special power specific compensation.
Reliability optimization of friction-damped systems using nonlinear modes
Krack, Malte; Tatzko, Sebastian; Panning-von Scheidt, Lars; Wallaschek, Jörg
2014-06-01
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is achieved subject to parameter uncertainties. The practicability of the approach regarding the extensive amount of required design evaluations is strictly related to the computational efficiency of the nonlinear dynamic analysis. Therefore, it is proposed to employ a recently developed parametric reduced order model (ROM) based on nonlinear modes of vibration, which can facilitate a decrease of the computational burden by several orders of magnitude.
Quasi-Normal Modes of Stars and Black Holes
Directory of Open Access Journals (Sweden)
Kokkotas Kostas
1999-01-01
Full Text Available Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman and relativistic stars (non-rotating and slowly-rotating. The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.
Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes
Kirkendall, Christopher R.; Kwon, Jae W.
2016-03-01
Nonlinear modal interactions have recently become the focus of intense research in micro- and nanoscale resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. However, our understanding of modal coupling is largely restricted to clamped-clamped beams, and lacking in systems with both geometric and material nonlinearities. Here we report multistable energy transfer between internally resonant modes of an electroelastic crystal plate and use a mixed analytical-numerical approach to provide new insight into these complex interactions. Our results reveal a rich bifurcation structure marked by nested regions of multistability. Even the simple case of two coupled modes generates a host of topologically distinct dynamics over the parameter space, ranging from the usual Duffing bistability to complex multistable behaviour and quasiperiodic motion.
PV Degradation Curves: Non-Linearities and Failure Modes
Energy Technology Data Exchange (ETDEWEB)
Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill; Kurtz, Sarah R.
2016-09-03
Photovoltaic (PV) reliability and durability have seen increased interest in recent years. Historically, and as a preliminarily reasonable approximation, linear degradation rates have been used to quantify long-term module and system performance. The underlying assumption of linearity can be violated at the beginning of the life, as has been well documented, especially for thin-film technology. Additionally, non-linearities in the wear-out phase can have significant economic impact and appear to be linked to different failure modes. In addition, associating specific degradation and failure modes with specific time series behavior will aid in duplicating these degradation modes in accelerated tests and, eventually, in service life prediction. In this paper, we discuss different degradation modes and how some of these may cause approximately linear degradation within the measurement uncertainty (e.g., modules that were mainly affected by encapsulant discoloration) while other degradation modes lead to distinctly non-linear degradation (e.g., hot spots caused by cracked cells or solder bond failures and corrosion). The various behaviors are summarized with the goal of aiding in predictions of what may be seen in other systems.
Instantaneous normal mode analysis of melting of finite dust clusters.
Melzer, André; Schella, André; Schablinski, Jan; Block, Dietmar; Piel, Alexander
2012-06-01
The experimental melting transition of finite two-dimensional dust clusters in a dusty plasma is analyzed using the method of instantaneous normal modes. In the experiment, dust clusters are heated in a thermodynamic equilibrium from a solid to a liquid state using a four-axis laser manipulation system. The fluid properties of the dust cluster, such as the diffusion constant, are measured from the instantaneous normal mode analysis. Thereby, the phase transition of these finite clusters is approached from the liquid phase. From the diffusion constants, unique melting temperatures have been assigned to dust clusters of various sizes that very well reflect their dynamical stability properties.
Quasi-Normal Modes and Gravitational Wave Astronomy
Ferrari, V
2007-01-01
We review the main results obtained in the literature on quasi-normal modes of compact stars and black holes, in the light of recent exciting developments of gravitational wave detectors. Quasi-normal modes are a fundamental feature of the gravitational signal emitted by compact objects in many astrophysical processes; we will show that their eigenfrequencies encode interesting information on the nature and on the inner structure of the emitting source and we will discuss whether we are ready for a gravitational wave asteroseismology.
Normalization of sunspot cycles and eigen mode analysis
Institute of Scientific and Technical Information of China (English)
徐文耀
2002-01-01
The smoothed monthly sunspot numbers of the previous 22 complete sunspot cycles are normalized in time domain, and then an eigen mode analysis is carried out to draw the principle factors (or components) in the cycles. The results show that the main characteristics of the solar cycles can be described fairly well by the first 5 eigen modes. The obtained eigen modes are used to predict the declining phase of cycle 23 on the basis of the data prior to its maximum. The prediction indicates that cycle 23 will last for 127 months to December 2006, with the minimum of 6.2.
Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems
Junhai Luo; Heng Liu
2014-01-01
This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of th...
Nonlinear Interaction of Transversal Modes in a CO2 Laser
Lopez-Ruiz, Ricardo; Mindlin, G. B.; Perez-Garcia, C.; Tredicce, J. R.
2002-01-01
We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes ($l = \\pm 1$) in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by some symmetry-breaking effects that still preserve the $Z_2$ symmetry. The pattern dynamics near this codimension two bifurcation under such symmetries is described. This dynamics changes drastically when the laser properties are modified.
GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems
Directory of Open Access Journals (Sweden)
W. L. Chiang
2008-11-01
Full Text Available Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC or an adaptive fuzzy sliding mode controller (AFSMC capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.
Nonlinear Integral Sliding Mode Control for a Second Order Nonlinear System
Directory of Open Access Journals (Sweden)
Xie Zheng
2015-01-01
Full Text Available A nonlinear integral sliding-mode control (NISMC scheme is proposed for second order nonlinear systems. The new control scheme is characterized by a nonlinear integral sliding manifold which inherits the desired properties of the integral sliding manifold, such as robustness to system external disturbance. In particular, compared with four kinds of sliding mode control (SMC, the proposed control scheme is able to provide better transient performances. Furthermore, the proposed scheme ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance is proved by Lyapunov stability theory and LaSalle invariance principle. Finally, both the theoretical analysis and simulation examples demonstrate the validity of the proposed scheme.
Nonlinear electron transport in normally pinched-off quantum wire
Novoselov, K.S.; Dubrovskii, Yu. V.; Sablikov, V. A.; Ivanov, D. Yu.; Vdovin, E. E.; Khanin, Yu N.; Tulin, V. A.; Esteve, D.; Beaumont, S.
2000-01-01
Nonlinear electron transport in normally pinched-off quantum wires was studied. The wires were fabricated from AlGaAs/GaAs heterostructures with high-mobility two-dimensional electron gas by electron beam lithography and following wet etching. At certain critical source-drain voltage the samples exhibited a step rise of the conductance. The differential conductance of the open wires was noticeably lower than e^2/h as far as only part of the source-drain voltage dropped between source contact ...
CASTOR: Normal-mode analysis of resistive MHD plasmas
Kerner, W.; Goedbloed, J. P.; Huysmans, G. T. A.; Poedts, S.; Schwarz, E.
1998-01-01
The CASTOR (complex Alfven spectrum of toroidal plasmas) code computes the entire spectrum of normal-modes in resistive MHD for general tokamak configurations. The applied Galerkin method, in conjunction with a Fourier finite-element discretisation, leads to a large scale eigenvalue problem A (x)
Bergquist, R. R.; Carlson, R. G.; Landgrebe, A. J.; Egolf, T. A.
1974-01-01
This User's Manual was prepared to provide the engineer with the information required to run the coupled mode version of the Normal Modes Rotor Aeroelastic Analysis Computer Program. The manual provides a full set of instructions for running the program, including calculation of blade modes, calculations of variable induced velocity distribution and the calculation of the time history of the response for either a single blade or a complete rotor with an airframe (the latter with constant inflow).
Electromagnetic normal modes and Casimir effects in layered structures
Sernelius, Bo E
2014-01-01
We derive a general procedure for finding the electromagnetic normal modes in layered structures. We apply this procedure to planar, spherical and cylindrical structures. These normal modes are important in a variety of applications. They are the only input needed in calculations of Casimir interactions. We present explicit expression for the condition for modes and Casimir energy for a large number of specific geometries. The layers are allowed to be two-dimensional so graphene and graphene-like sheets as well as two-dimensional electron gases can be handled within the formalism. Also forces on atoms in layered structures are obtained. One side-result is the van der Waals and Casimir-Polder interaction between two atoms.
The non-linear evolution of edge localized modes
Energy Technology Data Exchange (ETDEWEB)
Wenninger, Ronald
2013-01-09
Edge localized modes (ELMs) are instabilities in the edge of tokamak plasmas in the high confinement regime (H-mode). Without them the edge transport in ordinary H-mode plasmas is too low to establish a stationary situation. However in a future device large unmitigated ELMs are believed to cause divertor power flux densities far in excess of tolerable material limits. Hence the size of energy loss per ELM and the resulting ELM frequency must be controlled. To proceed in understanding how the ELM size is determined and how ELM mitigation methods work it is necessary to characterize the non-linear evolution of pedestal erosion. In order to achieve this experimental data is compared to the results of ELM simulations with the code JOREK (reduced MHD, non-linear) applying a specially developed synthetic magnetic diagnostic. The experimental data are acquired by several fast sampling diagnostics at the experiments ASDEX Upgrade and TCV at a large number of toroidal/poloidal positions. A central element of the presented work is the detailed characterization of dominant magnetic perturbations during ELMs. These footprints of the instability can be observed most intensely in close temporal vicinity to the onset of pedestal erosion. Dominant magnetic perturbations are caused by current perturbations located at or inside the last closed flux surface. In ASDEX Upgrade under certain conditions dominant magnetic perturbations like other H-mode edge instabilities display a similarity to solitons. Furthermore - as expected - they are often observed to be correlated to a perturbation of electron temperature. In TCV it is possible to characterize the evolution of the toroidal structure of dominant magnetic perturbations. Between growing above the level of background fluctuations and the maximum perturbation level for all time instance a similar toroidal structure is observed. This rigid mode-structure is an indication for non-linear coupling. Most frequently the dominant toroidal
Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.
Nagarale, Ravindrakumar M; Patre, B M
2014-05-01
This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller.
Quasi-Normal Modes from Non-Commutative Matrix Dynamics
Aprile, Francesco
2016-01-01
We explore the connection between the process of relaxation in the BMN matrix model and the physics of black holes in AdS/CFT. Focusing on Dyson-fluid solutions of the matrix model, we perform numerical simulations of the real time dynamics of the system. By quenching the equilibrium distribution we study the quasi-normal oscillations of scalar single trace observables, we isolate the lowest quasi-normal mode, and we determine its frequencies as function of the energy. Considering the BMN matrix model as a truncation of $\\mathcal{N}=4$ SYM, we also compute the frequencies of the quasi-normal modes of the dual scalar fields in the AdS$_5$-Schwarzschild background. We compare the results of the black hole and the classical Dyson fluid, and we point out a correspondence between the two descriptions.
Resolving nanophotonic spectra with quasi-normal modes (Conference Presentation)
Powell, David A.
2016-09-01
Many nanophotonic systems are strongly coupled to radiating waves, or suffer significant dissipative losses. Furthermore, they may have complex shapes which are not amenable to closed form calculations. This makes it challenging to determine their modes without resorting to quasi-static or point dipole approximations. To solve this problem, the quasi-normal modes (QNMs) are found from an integral equation model of the particle. These give complex frequencies where excitation can be supported without any incident field. The corresponding eigenvectors yield the modal distributions, which are non-orthogonal due to the non-Hermitian nature of the system. The model based on quasi-normal modes is applied to plasmonic and dielectric particles, and compared with a spherical multipole decomposition. Only with the QNMs is it possible to resolve all features of the extinction spectrum, as each peak in the spectrum can be attributed to a particular mode. In contrast, many of the multipole coefficient have multiple peaks and dips. Furthermore, by performing a multipolar decomposition of each QNM, the spectrum of multipole coefficients is explained in terms of destructive interference between modes of the same multipole order.
Nonlinear dynamics of hidden modes in a system with internal symmetry
Perchikov, Nathan; Gendelman, O. V.
2016-09-01
We consider a discrete dynamical system with internal degrees of freedom (DOF). Due to the symmetry between the internal DOFs, certain internal modes cannot be excited by external forcing (in a case of linear interactions) and thus are considered "hidden". If such a system is weakly asymmetric, the internal modes remain approximately "hidden" from the external excitation, given that small damping is taken into account. However, already in the case of weak cubic nonlinearity, these hidden modes can be excited, even as the exact symmetry is preserved. This excitation occurs through parametric resonance. Floquet analysis reveals instability patterns for the explored modes. To perform this analysis with the required accuracy, we suggest a special method for obtaining the Fourier series of the unperturbed solution for the nonlinear normal mode. This method does not require explicit integration of the arising quadratures. Instead, it employs expansion of the solution at the stage of the implicit quadrature in terms of Chebyshev polynomials. The emerging implicit equations are solved by using a fixed-point iteration scheme. Poincaré sections help to clarify the correspondence between the loss of stability of the modes and the global structure of the dynamical flow. In particular, the conditions for intensive energy exchange in the system are characterized.
Directory of Open Access Journals (Sweden)
Mostafa H. Ali, Ahmed E. Elsamahy, Maher A. Farhoud and Taymour A. Hamdalla
2012-10-01
Full Text Available Near field distribution, propagation constant and dispersion characteristics of nonlinear single-mode optical fibers have been investigated. Shooting-method technique is used and implemented into a computer code for both profiles of step-index and graded-index fibers. An error function is defined to estimate the discrepancy between the expected electric-field radial derivative at the core-cladding interface and that obtained by numerically integrating the wave equation through the use of Runge-Kutta method. All of the above calculations done under the ocean depth in which the depth will affect the refractive index that have a direct effect on all the optical fiber parameters.KeyWords: Nonlinear refractive index, Normalized propagation constant, Mode delay factor, Material dispersion, Waveguide dispersion.
Tunable rotary orbits of matter-wave nonlinear modes in attractive Bose-Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
He, Y J; Wang, H Z [State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-Sen University, Guangzhou, 510275 (China); Malomed, Boris A [Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel); Mihalache, Dumitru [Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest 077125 (Romania)], E-mail: stswhz@mail.sysu.edu.cn
2008-03-14
We demonstrate that by spatially modulating the Bessel optical lattice where a Bose-Einstein condensate is loaded, we get tunable rotary orbits of nonlinear lattice modes. We show that the radially expanding or shrinking Bessel lattice can drag the nonlinear localized modes to orbits of either larger or smaller radii and the rotary velocity of nonlinear modes can be changed accordingly. The localized modes can even be transferred to the Bessel lattice core when the localized modes' rotations are stopped. Effects beyond the quasi-particle approximation such as destruction of the nonlinear modes by nonadiabatic dragging are also explored.
Adaptive Fractional Fuzzy Sliding Mode Control for Multivariable Nonlinear Systems
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available This paper presents a robust adaptive fuzzy sliding mode control method for a class of uncertain nonlinear systems. The fractional order calculus is employed in the parameter updating stage. The underlying stability analysis as well as parameter update law design is carried out by Lyapunov based technique. In the simulation, two examples including a comparison with the traditional integer order counterpart are given to show the effectiveness of the proposed method. The main contribution of this paper consists in the control performance is better for the fractional order updating law than that of traditional integer order.
Entanglement Dynamics in Typical Local- and Normal-Mode Molecules
Institute of Scientific and Technical Information of China (English)
HOU Xi-Wen; WAN Ming-Fang; MA Zhong-Qi
2007-01-01
The entanglement dynamics of two stretching vibrations in theoretically typical local- and normal-mode molecules and realistic molecules H2O and SO2 in an algebraic model is studied in terms of the reduced-density linear entropy with initial entangled states taken to be two-mode squeezed vacuum states. It is shown that the behaviour of the entropy in theoretically typical molecules appears to be more regular than that in realistic ones, and that the entropy becomes irregular as the amplitude of two-mode squeezed vacuum states increases. For initial states with a small amplitude, it is demonstrated that the periodicity and the "classical" beat phenomenon of the entropy occur with the beat in theoretically typical molecules being more regular than that in realistic molecules H2O and SO2.
Directory of Open Access Journals (Sweden)
Predrag Pejovic
2013-12-01
Full Text Available Application of a single phase rectifier as an example in teaching circuit modeling, normalization, operating modes of nonlinear circuits, and circuit analysis methods is proposed.The rectifier supplied from a voltage source by an inductive impedance is analyzed in the discontinuous as well as in the continuous conduction mode. Completely analytical solution for the continuous conduction mode is derived. Appropriate numerical methods are proposed to obtain the circuit waveforms in both of the operating modes, and to compute the performance parameters. Source code of the program that performs such computation is provided.
Zaytsev, Alexey; Lin, Chih-Hsuan; You, Yi-Jing; Chung, Chia-Chun; Wang, Chi-Luen; Pan, Ci-Ling
2013-07-01
We report generation of broadband supercontinuum (SC) by noise-like pulses (NLPs) with a central wavelength of 1070 nm propagating through a long piece of standard single-mode fibers (~100 meters) in normal dispersion region far from the zero-dispersion point. Theoretical simulations indicate that the physical mechanism of SC generation is due to nonlinear effects in fibers. The cascaded Raman scattering is responsible for significant spectral broadening in the longer wavelength regions whereas the Kerr effect results in smoothing of SC generated spectrum. The SC exhibits low threshold (43 nJ) and a flat spectrum over 1050-1250 nm.
Normal mode-based approaches in receptor ensemble docking.
Cavasotto, Claudio N
2012-01-01
Explicitly accounting for target flexibility in docking still constitutes a difficult challenge due to the high dimensionality of the conformational space to be sampled. This especially applies to the high-throughput scenario, where the screening of hundreds of thousands compounds takes place. The use of multiple receptor conformations (MRCs) to perform ensemble docking in a sequential fashion is a simple but powerful approach that allows to incorporate binding site structural diversity in the docking process. Whenever enough experimental structures to build a diverse ensemble are not available, normal mode analysis provides an appealing and efficient approach to in silico generate MRCs by distortion along few low-frequency modes that represent collective mid- and large-scale displacements. In this way, the dimension of the conformational space to be sampled is heavily reduced. This methodology is especially suited to incorporate target flexibility at the backbone level. In this chapter, the main components of normal mode-based approaches in the context of ensemble docking are presented and explained, including the theoretical and practical considerations needed for the successful development and implementation of this methodology.
Normal modes of relativistic systems in post Newtonian approximation
Sobouti, Y
1998-01-01
We use the post Newtonian (pn) order of Liouville's equation (pnl) to study the normal modes of oscillation of a relativistic system. In addition to classical modes, we are able to isolate a new class of oscillations that arise from perturbations of the space-time metric. In the first pn order; a) their frequency is an order q smaller than the classical frequencies, where q is a pn expansion parameter; b) they are not damped, for there is no gravitational wave radiation in this order; c) they are not coupled with the classical modes in q order; d) in a spherically symmetric system, they are designated by a pair of angular momentum eigennumbers, (j,m), of a pair of phase space angular momentum operators (J^2,J_z). Hydrodynamical behavior of these new modes is also investigated; a) they do not disturb the equilibrium of the classical fluid; b) they generate macroscopic toroidal motions that in classical case would be neutral; c) they give rise to an oscillatory g_{0i} component of the metric tensor that otherwi...
Nonlinear high-order mode locking in stochastic sensory neurons
Rowe, Michael; Afghan, Muhammad; Neiman, Alexander
2004-03-01
Excitable systems demonstrate various mode locking regimes when driven by periodic external signals. With noise taken into account, such regimes represent complex nonlinear responses which depend crucially on the frequency and amplitude of the periodic drive as well as on the noise intensity. We study this using a computational model of a stochastic Hodgkin-Huxley neuron in combination with the turtle vestibular sensory system as an experimental model. A bifurcation analysis of the model is performed. Extracellular recordings from primary vestibular afferent neurons with two types of stimuli are used in the experimental study. First, mechanical stimuli applied to the labyrinth allow us to study the responses of the entire system, including transduction by the hair cells and spike generation in the primary afferents. Second, a galvanic stimuli applied directly to an afferent are used to study the responses of afferent spike generator directly. The responses to galvanic stimuli reveal multiple high-order mode locking regimes which are well reproduced in numerical simulation. Responses to mechanical stimulation are characterized by larger variability so that fewer mode-locking regimes can be observed.
Nonlinear asymmetric tearing mode evolution in cylindrical geometry
Teng, Q.; Ferraro, N.; Gates, D. A.; Jardin, S. C.; White, R. B.
2016-10-01
The growth of a tearing mode is described by reduced MHD equations. For a cylindrical equilibrium, tearing mode growth is governed by the modified Rutherford equation, i.e., the nonlinear Δ'(w ) . For a low beta plasma without external heating, Δ'(w ) can be approximately described by two terms, Δ'ql(w ), ΔA'(w ) [White et al., Phys. Fluids 20, 800 (1977); Phys. Plasmas 22, 022514 (2015)]. In this work, we present a simple method to calculate the quasilinear stability index Δql' rigorously, for poloidal mode number m ≥2 . Δql' is derived by solving the outer equation through the Frobenius method. Δ'ql is composed of four terms proportional to: constant Δ'0 , w, w ln w , and w2. ΔA' is proportional to the asymmetry of island that is roughly proportional to w. The sum of Δql' and ΔA' is consistent with the more accurate expression calculated perturbatively [Arcis et al., Phys. Plasmas 13, 052305 (2006)]. The reduced MHD equations are also solved numerically through a 3D MHD code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)]. The analytical expression of the perturbed helical flux and the saturated island width agree with the simulation results. It is also confirmed by the simulation that the ΔA' has to be considered in calculating island saturation.
Mortensen, Henrik Lund; Mølmer, Klaus; Andersen, Christian Kraglund
2016-11-01
We present a method to identify the coupled, normal modes of a superconducting transmission line with an embedded lumped element circuit. We evaluate the effective transmission-line nonlinearities in the case of Kerr-like Josephson interactions in the circuit and in the case where the embedded circuit constitutes a qubit degree of freedom, which is Rabi coupled to the field in the transmission line. Our theory quantitatively accounts for the very high and positive Kerr nonlinearities observed in a recent experiment [M. Rehák, P. Neilinger, M. Grajcar, G. Oelsner, U. Hübner, E. Il'ichev, and H.-G. Meyer, Appl. Phys. Lett. 104, 162604 (2014), 10.1063/1.4873719], and we can evaluate the accomplishments of modified versions of the experimental circuit.
Linear and nonlinear analysis of normal and CAD-affected heart rate signals.
Acharya, U Rajendra; Faust, Oliver; Sree, Vinitha; Swapna, G; Martis, Roshan Joy; Kadri, Nahrizul Adib; Suri, Jasjit S
2014-01-01
Coronary artery disease (CAD) is one of the dangerous cardiac disease, often may lead to sudden cardiac death. It is difficult to diagnose CAD by manual inspection of electrocardiogram (ECG) signals. To automate this detection task, in this study, we extracted the heart rate (HR) from the ECG signals and used them as base signal for further analysis. We then analyzed the HR signals of both normal and CAD subjects using (i) time domain, (ii) frequency domain and (iii) nonlinear techniques. The following are the nonlinear methods that were used in this work: Poincare plots, Recurrence Quantification Analysis (RQA) parameters, Shannon entropy, Approximate Entropy (ApEn), Sample Entropy (SampEn), Higher Order Spectra (HOS) methods, Detrended Fluctuation Analysis (DFA), Empirical Mode Decomposition (EMD), Cumulants, and Correlation Dimension. As a result of the analysis, we present unique recurrence, Poincare and HOS plots for normal and CAD subjects. We have also observed significant variations in the range of these features with respect to normal and CAD classes, and have presented the same in this paper. We found that the RQA parameters were higher for CAD subjects indicating more rhythm. Since the activity of CAD subjects is less, similar signal patterns repeat more frequently compared to the normal subjects. The entropy based parameters, ApEn and SampEn, are lower for CAD subjects indicating lower entropy (less activity due to impairment) for CAD. Almost all HOS parameters showed higher values for the CAD group, indicating the presence of higher frequency content in the CAD signals. Thus, our study provides a deep insight into how such nonlinear features could be exploited to effectively and reliably detect the presence of CAD. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Yang, T C
2014-02-01
This paper applies the mode coupling equation to calculate the mode-coupling matrix for nonlinear internal waves appearing as a train of solitons. The calculation is applied to an individual soliton up to second order expansion in sound speed perturbation in the Dyson series. The expansion is valid so long as the fractional sound speed change due to a single soliton, integrated over range and depth, times the wavenumber is smaller than unity. Scattering between the solitons are included by coupling the mode coupling matrices between the solitons. Acoustic fields calculated using this mode-coupling matrix formulation are compared with that obtained using a parabolic equation (PE) code. The results agree very well in terms of the depth integrated acoustic energy at the receivers for moving solitary internal waves. The advantages of using the proposed approach are: (1) The effects of mode coupling can be studied as a function of range and time as the solitons travel along the propagation path, and (2) it allows speedy calculations of sound propagation through a packet or packets of solitons saving orders of magnitude computations compared with the PE code. The mode coupling theory is applied to at-sea data to illustrate the underlying physics.
The normal modes of lattice vibrations of ice XI
Zhang, Peng; Wang, Zhe; Lu, Ying-Bo; Ding, Zheng-Wen
2016-07-01
The vibrational spectrum of ice XI at thermal wavelengths using the CASTEP code, a first-principles simulation method, is investigated. A dual-track approach is constructed to verify the validity for the computational phonon spectrum: collate the simulated spectrum with inelastic neutron scattering experiments and assign the photon scattering peaks according to the calculated normal vibration frequencies. The 33 optical normal vibrations at the Brillouin center are illustrated definitely from the ab initio outcomes. The depolarizing field effect of the hydrogen bond vibrations at frequencies of 229 cm‑1 and 310 cm‑1 is found to agree well with the LST relationship. It is a convincing evidence to manifest the LO-TO splitting of hydrogen bonds in ice crystal. We attribute the two hydrogen bond peaks to the depolarization effect and apply this viewpoint to ordinary ice phase, ice Ih, which is difficult to analyse their vibration modes due to proton disorder.
Kelvin waves in ECMWF analysis: normal-mode diagnostics
Blaauw, Marten; Zagar, Nedjeljka
2013-04-01
Equatorial Kelvin waves show a large spread in spatial and temporal variability similar to their source of tropical convective forcing. Once decoupled from their source, Kelvin waves are modulated during their ascent by changes in the background wind and stability. In this presentation, we focus on the seasonal and interannual variability of Kelvin waves in relation with variability of (i) tropical convection and (ii) background zonal wind and static stability. Global data is extracted from ECMWF operational analysis from January 2007 till May 2011 on 91 model levels (top level at 0.01 hPa) and ~ 25 km horizontal resolution. Using three-dimensional orthogonal normal-mode expansions, we project input mass and wind data simultaneously onto balanced rotational modes and unbalanced inertia-gravity modes including Kelvin modes. Next, an inverse transformation of Kelvin modes to physical space is performed under the linearity assumption, allowing a study on the spatial and temporal variability of Kelvin wave zonal wind and temperature. Results show an annual cycle in KW zonal wind in agreement with other studies. Minima resp. maxima in zonal wind amplitudes are found in the Indian ocean resp. Western Pacific and are most pronounced in the tropical tropopause at 150 hPa in January and 100 hPa in July. The annual cycle is enhanced (reduced) through interaction with a descending westerly QBO phase and enhanced (reduced) convective forcing. We also note a gradual eastward shift of KW zonal wind maxima till January 2010 in correspondence with an eastward shift of tropical convection.
Nonlinear interface optical switch structure for dual mode switching revisited
Bussjager, Rebecca J.; Osman, Joseph M.; Chaiken, Joseph
1998-07-01
There is a need for devices which will allow integration of photonic/optical computing subsystems into electronic computing architectures. This presentation reviews the nonlinear interface optical switch (NIOS) concept and then describes a new effect, the erasable optical memory (EOM) effect. We evaluate an extension of the NIOS device to allow simultaneous optical/electronic, i.e. dual mode, switching of light utilizing the EOM effect. Specific devices involve the fabrication of thin film tungsten (VI) oxide (WO3) and tungsten (V) oxide (W2O5) on the hypotenuse of glass (BK-7), fused silica (SiO2) and zinc selenide (ZnSe) right angle prisms. Chemical reactions and temporal response tests were performed and are discussed.
Chen, Yong; Yan, Zhenya
2017-01-01
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
Black holes in nonlinear electrodynamics: quasi-normal spectra and parity splitting
Chaverra, Eliana; Moreno, Claudia; Sarbach, Olivier
2016-01-01
We discuss the quasi-normal oscillations of black holes which are sourced by a nonlinear electrodynamic field. While previous studies have focused on the computation of quasi-normal frequencies for the wave or higher spin equation on a fixed background geometry described by such black holes, here we compute for the first time the quasi-normal frequencies for the coupled electromagnetic-gravitational linear perturbations. To this purpose, we consider a parametrized family of Lagrangians for the electromagnetic field which contains the Maxwell Lagrangian as a special case. In the Maxwell case, the unique spherically symmetric black hole solutions are described by the Reissner-Nordstr\\"om family and in this case it is well-known that the quasi-normal spectra in the even- and odd-parity sectors are identical to each other. However, when moving away from the Maxwell case, we obtain deformed Reissner-Nordstr\\"om black holes, and we show that in this case there is a parity splitting in the quasi-normal mode spectra....
Nonlinear mode decomposition: A noise-robust, adaptive decomposition method
Iatsenko, Dmytro; McClintock, Peter V. E.; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool—nonlinear mode decomposition (NMD)—which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques—which, together with the adaptive choice of their parameters, make it extremely noise robust—and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.
Iatsenko, Dmytro; McClintock, Peter V E; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Li, Kexuan; Tian, Jinrong; Guoyu, Heyang; Xu, Runqin; Song, Yanrong
2017-04-01
Self-mode-locked noise-like pulses (NLPs) were experimentally investigated from a normal dispersion erbium-doped fiber laser. Different from noise-like pulses with a broadband spectrum, the self-mode-locked NLPs have a narrow optical spectrum of 1-2 nm and hundreds of nanoseconds duration. However, the intra-cavity maximum energy of NLPs is up to 560 nJ without pulse breaking. The higher pulse energy output is promising in the proposed fiber laser. To confirm whether self-mode-locked NLPs are caused by an invisible nonlinear polarization rotation (NPR) mechanism owing to slight residual polarization asymmetry of the fiber and components used, we compared the output characteristics between self-mode-locked NLPs and NPR mode-locked pulses in the same cavity. The experimental results show that the formation mechanism of such self-mode-locked NLPs could be related to a weak NPR effect.
Scherpen, Jacquelien M.A.
2006-01-01
This paper considers the relation between the singular value functions of the nonlinear normalized left coprime factorization (NLCF) and the nonlinear normalized right coprime factorization (NRCF). In previous work a new duality notion gave rise to a relation between the controllability, observabili
Higher and sub-harmonic Lamb wave mode generation due to debond-induced contact nonlinearity
Guha, Anurup; Bijudas, C. R.
2016-04-01
Non-cumulative higher and sub-harmonic Lamb wave mode generation as a result of partial-debond of piezoelectric wafer transducers (PWT) bonded onto an Aluminium plate, is numerically investigated and experimentally validated. The influence of excitation frequency on the extent of nonlinearity due to clapping mechanism of the partially-debonded PWTs is discussed. A set of specific frequency range is arrived at based on the Eigen-value and Harmonic analyses of PWTs used in the model. It is found that, at these frequencies, which are integral multiple of the first width-direction mode of a PWT, significantly higher amplitudes of higher-harmonics are observed. It is also seen that at specific debond-positions and lengths, sharp sub-harmonics in addition to higher-harmonics are present. Signal processing is carried out using Fast Fourier transform, which is normalized for comparisons.
Neural Feedback Passivity of Unknown Nonlinear Systems via Sliding Mode Technique.
Yu, Wen
2015-07-01
Passivity method is very effective to analyze large-scale nonlinear systems with strong nonlinearities. However, when most parts of the nonlinear system are unknown, the published neural passivity methods are not suitable for feedback stability. In this brief, we propose a novel sliding mode learning algorithm and sliding mode feedback passivity control. We prove that for a wide class of unknown nonlinear systems, this neural sliding mode control can passify and stabilize them. This passivity method is validated with a simulation and real experiment tests.
Maksimovic, Milan; Lohmeyer, Manfred; van Groesen, Embrecht W.C.
2008-01-01
Quasi-normal modes are used to directly characterize defect resonances in composite 1D Photonic Crystal structures. Variational coupled mode theory using QNMs enables quantification of the eigenfrequency splitting in composite structures. Also, variational perturbation analysis of complex
Indian Academy of Sciences (India)
P K Karmakar
2007-04-01
Application of inertia-induced acoustic excitation theory offers a new resonant excitation source channel of acoustic turbulence in the transonic domain of plasma flow. In bi-ion plasmas like colloidal plasma, two well-defined transonic points exist corresponding to the parent ion and the dust grain-associated acoustic modes. As usual, the modified ion acoustic mode (also known as dust ion-acoustic (DIA) wave) dynamics associated with parent ion inertia is excitable for both nanoscale- and micronscale-sized dust grains. It is found that the so-called (ion) acoustic mode (also known as dust-acoustic (DA) wave) associated with nanoscale dust grain inertia is indeed resonantly excitable through the active role of weak but finite parent ion inertia. It is interestingly conjectured that the same excitation physics, as in the case of normal plasma sound mode, operates through the active inertial role of plasma thermal species. Details of the nonlinear acoustic mode analyses of current interest in transonic domains of such impure plasmas in hydrodynamic flow are presented.
Integral Terminal Sliding Mode Control for a Class of Nonaffine Nonlinear Systems with Uncertainty
Qiang Zhang; Hongliang Yu; Xiaohong Wang
2013-01-01
This paper is concerned with an integral terminal sliding mode tracking control for a class of uncertain nonaffine nonlinear systems. Firstly, the nonaffine nonlinear systems is approximated to facilitate the desired control design via a novel dynamic modeling technique. Next, for the unmeasured disturbance of nonlinear systems, integral terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to ...
Quasi-Normal Modes of Black Holes in Lovelock Gravity
Yoshida, Daiske
2015-01-01
We study quasi-normal modes of black holes in Lovelock gravity. We formulate the WKB method adapted to Lovelock gravity for the calculation of quasi-normal frequencies (QNFs). As a demonstration, we calculate various QNFs of Lovelock black holes in seven and eight dimensions. We find that the QNFs show remarkable features depending on the coefficients of the Lovelock terms, the species of perturbations, and spacetime dimensions. In the case of the scalar field, when we increase the coefficient of the third order Lovelock term, the real part of QNFs increases, but the decay rate becomes small irrespective of the mass of the black hole. For small black holes, the decay rate ceases to depend on the Gauss-Bonnet term. In the case of tensor type perturbations of the metric field, the tendency of the real part of QNFs is opposite to that of the scalar field. The QNFs of vector type perturbations of the metric show no particular behavior. The behavior of QNFs of the scalar type perturbations of the metric field is s...
Alippi, A.; Biagioni, A.; Germano, M.; Passeri, D.
2008-06-01
Local probing of nonlinear generation of harmonic vibrations has been done on bone plate samples and the evaluation of the nonlinear term is derived from a limited number of cases of bovine thigh bones, that shows that a low level of nonlinearity is present in bone structures. This is consistent with the assumption that in low level nonlinear samples the distribution of harmonic vibrations matches the corresponding power distribution of the fundamental mode.
Nonlinear Coherent Directional Coupler: Coupled Mode Theory and BPM Simulation
National Research Council Canada - National Science Library
Kumbhakar, Dharmadas
2012-01-01
.... The coupling lengths derived from this simulation are compared with coupled mode theories. BPM results for the critical power follow the trend of the coupled mode theories, but it lies in between two coupled mode theories...
Nonlinear breathing modes at a defect site in DNA.
Duduială, Ciprian-Ionuţ; Wattis, Jonathan A D; Dryden, Ian L; Laughton, Charles A
2009-12-01
Molecular-dynamics simulations of a normal DNA duplex show that breathing events typically occur on the microsecond time scale. This paper analyzes a 12 base pairs DNA duplex containing the "rogue" base difluorotoluene (F) in place of a thymine base (T), for which the breathing events occur on the nanosecond time scale. Starting from a nonlinear Klein-Gordon lattice model and adding noise and damping, we obtain a mesoscopic model of the DNA duplex close to that observed in experiments and all-atom molecular dynamics simulations. The mesoscopic model is calibrated to data from the all-atom molecular dynamics package AMBER for a variety of twist angles of the DNA duplex. Defects are considered in the interchain interactions as well as in the along-chain interactions. This paper also discusses the role of the fluctuation-dissipation relations in the derivation of reduced (mesoscopic) models, the differences between the potential of mean force and the potential energies used in Klein-Gordon lattices, and how breathing can be viewed as competition between the along-chain elastic energy and the interchain binding energy.
"Good Vibrations": A workshop on oscillations and normal modes
Barbieri, Sara; Carpineti, Marina; Giliberti, Marco; Rigon, Enrico; Stellato, Marco; Tamborini, Marina
2016-05-01
We describe some theatrical strategies adopted in a two hour workshop in order to show some meaningful experiments and the underlying useful ideas to describe a secondary school path on oscillations, that develops from harmonic motion to normal modes of oscillations, and makes extensive use of video analysis, data logging, slow motions and applet simulations. Theatre is an extremely useful tool to stimulate motivation starting from positive emotions. That is the reason why the theatrical approach to the presentation of physical themes has been explored by the group "Lo spettacolo della Fisica" (http://spettacolo.fisica.unimi.it) of the Physics Department of University of Milano for the last ten years (Carpineti et al., JCOM, 10 (2011) 1; Nuovo Cimento B, 121 (2006) 901) and has been inserted also in the European FP7 Project TEMI (Teaching Enquiry with Mysteries Incorporated, see http://teachingmysteries.eu/en) which involves 13 different partners coming from 11 European countries, among which the Italian (Milan) group. According to the TEMI guidelines, this workshop has a written script based on emotionally engaging activities of presenting mysteries to be solved while participants have been involved in nice experiments following the developed path.
Quasi-Normal Modes for Subtracted Rotating and Magnetised Geometries
Cvetic, M; Saleem, Z H
2014-01-01
We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden SL(2,R) x SL(2,R) x SO(3) symmetry and faithfully model the near horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasi-normal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a BTZ black hole with a a two-sphere. Th...
Non-linear vibrational modes in biomolecules: A periodic orbits description
Energy Technology Data Exchange (ETDEWEB)
Kampanarakis, Alexandros [Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas (FORTH), Vasilika Vouton, Heraklion 71110, Crete (Greece); Farantos, Stavros C., E-mail: farantos@iesl.forth.gr [Department of Chemistry, University of Crete, and Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas (FORTH), Vasilika Vouton, Heraklion 71110, Crete (Greece); Daskalakis, Vangelis; Varotsis, Constantinos [Department of Environmental Science and Technology, Cyprus University of Technology, 31 Archbishop Kyprianos St., P.O. Box 50329, 3603 Lemesos (Cyprus)
2012-05-03
Graphical abstract: Vibrational frequency shifts in Fe{sup IV} = O species of the active site of cytochrome c oxidase are attributed to changes in the surrounding Coulomb field. Periodic orbits analysis assists to find the most anharmonic modes in model biomolecules. Highlights: Black-Right-Pointing-Pointer Periodic orbits are extended to multidimensional potentials of biomolecules. Black-Right-Pointing-Pointer Highly anharmonic vibrational modes and center-saddle bifurcations are detected. Black-Right-Pointing-Pointer Vibrational frequencies shifts in Oxoferryl species of CcO are observed. - Abstract: The vibrational harmonic normal modes of a molecule, which are valid at energies close to an equilibrium point (a minimum, maximum or saddle of the potential energy surface), are extended by periodic orbits to high energies where anharmonicity and coupling of the degrees of freedom are significant. In this way the assignment of the spectra, and thus the extraction of dynamics in highly excited molecules, can be obtained. New vibrational modes emanating from bifurcations of periodic orbits and long living localized trajectories signal the birth and localization of new quantum states. In this article we review and further study non-linear vibrational modes for model biomolecules such as alanine dipeptide and the active site in the oxoferryl oxidation state of the enzyme cytochrome c oxidase. We locate periodic orbits which exhibit high anhamonicity and lead to center-saddle bifurcations. These modes are associated to an isomerization process in alanine dipeptide and to frequency shifts in the oxoferryl observed by modifying the Coulomb field around the Imidazole-Fe{sup IV} = O species.
Nonlinear tearing mode study using the almost ideal magnetohydrodynamics (MHD) constraint
Energy Technology Data Exchange (ETDEWEB)
Ren, C.; Callen, J.D. [Univ. of Wisconsin, Madison, WI (United States); Jensen, T.H. [General Atomics, San Diego, CA (United States)
1998-12-31
The tearing mode is an important resistive magnetohydrodynamics (MHD) mode. It perturbs the initial equilibrium magnetic flux surfaces through magnetic field line reconnection to form new flux surfaces with magnetic islands. In the study of the tearing mode, usually the initial equilibria are one dimensional with two ignorable coordinates and the perturbed equilibria are two dimensional with one ignorable coordinate. The tearing mode can be linearly unstable and its growth saturates at a fine amplitude. The neoclassical tearing mode theory shows that the mode can be nonlinearly driven by the bootstrap current even when it is linearly stable to the classical tearing mode. It is important to study the nonlinear behavior of the tearing mode. As an intrinsically nonlinear approach, the use of the almost ideal MHD constraint is suited to study the nonlinear properties of the tearing mode. In this paper, as a validation of the method, the authors study two characteristics of the tearing mode using the almost ideal MHD constraint: (1) the linear stability condition for the initial one dimensional equilibrium; and (2) the final saturation level for the unstable case. In this work, they only consider the simplest case where no gradient of pressure or current density exists at the mode resonant surface.
Semiclassical mode-coupling factorizations of coherent nonlinear optical response
Jansen, TL; Mukamel, S
2003-01-01
The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an h expansion of Liouville space generating functions, we show how to factorize multitime nonlinear response functions into products o
Excitations and management of the nonlinear localized gap modes
Indian Academy of Sciences (India)
Bishwajyoti Dey
2015-11-01
We discuss about the theory of nonlinear localized excitations, such as soliton and compactons in the gap of the linear spectrum of the nonlinear systems. We show how the gap originates in the linear spectrum using examples of a few systems, such as nonlinear lattices, Bose–Einstein condensates in optical lattice and systems represented by coupled nonlinear evolution equations. We then analytically show the excitation of solitons and compacton-like solutions in the gap of the linear spectrum of a system of coupled Korteweg–de Vries (KdV) equations with linear and nonlinear dispersions. Finally, we discuss about the theory of Feshbach resonance management and dispersion management of the soliton solutions.
Excitation Thresholds for Nonlinear Localized Modes on Lattices
Weinstein, M I
1999-01-01
Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schrödinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schrödinger systems (DNLS). We prove that if $\\sigma\\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, the context of DNLS. We also discuss upper and lower bounds for excitation threshol...
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.
Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
Midya, Bikashkali
2013-01-01
We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters although corresponding linear Schroedinger eigenvalue problem possesses unbroken PT-symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power flow density associated with these localized modes has also been examined.
Quasinormal modes of four-dimensional topological nonlinear charged Lifshitz black holes
Energy Technology Data Exchange (ETDEWEB)
Becar, Ramon [Universidad Cato lica de Temuco, Departamento de Ciencias Matematicas y Fisicas, Temuco (Chile); Gonzalez, P.A. [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Vasquez, Yerko [Universidad de La Serena, Departamento de Fisica, Facultad de Ciencias, La Serena (Chile)
2016-02-15
We study scalar perturbations of four- dimensional topological nonlinear charged Lifshitz black holes with spherical and plane transverse sections, and we find numerically the quasinormal modes for scalar fields. Then we study the stability of these black holes under massive and massless scalar field perturbations. We focus our study on the dependence of the dynamical exponent, the nonlinear exponent, the angular momentum, and the mass of the scalar field in the modes. It is found that the modes are overdamped, depending strongly on the dynamical exponent and the angular momentum of the scalar field for a spherical transverse section. In contrast, for plane transverse sections the modes are always overdamped. (orig.)
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...
Heli Hu; Dan Zhao; Qingling Zhang
2013-01-01
The sliding mode control and optimization are investigated for a class of nonlinear neutral systems with the unmatched nonlinear term. In the framework of Lyapunov stability theory, the existence conditions for the designed sliding surface and the stability bound ${\\alpha }^{\\ast }$ are derived via twice transformations. The further results are to develop an efficient sliding mode control law with tuned parameters to attract the state trajectories onto the sliding surface in finit...
Second Order Quasi-Normal Mode of the Schwarzschild Black Hole
Nakano, Hiroyuki
2007-01-01
We formulate and calculate the second order quasi-normal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational wave (GW) from a distorted BH, so called ringdown, is well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numerically solve the second order Zerilli equation by implementing the modified Leaver's continued fraction method. The second order QNM frequencies are found to be twice the first order ones, and the GW amplitude is up to $\\sim 10%$ that of the first order for the binary BH mergers. Since the second order QNMs always exist, we can use their detections (i) to test the nonlinearity of ...
Capdeville, Y.
2005-11-01
We present an alternative to the classical mode coupling method scheme often used in global seismology to compute synthetic seismograms in laterally heterogeneous earth model and Frechet derivatives for tomographic inverse problem with the normal modes first-order Born approximation. We start from the first-order Born solution in the frequency domain and we use a numerical scheme for the volume integration, which means that we have to compute the effect of a finite number of scattering points and sum them with the appropriate integration weight. For each scattering point, `source to scattering point' and `scattering point to receivers' expressions are separated before applying a Fourier transform to return to the time domain. Doing so, the perturbed displacement is obtained, for each scattering point, as the convolution of a forward wavefield from the source to the scattering point with a backward wavefield from the scattering integration point to the receiver. For one scattering point and for a given number of time steps, the numerical cost of such a scheme grows as (number of receivers + the number of sources) × (corner frequency)2 to be compared to (number of receivers × the number of sources) × (corner frequency)4 when the classical normal mode coupling algorithm is used. Another interesting point is, when used for Frechet kernel, the computing cost is (almost) independent of the number of parameters used for the inversion. This algorithm is similar to the one obtained when solving the adjoint problem. Validation tests with respect to the spectral element method solution both in the Frechet derivative case and as a synthetic seismogram tool shows a good agreement. In the latter case, we show that non-linearity can be significant even at long periods and when using existing smooth global tomographic models.
Normal modes of a defected linear system of beaded springs
Aghamohammadi, Amir; Foulaadvand, M. Ebrahim; Yaghoubi, Mohammad Hassan; Mousavi, Amir Hossein
2017-03-01
A model of a one-dimensional mass-spring chain with mass or spring defects is investigated. With a mass defect, all oscillators except the central one have the same mass, and with a spring defect, all the springs except those connected to the central oscillator have the same stiffness constant. The motion is assumed to be one-dimensional and frictionless, and both ends of the chain are assumed to be fixed. The system vibrational modes are obtained analytically, and it is shown that if the defective mass is lighter than the others, then a high frequency mode appears in which the amplitudes decrease exponentially with the distance from the defect. In this sense, the mode is localized in space. If the defect mass is greater than the others, then there will be no localized mode and all modes are extended throughout the system. Analogously, for some values of the defective spring constant, there may be one or two localized modes. If the two defected spring constants are less than that of the others, there is no localized mode.
Nonlinear Mirror and Weibel modes: peculiarities of quasi-linear dynamics
Directory of Open Access Journals (Sweden)
O. A. Pokhotelov
2010-12-01
Full Text Available A theory for nonlinear evolution of the mirror modes near the instability threshold is developed. It is shown that during initial stage the major instability saturation is provided by the flattening of the velocity distribution function in the vicinity of small parallel ion velocities. The relaxation scenario in this case is accompanied by rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic BGK modes. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by relevant numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode. The similarity with resonant Weibel instability is discussed.
Nonlinear optics in the LP(02) higher-order mode of a fiber.
Chen, Y; Chen, Z; Wadsworth, W J; Birks, T A
2013-07-29
The distinct disperion properties of higher-order modes in optical fibers permit the nonlinear generation of radiation deeper into the ultraviolet than is possible with the fundamental mode. This is exploited using adiabatic, broadband mode convertors to couple light efficiently from an input fundamental mode and also to return the generated light to an output fundamental mode over a broad spectral range. For example, we generate visible and UV supercontinuum light in the LP(02) mode of a photonic crystal fiber from sub-ns pulses with a wavelength of 532 nm.
Institute of Scientific and Technical Information of China (English)
吕国; 滕浩; 王立娜; 王睿; 王军利; 魏志义
2015-01-01
A mode-locked ytterbium-doped rod-type fiber laser with 85 µm core diameter is developed based on the nonlinear polarization evolution in an all-normal-dispersion ring cavity, in which a uniaxial birefringent plate is used as the spectral filter. Average power up to 16 W is obtained at the repetition rate of 58 MHz, and the pulse duration is compressed to 182 fs with a grating-pair compressor. The output laser pulses show very good beam quality and power stability.
Comparative study of nonlinear properties of EEG signals of a normal person and an epileptic patient
Nurujjaman, Md; Iyengar, A N Sekar
2007-01-01
Electroencephalography (EEG) for a normal person is different from an epileptic patient. We have studied EEG of normal men and epileptic patients for different mental conditions using nonlinear techniques like the surrogate analysis and the estimations of the correlation dimensions and Hurst exponents.
Hosseinifard, Behshad; Moradi, Mohammad Hassan; Rostami, Reza
2013-03-01
Diagnosing depression in the early curable stages is very important and may even save the life of a patient. In this paper, we study nonlinear analysis of EEG signal for discriminating depression patients and normal controls. Forty-five unmedicated depressed patients and 45 normal subjects were participated in this study. Power of four EEG bands and four nonlinear features including detrended fluctuation analysis (DFA), higuchi fractal, correlation dimension and lyapunov exponent were extracted from EEG signal. For discriminating the two groups, k-nearest neighbor, linear discriminant analysis and logistic regression as the classifiers are then used. Highest classification accuracy of 83.3% is obtained by correlation dimension and LR classifier among other nonlinear features. For further improvement, all nonlinear features are combined and applied to classifiers. A classification accuracy of 90% is achieved by all nonlinear features and LR classifier. In all experiments, genetic algorithm is employed to select the most important features. The proposed technique is compared and contrasted with the other reported methods and it is demonstrated that by combining nonlinear features, the performance is enhanced. This study shows that nonlinear analysis of EEG can be a useful method for discriminating depressed patients and normal subjects. It is suggested that this analysis may be a complementary tool to help psychiatrists for diagnosing depressed patients. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Nonlinear Dynamical analysis of an AFM tapping mode microcantilever beam
Directory of Open Access Journals (Sweden)
Choura S.
2012-07-01
Full Text Available We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM microcantilever beam. This latter is subjected to a harmonic excitation of its base displacement and to Van der Waals and DMT contact forces at its free end. For AFM design purposes, we derive a mathematical model for accurate description of the AFM microbeam dynamics. We solve the resulting equations of motions and associated boundary conditions using the Galerkin method. We find that using one-mode approximation in tapping mode operating in the neighborhood of the contact region one-mode approximation may lead to erroneous results.
Mode interaction in horses, tea, and other nonlinear oscillators: the universal role of symmetry
Weele, van der Jacobus P.; Banning, Erik J.
2001-01-01
This paper is about mode interaction in systems of coupled nonlinear oscillators. The main ideas are demonstrated by means of a model consisting of two coupled, parametrically driven pendulums. On the basis of this we also discuss mode interaction in the Faraday experiment (as observed by Ciliberto
Nonlinear resonances of three modes in a high-T{sub c} superconducting magnetic levitation system
Energy Technology Data Exchange (ETDEWEB)
Sasaki, Masahiko, E-mail: galian@z2.keio.jp; Sakaguchi, Ryunosuke; Sugiura, Toshihiko, E-mail: sugiura@mach.keio.ac.jp
2013-11-15
Highlights: •We studied two nonlinear vibrations of a levitated beam supported by superconductors. •One of the vibrations is combination resonance of the 1st mode and the 3rd mode. •The other vibration is autoparametric resonance of the 2nd mode. •When the amplitude of the 2nd mode is small, the combination resonance is suppressed. •Otherwise, the two resonances can be resonated simultaneously. -- Abstract: In a high-T{sub c} superconducting magnetic levitation system, an object can levitate without control and contact. So it is expected to be applied to magnetically levitated transportation. To use it safely, lightening the levitated object is necessary. But this reduces the bending stiffness of the object. Besides, the system has nonlinearity. Therefore nonlinear elastic vibration can occur. This study focused on how plural nonlinear elastic vibrations of the 1st, 2nd and 3rd modes simultaneously occur. Our numerical calculation and experiment found out that the three modes simultaneously resonate when the amplitude of the 2nd mode is large enough whereas only the 2nd mode resonates when it is small.
Energy Technology Data Exchange (ETDEWEB)
Dhote, Sharvari, E-mail: sharvari.dhote@mail.utoronto.ca; Zu, Jean; Zhu, Yang [Department of Mechanical and Industrial Engineering, University of Toronto, 5 King' s College Road, Toronto, Ontario M5S-3G8 (Canada)
2015-04-20
In this paper, a nonlinear wideband multi-mode piezoelectric vibration-based energy harvester (PVEH) is proposed based on a compliant orthoplanar spring (COPS), which has an advantage of providing multiple vibration modes at relatively low frequencies. The PVEH is made of a tri-leg COPS flexible structure, where three fixed-guided beams are capable of generating strong nonlinear oscillations under certain base excitation. A prototype harvester was fabricated and investigated through both finite-element analysis and experiments. The frequency response shows multiple resonance which corresponds to a hardening type of nonlinear resonance. By adding masses at different locations on the COPS structure, the first three vibration modes are brought close to each other, where the three hardening nonlinear resonances provide a wide bandwidth for the PVEH. The proposed PVEH has enhanced performance of the energy harvester in terms of a wide frequency bandwidth and a high-voltage output under base excitations.
Directory of Open Access Journals (Sweden)
Mourad Kchaou
2017-01-01
Full Text Available This paper addresses the problem of sliding mode control (SMC design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delay-dependent sufficient condition is established such that the admissibility as well as the H∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.
Institute of Scientific and Technical Information of China (English)
LI De-Jun; MI Xian-Wu; DENG Ke; TANG Yi
2006-01-01
In the classical lattice theory, solitons and locaLized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j0.
Attractor-repeller pair of topological zero modes in a nonlinear quantum walk
Gerasimenko, Y.; Tarasinski, B.; Beenakker, C. W. J.
2016-02-01
The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero modes) at boundaries or domain walls. Here we show that a topological zero mode may acquire a dynamical role in the presence of nonlinearities. We consider a one-dimensional discrete-time quantum walk that combines zero modes with a particle-conserving nonlinear relaxation mechanism. The presence of both particle-hole and chiral symmetry converts two zero modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics. This makes it possible to steer the walker towards a domain wall and trap it there.
Non-linear evolution of double tearing modes in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Fredrickson, E.; Bell, M.; Budny, R.V.; Synakowski, E.
1999-12-17
The delta prime formalism with neoclassical modifications has proven to be a useful tool in the study of tearing modes in high beta, collisionless plasmas. In this paper the formalism developed for the inclusion of neoclassical effects on tearing modes in monotonic q-profile plasmas is extended to plasmas with hollow current profiles and double rational surfaces. First, the classical formalism of tearing modes in the Rutherford regime in low beta plasmas is extended to q profiles with two rational surfaces. Then it is shown that this formalism is readily extended to include neoclassical effects.
Nonlinear Mixing of Collective Modes in Harmonically Trapped Bose-Einstein Condensates
Mizoguchi, Takahiro; Watabe, Shohei; Nikuni, Tetsuro
2016-01-01
We study nonlinear mixing effects among quadrupole modes and scissors modes in a harmonically trapped Bose-Einstein condensate. Using a perturbative technique in conjunction with a variational approach with a Gaussian trial wave function for the Gross-Pitaevskii equation, we find that mode mixing selectively occurs. Our perturbative approach is useful in gaining qualitative understanding of the recent experiment [Yamazaki et al., J. Phys. Soc. Japan 84, 44001 (2015)], exhibiting a beating phe...
Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators
Kristensen, Philip Trøst; Hughes, Stephen
2015-01-01
We discuss three formally different formulas for normalization of quasinormal modes currently in use for modeling optical cavities and plasmonic resonators and show that they are complementary and provide the same result. Regardless of the formula used for normalization, one can use the norm to define an effective mode volume for use in Purcell factor calculations.
Determining the long living quasi-normal modes of relativistic stars
Institute of Scientific and Technical Information of China (English)
Lü Jun-Li; Suen Wai-Mo
2011-01-01
Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established, however, none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time, e.g., the p and g mode series, or the f modes for stars with low compactness ratio(M/R). In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1)provide detailed steps in our treatment to facilitate future effort in this direction;2)correct mistakes in the literature on the formulation;and 3)analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.
Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.
2017-10-01
The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg–Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.
Pharmacokinetics of stiripentol in normal man: evidence of nonlinearity.
Levy, R H; Lin, H S; Blehaut, H M; Tor, J A
1983-01-01
The pharmacokinetics and metabolism of stiripentol, a new antiepileptic drug, were investigated in normal male subjects after single-dose and multiple-dose administration. Each of six subjects received single doses of 300, 600, and 1200 mg of stiripentol in powder form and another 600 mg in solution. In the multiple-dose study, each of six subjects received a 300-mg dose on day 1 and multiple doses (1200 mg/day) from day 2 to day 8. Five of these six subjects participated also in the single-dose study. Stiripentol and several of its metabolites, namely, stiripentol conjugate, DiOH, P-OH, and M-OH, were analyzed in plasma and urine. After single doses, the elimination curve of stiripentol appeared multiphasic. The oral clearance was 1.3 to 1.8 liter/hr/kg. The average mean residence time was 4 hours. There were no statistically significant differences in clearance or mean residence time among the three doses. However, dose dependence was found in all the four pathways when formation clearances were compared. Only trace amounts of the drug were excreted unchanged in urine. The active metabolite, P-OH, was not detectable in plasma. Stiripentol was very highly bound to plasma proteins in plasma from dosed subjects as well as spiked human plasma (free fraction of 1 per cent). In the multiple-dose study, there was a decrease (nearly eightfold) in oral clearance of stiripentol between day 1 and day 8. The fractions of dose metabolized through conjugation and methylenedioxy ring opening increased 183 and 49 per cent, respectively, but the formation clearances for all the pathways were decreased. These findings suggest that the steady-state plasma level/dose ratio of stiripentol will increase with the daily dose.
Comparative Investigation of Normal Modes and Molecular Dynamics of Hepatitis C NS5B Protein
Asafi, M. S.; Yildirim, A.; Tekpinar, M.
2016-04-01
Understanding dynamics of proteins has many practical implications in terms of finding a cure for many protein related diseases. Normal mode analysis and molecular dynamics methods are widely used physics-based computational methods for investigating dynamics of proteins. In this work, we studied dynamics of Hepatitis C NS5B protein with molecular dynamics and normal mode analysis. Principal components obtained from a 100 nanoseconds molecular dynamics simulation show good overlaps with normal modes calculated with a coarse-grained elastic network model. Coarse-grained normal mode analysis takes at least an order of magnitude shorter time. Encouraged by this good overlaps and short computation times, we analyzed further low frequency normal modes of Hepatitis C NS5B. Motion directions and average spatial fluctuations have been analyzed in detail. Finally, biological implications of these motions in drug design efforts against Hepatitis C infections have been elaborated.
Guo, Jianguang; Ward, Joshua M; Prohofsky, Earl W
2010-01-01
Self Consistent Normal Mode Analysis (SCNMA) is applied to heme c type cytochrome f to study temperature dependent protein motion. Classical Normal Mode Analysis (NMA) assumes harmonic behavior and the protein Mean Square Displacement (MSD) has a linear dependence on temperature. This is only consistent with low temperature experimental results. To connect the protein vibrational motions between low temperature and physiological temperature, we have incorporated a fitted set of anharmonic potentials into SCNMA. In addition, Quantum Harmonic Oscillator (QHO) theory has been used to calculate the displacement distribution for individual vibrational modes. We find that the modes involving soft bonds exhibit significant non-Gaussian dynamics at physiological temperature, which suggests it may be the cause of the non-Gaussian behavior of the protein motions probed by Elastic Incoherent Neutron Scattering (EINS). The combined theory displays a dynamical transition caused by the softening of few "torsional" modes in...
Spectral characteristics of Compton backscattering sources. Linear and nonlinear modes
Energy Technology Data Exchange (ETDEWEB)
Potylitsyn, A.P., E-mail: potylitsyn@tpu.ru [National Research Tomsk Polytechnic University, 634050 Tomsk (Russian Federation); National Research Nuclear University MEPhI, 115409 Moscow (Russian Federation); Kolchuzhkin, A.M. [Moscow State University of Technology “STANKIN”, 127994 Moscow (Russian Federation)
2015-07-15
Compton backscattering (CBS) of laser photons by relativistic electrons is widely used to design X-ray and gamma sources with a bandwidth better than 1% using a tight collimation. In order to obtain a reasonable intensity of the resulting beam one has to increase power of a laser pulse simultaneously with narrowing of the waist in the interaction point. It can lead to nonlinearity of CBS process which is affected on spectral characteristics of the collimated gamma beam (so-called “red-shift” of the spectral line, emission of “soft” photons with energy much less than the spectral line energy). In this paper we have analyzed such an influence using Monte-Carlo technique and have shown that even weak nonlinearity should be taken into account if the gamma beam is formed by a narrow aperture.
Nonlinear localized flatband modes with spin-orbit coupling
Gligorić, G; Hadžievski, Lj; Flach, S; Malomed, B
2016-01-01
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flatband network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's bandgap structure, and preserves the existence of CLSs at the flatband frequency, simultaneously lowering their symmetry. Adding onsite cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies which are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
Global Stabilization of Nonlinear Systems with Byrnes-Isidori Normal Form
Institute of Scientific and Technical Information of China (English)
WU Yu-qiang; YU Xing-huo
2002-01-01
The global stabilization of nonlinear cascade systems with partially linear composite dynamics is discussed in this paper using continuous terminal sliding modes (TSM). A two phase control strategy is proposed. The first phase is to use a linear control, called pre-TSM control, to bring the system state into a region where the TSM control is not singular. The second phase is to employ the TSM control in the region such that the equilibrium of the linear subsystem is reached in a finite time whose value is tunable by parameter setting of the TSMs. The finite time convergence of the proposed control strategy enables elimination of the effect of asymptotic convergence on the nonlinear systems. Although the proposed control strategy is sliding mode based, the control signal is continuous except at a single discontinuous point.Chattering phenomenon commonly associated with sliding mode control does not occur.
Maquer, Ghislain; Laurent, Marc; Brandejsky, Vaclav; Pretterklieber, Michael L; Zysset, Philippe K
2014-06-01
Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently
Nonlinear simulations of particle source effects on edge localized mode
Energy Technology Data Exchange (ETDEWEB)
Huang, J.; Tang, C. J. [College of Physical Science and Technology, Sichuan University, Chengdu 610065 (China); Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064 (China); Chen, S. Y., E-mail: sychen531@163.com [College of Physical Science and Technology, Sichuan University, Chengdu 610065 (China); Key Laboratory of High Energy Density Physics and Technology of Ministry of Education, Sichuan University, Chengdu 610064 (China); Southwestern Institute of Physics, Chengdu 610041 (China); Wang, Z. H. [Southwestern Institute of Physics, Chengdu 610041 (China)
2015-12-15
The effects of particle source (PS) with different intensities and located positions on Edge Localized Mode (ELM) are systematically studied with BOUT++ code. The results show the ELM size strongly decreases with increasing the PS intensity once the PS is located in the middle or bottom of the pedestal. The effects of PS on ELM depend on the located position of PS. When it is located at the top of the pedestal, peeling-ballooning (P-B) modes can extract more free energy from the pressure gradient and grow up to be a large filament at the initial crash phase and the broadening of mode spectrum can be suppressed by PS, which leads to more energy loss. When it is located in the middle or bottom of the pedestal, the extraction of free energy by P-B modes can be suppressed, and a small filament is generated. During the turbulence transport phase, the broader mode spectrum suppresses the turbulence transport when PS is located in the middle, while the zonal flow plays an important role in damping the turbulence transport when PS is located at the bottom.
Institute of Scientific and Technical Information of China (English)
Mohammad Pourmahmood Aghababa; Hassan Feizi
2012-01-01
This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchronization of two different chaotic systems with fully unknown parameters and nonlinear inputs.We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero.We assume that both the master's and the slave's system parameters are unknown in advance.Proper adaptation laws are derived to tackle the unknown parameters.An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time.We prove that both reaching and sliding mode phases are stable in finite time.An estimation of convergence time is given.Two illustrative examples show the effectiveness and usefulness of the proposed technique.It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali
2014-01-01
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined.
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.
Errouissi, Rachid; Yang, Jun; Chen, Wen-Hua; Al-Durra, Ahmed
2016-08-01
In this paper, a robust nonlinear generalised predictive control (GPC) method is proposed by combining an integral sliding mode approach. The composite controller can guarantee zero steady-state error for a class of uncertain nonlinear systems in the presence of both matched and unmatched disturbances. Indeed, it is well known that the traditional GPC based on Taylor series expansion cannot completely reject unknown disturbance and achieve offset-free tracking performance. To deal with this problem, the existing approaches are enhanced by avoiding the use of the disturbance observer and modifying the gain function of the nonlinear integral sliding surface. This modified strategy appears to be more capable of achieving both the disturbance rejection and the nominal prescribed specifications for matched disturbance. Simulation results demonstrate the effectiveness of the proposed approach.
Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems.
Chen, Mou; Wu, Qing-Xian; Cui, Rong-Xin
2013-03-01
In this paper, the terminal sliding mode tracking control is proposed for the uncertain single-input and single-output (SISO) nonlinear system with unknown external disturbance. For the unmeasured disturbance of nonlinear systems, terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to zero in the finite time. Based on the output of designed disturbance observer, the terminal sliding mode tracking control is presented for uncertain SISO nonlinear systems. Subsequently, terminal sliding mode tracking control is developed using disturbance observer technique for the uncertain SISO nonlinear system with control singularity and unknown non-symmetric input saturation. The effects of the control singularity and unknown input saturation are combined with the external disturbance which is approximated using the disturbance observer. Under the proposed terminal sliding mode tracking control techniques, the finite time convergence of all closed-loop signals are guaranteed via Lyapunov analysis. Numerical simulation results are given to illustrate the effectiveness of the proposed terminal sliding mode tracking control.
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...
Chattering-Free Sliding-Mode Control for Electromechanical Actuator with Backlash Nonlinearity
Directory of Open Access Journals (Sweden)
Dongqi Ma
2017-01-01
Full Text Available Considering the backlash nonlinearity and parameter time-varying characteristics in electromechanical actuators, a chattering-free sliding-mode control strategy is proposed in this paper to regulate the rudder angle and suppress unknown external disturbances. Different from most existing backlash compensation methods, a special continuous function is addressed to approximate the backlash nonlinear dead-zone model. Regarding the approximation error, unmodeled dynamics, and unknown external disturbances as a disturbance-like term, a strict feedback nonlinear model is established. Based on this nonlinear model, a chattering-free nonsingular terminal sliding-mode controller is proposed to achieve the rudder angle tracking with a chattering elimination and tracking dynamic performance improvement. A Lyapunov-based proof ensures the asymptotic stability and finite-time convergence of the closed-loop system. Experimental results have verified the effectiveness of the proposed method.
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.
Nonlinear spatial mode imaging of hybrid photonic crystal fibers
DEFF Research Database (Denmark)
Petersen, Sidsel Rübner; Alkeskjold, Thomas Tanggaard; Laurila, Marko;
2013-01-01
Degenerate spontaneous four wave mixing is studied for the rst time in a large mode area hybrid photonic crystal ber, where light con nement is achieved by combined index- and bandgap guiding. Four wave mixing products are generated on the edges of the bandgaps, which is veri ed by numerical...
The simplex method for nonlinear sliding mode control
Directory of Open Access Journals (Sweden)
Bartolini G.
1998-01-01
Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
Nonlinear tearing mode in inhomogeneous plasma: I. Unmagnetized islands
Energy Technology Data Exchange (ETDEWEB)
Waelbroeck, F L [Institute for Fusion Studies, University of Texas, Austin, TX 78712-0262 (United States)
2007-06-15
A theory of the nonlinear growth and propagation of magnetic islands in the semi-collisional regime is presented. The theory includes the effects of finite electron temperature gradients and uses a fluid model with cold ions in slab geometry to describe islands that are unmagnetized in the sense that their width is less than {rho}{sub s}, the ion Larmor radius calculated with the electron temperature. The polarization integral and the natural phase velocity are both calculated. It is found that increasing the electron temperature gradient reduces the natural phase velocity below the electron diamagnetic frequency and thus causes the polarization current to become stabilizing.
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.
Simplex sliding mode control for nonlinear uncertain systems via chaos optimization
Energy Technology Data Exchange (ETDEWEB)
Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P
2005-02-01
As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.
Sliding Mode Control for Nonlinear System Based on T-S Model
Institute of Scientific and Technical Information of China (English)
WU Zhong-qiang
2002-01-01
Using T-S model as an approximation for nonlinear system, the nonlinear system has been fuzzy into local linear model. The variable structure controller designed by using Lyapunov theory insures the stability of system. The sliding mode controller is designed by using unit vector style, and it suit the uncertain elements satisfying matching condition or do not satisfy matching condition. The effect of the scheme has been tasted with a simulation of an inverted pendulum.
2011-01-01
International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a...
Current-mode analog nonlinear function synthesizer structures
Popa, Cosmin Radu
2013-01-01
This book is dedicated to the analysis and design of analog CMOS nonlinear function synthesizer structures, based on original superior-order approximation functions. A variety of analog function synthesizer structures are discussed, based on accurate approximation functions. Readers will be enabled to implement numerous circuit functions with applications in analog signal processing, including exponential, Gaussian or hyperbolic functions. Generalizing the methods for obtaining these particular functions, the author analyzes superior-order approximation functions, which represent the core for developing CMOS analog nonlinear function synthesizers. · Describes novel methods for generating a multitude of circuit functions, based on superior-order improved accuracy approximation functions; · Presents techniques for analog function synthesizers that can be applied easily to a wide variety of analog signal processing circuits; · Enables the design of analog s...
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
Energy Technology Data Exchange (ETDEWEB)
Romera, M.; Monteblanco, E.; Garcia-Sanchez, F.; Buda-Prejbeanu, L. D.; Ebels, U. [Univ. Grenoble Alpes, F-38000 Grenoble (France); CEA, INAC-SPINTEC, F-38000 Grenoble (France); CNRS, SPINTEC, F-38000 Grenoble (France); Delaët, B. [CEA-LETI, MINATEC, DRT/LETI/DIHS, 38054 Grenoble (France)
2015-05-11
The influence of dynamic coupling in between magnetic layers of a standard spin torque nano-oscillator composed of a synthetic antiferromagnet (SyF) as a polarizer and an in-plane magnetized free layer has been investigated. Experiments on spin valve nanopillars reveal non-continuous features such as kinks in the frequency field dependence that cannot be explained without such interactions. Comparison of experiments to numerical macrospin simulations shows that this is due to non-linear interaction between the spin torque (STT) driven mode and a damped mode that is mediated via the third harmonics of the STT mode. It only occurs at large applied currents and thus at large excitation amplitudes of the STT mode. Under these conditions, a hybridized mode characterized by a strong reduction of the linewidth appears. The reduced linewidth can be explained by a reduction of the non-linear contribution to the linewidth via an enhanced effective damping. Interestingly, the effect depends also on the exchange interaction within the SyF. An enhancement of the current range of reduced linewidth by a factor of two and a reduction of the minimum linewidth by a factor of two are predicted from simulation when the exchange interaction strength is reduced by 30%. These results open directions to optimize the design and microwave performances of spin torque nano-oscillators taking advantage of the coupling mechanisms.
Nonlinear Generation of Fluting Perturbations by Kink Mode
Ruderman, M. S.
2017-08-01
We study the excitation of fluting perturbations in a magnetic tube by an initially imposed kink mode. We use the ideal magnetohydrodynamic (MHD) equations in the cold-plasma approximation. We also use the thin-tube approximation and scale the dependent and independent variables accordingly. Then we assume that the dimensionless amplitude of the kink mode is small and use it as an expansion parameter in the regular perturbation method. We obtain the expression for the tube boundary perturbation in the second-order approximation. This perturbation is a superposition of sausage and fluting perturbations. The amplitude of the fluting perturbation takes its maximum at the middle of the tube, and it monotonically decreases with the distance from the middle of the tube.
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
Hesketh, Graham D
2015-01-01
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\\chi_2$ type nonlinearity as well as two mode systems coupled via cubic $\\chi_3$ type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum and difference frequency generation, polarization dynamics, parity-time dynamics and optical processing applications.
New adaptive quasi-sliding mode control for nonlinear discrete-time systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A new adaptive quasi-sliding mode control algorithm is developed for a class of nonlinear diecrete-time systems,which is especially useful for nonlinear systems with vaguely known dynamics.This design is model-free,and is based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using an improved recursive projection type of identification algorithm.The theoretical analysis and simulation results show that the adaptive quasi-sliding mode control system is stable and convergent.
Integral sliding mode control for a class of nonlinear neutral systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Lou Xu-Yang; Cui Bao-Tong
2008-01-01
This paper focuses on sliding mode control problems for a class of nonlinear neutral systems with time-varying delays. An integral sliding surface is firstly constructed. Then it finds a useful criteria to guarantee the global stability for the nonlinear neutral systems with time-varying delays in the specified switching surface, whose condition is formulated as linear matrix inequality. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a numerical simulation validates the effectiveness and feasibility of the proposed technique.
Nonlinear interaction of two trapped-mode resonances in a bilayer "fish-scale" metamaterial
Tuz, Vladimir R; Mladyonov, Pavel L; Prosvirnin, Sergey L; Novitsky, Andrey V
2014-01-01
We report on a bistable light transmission through a bilayer "fish-scale" (meander-line) metamaterial. It is demonstrated that an all-optical switching may be achieved nearly the frequency of the high-quality-factor Fano-shaped trapped-mode resonance excitation. The nonlinear interaction of two closely spaced trapped-mode resonances in the bilayer structure composed with a Kerr-type nonlinear dielectric slab is analyzed in both frequency and time domains. It is demonstrated that these two resonances react differently on the applied intense light which leads to destination of a multistable transmission.
Free chattering hybrid sliding mode control for a class of non-linear systems
DEFF Research Database (Denmark)
Khooban, Mohammad-Hassan; Niknam, Taher; Blaabjerg, Frede
2016-01-01
In current study, in order to find the control of general uncertain nonlinear systems, a new optimal hybrid control approach called Optimal General Type II Fuzzy Sliding Mode (OGT2FSM) is presented. In order to estimate unknown nonlinear activities in monitoring dynamic uncertainties, the benefits...... on the same topic, which are an Adaptive Interval Type-2 Fuzzy Logic Controller (AGT2FLC) and Conventional Sliding Mode Controller (CSMC), to assess the efficiency of the suggested controller. The suggested control scheme is finally used to the Electric Vehicles type as a case study. Results of simulation...
Differential rotation of the unstable nonlinear r -modes
Friedman, John L.; Lindblom, Lee; Lockitch, Keith H.
2016-01-01
At second order in perturbation theory, the r -modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation reaction, the differential rotation is constant in time and has been computed by Sá. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance ϖ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the r -mode instability removes this gauge freedom; the exponentially growing differential rotation of the unstable second-order r -mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for slowly rotating models with polytropic equations of state.
Differential rotation of the unstable nonlinear r-modes
Friedman, John L; Lockitch, Keith H
2016-01-01
At second order in perturbation theory, the $r$-modes of uniformly rotating stars include an axisymmetric part that can be identified with differential rotation of the background star. If one does not include radiation-reaction, the differential rotation is constant in time and has been computed by S\\'a. It has a gauge dependence associated with the family of time-independent perturbations that add differential rotation to the unperturbed equilibrium star: For stars with a barotropic equation of state, one can add to the time-independent second-order solution arbitrary differential rotation that is stratified on cylinders (that is a function of distance $\\varpi$ to the axis of rotation). We show here that the gravitational radiation-reaction force that drives the $r$-mode instability removes this gauge freedom: The expontially growing differential rotation of the unstable second-order $r$-mode is unique. We derive a general expression for this rotation law for Newtonian models and evaluate it explicitly for s...
SwarmDock and the Use of Normal Modes in Protein-Protein Docking
Directory of Open Access Journals (Sweden)
Paul A. Bates
2010-09-01
Full Text Available Here is presented an investigation of the use of normal modes in protein-protein docking, both in theory and in practice. Upper limits of the ability of normal modes to capture the unbound to bound conformational change are calculated on a large test set, with particular focus on the binding interface, the subset of residues from which the binding energy is calculated. Further, the SwarmDock algorithm is presented, to demonstrate that the modelling of conformational change as a linear combination of normal modes is an effective method of modelling flexibility in protein-protein docking.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali, E-mail: bikash.midya@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Advanced Center for Nonlinear and Complex Phenomena, Kolkata 700075 (India)
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Walasik, Wiktor; Renversez, Gilles
2014-01-01
We study the nonlinear waves propagating in metal slot waveguides with a Kerr-type dielectric core. We develop two independent semi-analytical models to describe the properties of such waveguides. Using those models we compute the dispersion curves for the first ten modes of a nonlinear slot waveguide. For symmetric waveguides we find symmetric, antisymmetric, and asymmetric modes which are grouped in two families. In addition, we study the influence of the slot width on the first symmetric and asymmetric modes, and we show that the dispersion curve of the first asymmetric mode is invariant with respect to the slot width for high propagation constant values and we provide analytical approximations of this curve.
Sibaev, M; Crittenden, D L
2016-06-01
In this paper, we outline a general, scalable, and black-box approach for calculating high-order strongly coupled force fields in rectilinear normal mode coordinates, based upon constructing low order expansions in curvilinear coordinates with naturally limited mode-mode coupling, and then transforming between coordinate sets analytically. The optimal balance between accuracy and efficiency is achieved by transforming from 3 mode representation quartic force fields in curvilinear normal mode coordinates to 4 mode representation sextic force fields in rectilinear normal modes. Using this reduced mode-representation strategy introduces an error of only 1 cm(-1) in fundamental frequencies, on average, across a sizable test set of molecules. We demonstrate that if it is feasible to generate an initial semi-quartic force field in curvilinear normal mode coordinates from ab initio data, then the subsequent coordinate transformation procedure will be relatively fast with modest memory demands. This procedure facilitates solving the nuclear vibrational problem, as all required integrals can be evaluated analytically. Our coordinate transformation code is implemented within the extensible PyPES library program package, at http://sourceforge.net/projects/pypes-lib-ext/.
Control of nonlinear systems using terminal sliding modes
Venkataraman, S. T.; Gulati, S.
1992-01-01
The development of an approach to control synthesis for robust robot operations in unstructured environments is discussed. To enhance control performance with full model information, the authors introduce the notion of terminal convergence and develop control laws based on a class of sliding modes, denoted as terminal sliders. They demonstrate that terminal sliders provide robustness to parametric uncertainty without having to resort to high-frequency control switching, as in the case of conventional sliders. It is shown that the proposed method leads to greater guaranteed precision in all control cases discussed.
Velizhanin, Kirill A; Kilina, Svetlana; Sewell, Thomas D; Piryatinski, Andrei
2008-10-23
Numerical studies of vibrational energy transport and associated (non)linear infrared and Raman response in polyatomic materials require knowledge of the multidimensional vibrational potential-energy surface and the ability to perform normal-mode analysis on that potential. The presence of translational symmetry, as in crystals, leads to the observed dispersion of the unit cell normal modes and has to be accounted for in calculations of energy transfer rates and other spectroscopic quantities. Here we report on the implementation of a computational approach that combines the generalized supercell method and density functional theory electronic structure calculations to investigate the vibrational structure in translationally symmetric materials containing relatively large numbers of atoms in the unit cell (58 atoms in the present study). The method is applied to calculate the phonon and vibron dispersion relations and the vibrational density of states in pentaerythritol tetranitrate (PETN) molecular crystal which is an important energetic material. The results set the stage for future investigations of vibrational energy transport and associated nonlinear spectroscopic signatures in this class of materials.
Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems
Roopaei, Mehdi; Zolghadri, Mansoor; Meshksar, Sina
2009-09-01
In this article, a novel Adaptive Fuzzy Sliding Mode Control (AFSMC) methodology is proposed based on the integration of Sliding Mode Control (SMC) and Adaptive Fuzzy Control (AFC). Making use of the SMC design framework, we propose two fuzzy systems to be used as reaching and equivalent parts of the SMC. In this way, we make use of the fuzzy logic to handle uncertainty/disturbance in the design of the equivalent part and provide a chattering free control for the design of the reaching part. To construct the equivalent control law, an adaptive fuzzy inference engine is used to approximate the unknown parts of the system. To get rid of the chattering, a fuzzy logic model is assigned for reaching control law, which acting like the saturation function technique. The main advantage of our proposed methodology is that the structure of the system is unknown and no knowledge of the bounds of parameters, uncertainties and external disturbance are required in advance. Using Lyapunov stability theory and Barbalat's lemma, the closed-loop system is proved to be stable and convergence properties of the system is assured. Simulation examples are presented to verify the effectiveness of the method. Results are compared with some other methods proposed in the past research.
Indian Academy of Sciences (India)
Hari Prakash; Devendra K Singh
2010-03-01
It is shown that all optical polarization states of light except plane and circular polarization states undergo an intensity-dependent change in normal incidence of light in an isotropic nonlinear Kerr medium. This effect should be detectable and we propose an experiment for detecting nonlinear susceptibility involved in that part of nonlinear polarization, which depends on the polarization state of light also.
Quasi-normal Modes of Rerssner-Nordström Black Hole
Jiang, Ji-Jian; Liu, Jing-Lun; Li, Chuan-An
2017-07-01
The minimum interval of event horizon area of Rerssner-Nordström black hole was calculated via using the loop quantum gravity theory. Based on the first law of black hole thermodynamics, the real part of quasi-normal modes frequency of the black hole was calculated. The expression of asymptotically quasi-normal mode frequency of Rerssner-Nordström black hole was deduced strictly. By analyzing the value of the minimum spin j m i n , the two families of quasi-normal mode spectra of the charged black hole were obtained for j m i n = 1/2 and j m i n = 1 respectively. Our conclusion is in complete agreement with the analytical results of Hod. Our results provide the theoretical basis for the source of the real part of the quasi-normal mode frequency of the black hole.
Sun, Limin; Chen, Lin
2017-10-01
Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.
Observability of nonlinear dynamics: Normalized results and a time-series approach
Aguirre, Luis A.; Bastos, Saulo B.; Alves, Marcela A.; Letellier, Christophe
2008-03-01
This paper investigates the observability of nonlinear dynamical systems. Two difficulties associated with previous studies are dealt with. First, a normalized degree observability is defined. This permits the comparison of different systems, which was not generally possible before. Second, a time-series approach is proposed based on omnidirectional nonlinear correlation functions to rank a set of time series of a system in terms of their potential use to reconstruct the original dynamics without requiring the knowledge of the system equations. The two approaches proposed in this paper and a former method were applied to five benchmark systems and an overall agreement of over 92% was found.
Complex Normal-mode Frequencies of External Perturbations in Generalized Schwarzschild Geometry
Institute of Scientific and Technical Information of China (English)
YUAN Ning-Yi; LI Xin-Zhou
2000-01-01
A moditied Wentzel-Kramers-Brillouin approach is used to determine the complex normal-mode frequencies of external perturbations in generalized Schwarzschild geometry. In the λ= 1 case (Schwarzschild geometry), the agreement with other methods is excellent for the low-lying modes. On the contrary, the λ ≠ 1 case of this geometry is unstable against external perturbations
Zeng, Hang-li
2010-01-01
This paper has made an investigation on the current writing teaching mode among English majors in normal universities in China, by means of questionnaire, interview and class observation. The study finds out that the current writing teaching mode is not purely product approach or process approach. In fact, the two approaches to writing co-exist in…
DEFF Research Database (Denmark)
Nielsen, J B; Sjöstrand, U H; Henneberg, S W
1991-01-01
A randomized study of 6 ventilatory modes was made in 7 piglets with normal lungs. Using a Servo HFV 970 (prototype system) and a Servo ventilator 900 C the ventilatory modes examined were as follows: SV-20V, i.e. volume-controlled intermittent positive-pressure ventilation (IPPV); SV-20VIosc, i...
Large Optical Nonlinearity of Surface Plasmon Modes on Thin Gold Films
DEFF Research Database (Denmark)
Huck, Alexander; Witthaut, Dirk; Kumar, Shailesh
2013-01-01
We investigate the optical nonlinear effects of a long-range surface plasmon polariton mode propagating on a thin gold film. These effects may play a key role in the design of future nanophotonic circuits as they allow for the realization of active plasmonic elements. We demonstrate a significant...
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.
On Landau damping of dipole modes by non-linear space charge and octupoles
Möhl, D
1995-01-01
The joint effect of space-charge non-linearities and octupole lenses is important for Landau damping of coherent instabilities. The octupole strength required for stabilisation can depend strongly on the sign of the excitation current of the lenses. This note tries to extend results, previously obtained for coasting beams and rigid bunches, to more general head--tail modes.
A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos
Institute of Scientific and Technical Information of China (English)
Yu Dong-Chuan; Wu Ai-Guo; Yang Chao-Ping
2005-01-01
A novel sliding mode nonlinear proportional-integral control (SMNPIC) scheme is proposed for driving a class of time-variant chaotic systems with uncertainty to arbitrarily desired trajectory with high accuracy. The SMNPIC differs from the previous sliding mode techniques in the sense that a nonlinear proportional-integral action of sliding function is involved in control law, so that both the steady-state error and the high-frequency chattering are reduced,and meanwhile, robustness and fastness are guaranteed. In addition, the proposed SMNPIC actually acts as a class of nonlinear proportional-integral-differential (PID) controller, in which the tracking error and its derivatives up to (n-1)thorder as well as the integral of tracking error are considered, so that more useful information than traditional PID can be implemented and better dynamic and static characteristics can obtained. Its good performance for chaotic control is illustrated through a During-Holmes system with uncertainty.
Nonlinear Dual-Mode Control of Variable-Speed Wind Turbines with Doubly Fed Induction Generators
Tang, Choon Yik; Jiang, John N
2010-01-01
This paper presents a feedback/feedforward nonlinear controller for variable-speed wind turbines with doubly fed induction generators. By appropriately adjusting the rotor voltages and the blade pitch angle, the controller simultaneously enables: (a) control of the active power in both the maximum power tracking and power regulation modes, (b) seamless switching between the two modes, and (c) control of the reactive power so that a desirable power factor is maintained. Unlike many existing designs, the controller is developed based on original, nonlinear, electromechanically-coupled models of wind turbines, without attempting approximate linearization. Its development consists of three steps: (i) employ feedback linearization to exactly cancel some of the nonlinearities and perform arbitrary pole placement, (ii) design a speed controller that makes the rotor angular velocity track a desired reference whenever possible, and (iii) introduce a Lyapunov-like function and present a gradient-based approach for mini...
Nazemosadat, Elham
2014-01-01
We explore the practical challenges which should be addressed when designing a multi-core fiber coupler for nonlinear switching or mode-locking applications. The inevitable geometric imperfections formed in these fiber couplers during the fabrication process affect the performance characteristics of the nonlinear switching device. Fabrication uncertainties are tolerable as long as the changes they impose on the propagation constant of the modes are smaller than the linear coupling between the cores. It is possible to reduce the effect of the propagation constant variations by bringing the cores closer to each other, hence, increasing the coupling. However, higher coupling translates into a higher switching power which may not be desirable in some practical situations. Therefore, fabrication errors limit the minimum achievable switching power in nonlinear couplers.
Matsas, V J; Richardson, D J; Newson, T P; Payne, D N
1993-03-01
A full characterization of a self-starting, passively mode-locked soliton ring fiber laser in terms of its various modes of mode-locked operation, cavity length, and type of fiber used is presented. Direct evidence, based on state-of-polarization measurements, that nonlinear polarization evolution is the responsible mode-locking mechanism is also given.
Kartashov, Yaroslav V
2014-01-01
We study specific features of resonant mode conversion in nonlinear waveguides stimulated by the bi-harmonic longitudinal modulation of its parameters, which includes changes of the waveguide depth as well as its bending (in the one-dimensional case) or spiraling (in the two-dimensional case). We demonstrate the possibility of simultaneous excitation of higher-order modes of different parities and topologies with controllable energy weights. The output mode composition is highly sensitive to the variation in the input power and detuning from the resonant modulation frequency.
Miranowicz, A; Miranowicz, Adam; Leonski, Wieslaw
2006-01-01
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
Possible Discovery of Nonlinear Tail and Quasinormal Modes in Black Hole Ringdown
Okuzumi, Satoshi; Sakagami, Masa-aki
2008-01-01
We investigate the nonlinear evolution of black hole ringdown in the framework of higher-order metric perturbation theory. By solving the initial-value problem of a simplified nonlinear field model analytically as well as numerically, we find that (i) second-order quasinormal modes (QNMs) are indeed excited at frequencies different from those of first-order QNMs, as predicted recently. We also find serendipitously that (ii) late-time evolution is dominated by a new type of power-law tail. This ``second-order power-law tail'' decays more slowly than any late-time tails known in the first-order (i.e., linear) perturbation theory, and is generated at the wavefront of the first-order perturbation by an essentially nonlinear mechanism. These nonlinear components should be particularly significant for binary black hole coalescences, and could open a new precision science in gravitational wave studies.
A new approach to the study of quasi-normal modes of rotating stars
Ferrari, V; Marassi, S
2007-01-01
We propose a new method to study the quasi-normal modes of rotating relativistic stars. Oscillations are treated as perturbations in the frequency domain of the stationary, axisymmetric background describing a rotating star. The perturbed quantities are expanded in circular harmonics, and the resulting 2D-equations they satisfy are integrated using spectral methods in the (r,theta)-plane. The asymptotic conditions at infinity, needed to find the mode frequencies, are implemented by generalizing the standing wave boundary condition commonly used in the non rotating case. As a test, the method is applied to find the quasi-normal mode frequencies of a slowly rotating star.
Adaptive Fuzzy Integral Sliding-Mode Regulator for Induction Motor Using Nonlinear Sliding Surface
Directory of Open Access Journals (Sweden)
Yong-Kun Lu
2015-02-01
Full Text Available An adaptive fuzzy integral sliding-mode controller using nonlinear sliding surface is designed for the speed regulator of a field-oriented induction motor drive in this paper. Combining the conventional integral sliding surface with fractional-order integral, a nonlinear sliding surface is proposed for the integral sliding-mode speed control, which can overcome the windup problem and the convergence speed problem. An adaptive fuzzy control term is utilized to approximate the uncertainty. The stability of the controller is analyzed by Lyapunov stability theory. The effectiveness of the proposed speed regulator is demonstrated by the simulation results in comparison with the conventional integral sliding-mode controller based on boundary layer.
Nonlinear modes and symmetry breaking in rotating double-well potentials
Li, Yongyao; Malomed, Boris A
2012-01-01
We study modes trapped in a rotating ring carrying the self-focusing (SF) or defocusing (SDF) cubic nonlinearity and double-well potential $\\cos^{2}\\theta $, where $\\theta $ is the angular coordinate. The model, based on the nonlinear Schr\\"{o}dinger (NLS) equation in the rotating reference frame, describes the light propagation in a twisted pipe waveguide, as well as in other optical settings, and also a Bose-Einstein condensate (BEC)trapped in a torus and dragged by the rotating potential. In the SF and SDF regimes, five and four trapped modes of different symmetries are found, respectively. The shapes and stability of the modes, and transitions between them are studied in the first rotational Brillouin zone. In the SF regime, two symmetry-breaking transitions are found, of subcritical and supercritical types. In the SDF regime, an antisymmetry-breaking transition occurs. Ground-states are identified in both the SF and SDF systems.
Nonlinear terahertz spectroscopy of Higgs mode in s-wave superconductors
Matsunaga, Ryusuke; Shimano, Ryo
2017-02-01
We review our recent experiments of ultrafast dynamics in s-wave superconductors Nb1-x Ti x N by using nonlinear terahertz (THz) spectroscopy. The free oscillation of the Higgs mode, i.e. the amplitude mode of the superconducting order parameter, is observed after instantaneous injection of quasiparticles at the superconducting gap edge by an intense monocycle THz pulse. The ultrafast nonequilibrium dynamics of the order parameter under the strong AC driving field with the photon energy tuned below the superconducting gap is also investigated. A resonant nonlinear interaction between the Higgs mode and the electromagnetic field is revealed, as manifested by an efficient THz third-harmonic generation from the superconductor.
Strozzi, Matteo; Smirnov, Valeri V.; Manevitch, Leonid I.; Milani, Massimo; Pellicano, Francesco
2016-10-01
In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are studied. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are considered. The circumferential flexural modes (CFMs) are investigated. Two different approaches based on numerical and analytical models are compared. In the numerical model, an energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved by using the implicit Runge-Kutta numerical method. In the analytical model, a reduced form of the Sanders-Koiter theory assuming small circumferential and tangential shear deformations is used to get the nonlinear ordinary differential equations of motion, which are solved by using the multiple scales analytical method. The transition from energy beating to energy localization in the nonlinear field is studied. The effect of the aspect ratio on the analytical and numerical values of the nonlinear energy localization threshold for different boundary conditions is investigated. Time evolution of the total energy distribution along the axis of a simply supported SWNT
Olivier, Michel; Gagnon, Marc-Daniel; Habel, Joé
2016-02-28
When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a new and inexpensive procedure to force mode locking in a pre-adjusted nonlinear polarization rotation fiber laser. This procedure is based on the detection of a sudden change in the output polarization state when mode locking occurs. This change is used to command the alignment of the intra-cavity polarization controller in order to find mode-locking conditions. More specifically, the value of the first Stokes parameter varies when the angle of the polarization controller is swept and, moreover, it undergoes an abrupt variation when the laser enters the mode-locked state. Monitoring this abrupt variation provides a practical easy-to-detect signal that can be used to command the alignment of the polarization controller and drive the laser towards mode locking. This monitoring is achieved by feeding a small portion of the signal to a polarization analyzer measuring the first Stokes parameter. A sudden change in the read out of this parameter from the analyzer will occur when the laser enters the mode-locked state. At this moment, the required angle of the polarization controller is kept fixed. The alignment is completed. This procedure provides an alternate way to existing automating procedures that use equipment such as an optical spectrum analyzer, an RF spectrum analyzer, a photodiode connected to an electronic pulse-counter or a nonlinear detecting scheme based on two-photon absorption or second harmonic generation. It is suitable for lasers mode locked by nonlinear polarization rotation. It is relatively easy to implement, it requires inexpensive means, especially at a wavelength of 1550 nm, and it lowers the production and operation costs incurred in comparison to the above-mentioned techniques.
A Study of Saturn's Normal Mode Oscillations and Their Forcing of Density Waves in the Rings
Friedson, Andrew James; Cao, Lyra
2016-10-01
Analysis of Cassini Visual and Infrared Mapping Spectrometer (VIMS) ring occultation profiles has revealed the presence of spiral density waves in Saturn's C ring that are consistent with being driven by gravitational perturbations associated with normal-mode oscillations of the planet [1]. These waves allow the C ring to serve as a sort of seismometer, since their pattern speeds (i.e., azimuthal phase speeds) can in principle be mapped onto the frequencies of the predominant normal oscillations of the planet. The resonant mode frequencies in turn are sensitive to Saturn's internal structure and rotational state. Characterization of the normal modes responsible for the forcing holds the potential to supply important new constraints on Saturn's internal structure and rotation. We perform numerical calculations to determine the resonant frequencies of the normal modes of a uniformly rotating planet for various assumptions regarding its internal stratification and compare the implied pattern speeds to those of density waves observed in the C ring. A question of particular interest that we address is whether quasi-toroidal modes are responsible for exciting a mysterious class of slowly propagating density waves in the ring. We also explore the implications of avoided crossings between modes for explaining observed fine splitting in the pattern speeds of spiral density waves having the same number of spiral arms, and weigh the role that convective overstability may play in exciting large-scale quasi-toroidal modes in Saturn. [1] Hedman, M.M. and Nicholson, P.D. 2014. MNRAS 444, 1369.
Dynamics of mode-coupling-induced microresonator frequency combs in normal dispersion
Jang, Jae K; Yu, Mengjie; Luke, Kevin; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L
2016-01-01
We experimentally and theoretically investigate the dynamics of microresonator-based frequency comb generation assisted by mode coupling in the normal group-velocity dispersion (GVD) regime. We show that mode coupling can initiate intracavity modulation instability (MI) by directly perturbing the pump-resonance mode. We also observe the formation of a low-noise comb as the pump frequency is tuned further into resonance from the MI point. We determine the phase-matching conditions that accurately predict all the essential features of the MI and comb spectra, and extend the existing analogy between mode coupling and high-order dispersion to the normal GVD regime. We discuss the applicability of our analysis to the possibility of broadband comb generation in the normal GVD regime.
Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems
Directory of Open Access Journals (Sweden)
Minh-Duc Tran
2015-01-01
Full Text Available This paper presents a high-performance nonsingular terminal sliding mode control method for uncertain second-order nonlinear systems. First, a nonsingular terminal sliding mode surface is introduced to eliminate the singularity problem that exists in conventional terminal sliding mode control. By using this method, the system not only can guarantee that the tracking errors reach the reference value in a finite time with high-precision tracking performance but also can overcome the complex-value and the restrictions of the exponent (the exponent should be fractional number with an odd numerator and an odd denominator in traditional terminal sliding mode. Then, in order to eliminate the chattering phenomenon, a super-twisting higher-order nonsingular terminal sliding mode control method is proposed. The stability of the closed-loop system is established using the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.
Nonlinear mode coupling and internal resonances in MoS2 nanoelectromechanical system
Samanta, C.; Yasasvi Gangavarapu, P. R.; Naik, A. K.
2015-10-01
Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS2 for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essential for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS2 resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances.
Studying Climate Response to Forcing by the Nonlinear Dynamical Mode Decomposition
Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander
2017-04-01
An analysis of global climate response to external forcing, both anthropogenic (mainly, CO2 and aerosol) and natural (solar and volcanic), is needed for adequate predictions of global climate change. Being complex dynamical system, the climate reacts to external perturbations exciting feedbacks (both positive and negative) making the response non-trivial and poorly predictable. Thus an extraction of internal modes of climate system, investigation of their interaction with external forcings and further modeling and forecast of their dynamics, are all the problems providing the success of climate modeling. In the report the new method for principal mode extraction from climate data is presented. The method is based on the Nonlinear Dynamical Mode (NDM) expansion [1,2], but takes into account a number of external forcings applied to the system. Each NDM is represented by hidden time series governing the observed variability, which, together with external forcing time series, are mapped onto data space. While forcing time series are considered to be known, the hidden unknown signals underlying the internal climate dynamics are extracted from observed data by the suggested method. In particular, it gives us an opportunity to study the evolution of principal system's mode structure in changing external conditions and separate the internal climate variability from trends forced by external perturbations. Furthermore, the modes so obtained can be extrapolated beyond the observational time series, and long-term prognosis of modes' structure including characteristics of interconnections and responses to external perturbations, can be carried out. In this work the method is used for reconstructing and studying the principal modes of climate variability on inter-annual and decadal time scales accounting the external forcings such as anthropogenic emissions, variations of the solar activity and volcanic activity. The structure of the obtained modes as well as their response to
Nonlinear r-modes in a spherical shell issues of principle
Levin, Y; Levin, Yuri; Ushomirsky, Greg
1999-01-01
We use a simple physical model to study the nonlinear behaviour of the r-mode instability. We assume that r-modes (Rossby waves) are excited in a thin spherical shell of rotating incompressible fluid. For this case, exact Rossby wave solutions of arbitrary amplitude are known. We find that: (a) These nonlinear Rossby waves carry ZERO physical angular momentum and positive physical energy, which is contrary to the folklore belief that the r-mode angular momentum and energy are negative. (b) Within our model, we confirm the differential drift reported by Rezzolla, Lamb and Shapiro (1999). Radiation reaction is introduced into the model by assuming that the fluid is electrically charged; r-modes are coupled to electromagnetic radiation through current (magnetic) multipole moments. We find that: (c) To linear order in the mode amplitude, r-modes are subject to the CFS instability, as expected. (d) Radiation reaction decreases the angular velocity of the shell and causes differential rotation (which is distinct fr...
Directory of Open Access Journals (Sweden)
Takeshi Yoshida
2015-11-01
Full Text Available Nonlinear ultrashort pulse propagation in a mode-locked Yb:YAG laser with a highly nonlinear intra-cavity medium is analyzed using a nonlinear Schrodinger equation. The output spectra are extended by the increased laser intensity, and spectral bandwidths wider than those of the gain medium are achieved. Moreover, pulse widths are shortened by increased laser intensity to considerably less than those of the gain medium. The simulation results qualitatively agree with the experimental results.
Oblique non-neutral solitary Alfven modes in weakly nonlinear pair plasmas
Energy Technology Data Exchange (ETDEWEB)
Verheest, Frank [Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281, B-9000 Gent (Belgium); School of Physics, Howard College Campus, University of KwaZulu-Natal, Durban 4041 (South Africa); Lakhina, G S [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410218 (India); Research Institute for Sustainable Humanosphere, Kyoto University, Gokasho, Uji, Kyoto 611-0011 (Japan)
2005-04-01
The equal charge-to-mass ratio for both species in pair plasmas induces a decoupling of the linear eigenmodes between waves that are charge neutral or non-neutral, also at oblique propagation with respect to a static magnetic field. While the charge-neutral linear modes have been studied in greater detail, including their weakly and strongly nonlinear counterparts, the non-neutral mode has received less attention. Here the nonlinear evolution of a solitary non-neutral mode at oblique propagation is investigated in an electron-positron plasma. Employing the framework of reductive perturbation analysis, a modified Korteweg-de Vries equation (with cubic nonlinearity) for the lowest-order wave magnetic field is obtained. In the linear approximation, the non-neutral mode has its magnetic component orthogonal to the plane spanned by the directions of wave propagation and of the static magnetic field. The linear polarization is not maintained at higher orders. The results may be relevant to the microstructure in pulsar radiation or to the subpulses.
Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.
Gao, Qing; Liu, Lu; Feng, Gang; Wang, Yong
2014-12-01
In this paper, the universal integral sliding-mode controller problem for the general stochastic nonlinear systems modeled by Itô type stochastic differential equations is investigated. One of the main contributions is that a novel dynamic integral sliding mode control (DISMC) scheme is developed for stochastic nonlinear systems based on their stochastic T-S fuzzy approximation models. The key advantage of the proposed DISMC scheme is that two very restrictive assumptions in most existing ISMC approaches to stochastic fuzzy systems have been removed. Based on the stochastic Lyapunov theory, it is shown that the closed-loop control system trajectories are kept on the integral sliding surface almost surely since the initial time, and moreover, the stochastic stability of the sliding motion can be guaranteed in terms of linear matrix inequalities. Another main contribution is that the results of universal fuzzy integral sliding-mode controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy integral sliding-mode controllers, are provided, respectively. Simulation results from an inverted pendulum example are presented to illustrate the advantages and effectiveness of the proposed approaches.
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.
Signatures of nonlinear mode interactions in the pulsating hot B subdwarf star KIC 10139564
Zong, W.; Charpinet, S.; Vauclair, G.
2016-10-01
Context. The unprecedented photometric quality and time coverage offered by the Kepler spacecraft has opened up new opportunities to search for signatures of nonlinear effects that affect oscillation modes in pulsating stars. Aims: The data accumulated on the pulsating hot B subdwarf KIC 10139564 are used to explore in detail the stability of its oscillation modes, focusing in particular on evidences of nonlinear behaviors. Methods: We analyzed 38 months of contiguous short-cadence data, concentrating on mode multiplets induced by the star rotation and on frequencies forming linear combinations that show intriguing behaviors during the course of the observations. Results: We find clear signatures that point toward nonlinear effects predicted by resonant mode coupling mechanisms. These couplings can induce various mode behaviors for the components of multiplets and for frequencies related by linear relationships. We find that a triplet at 5760 μHz, a quintuplet at 5287 μHz and a (ℓ > 2) multiplet at 5412 μHz, all induced by rotation, show clear frequency and amplitude modulations which are typical of the so-called intermediate regime of a resonance between the components. One triplet at 316 μHz and a doublet at 394 μHz show modulated amplitude and constant frequency which can be associated with a narrow transitory regime of the resonance. Another triplet at 519 μHz appears to be in a frequency-locked regime where both frequency and amplitude are constant. Additionally, three linear combinations of frequencies near 6076 μHz also show amplitude and frequency modulations, which are likely related to a three-mode direct resonance of the type ν0 ~ ν1 + ν2. Conclusions: The identified frequency and amplitude modulations are the first clear-cut signatures of nonlinear resonant couplings occurring in pulsating hot B subdwarf stars. However, the observed behaviors suggest that the resonances occurring in these stars usually follow more complicated patterns than
Nonlinear optical microscopy for histology of fresh normal and cancerous pancreatic tissues.
Directory of Open Access Journals (Sweden)
Wenyan Hu
Full Text Available BACKGROUND: Pancreatic cancer is a lethal disease with a 5-year survival rate of only 1-5%. The acceleration of intraoperative histological examination would be beneficial for better management of pancreatic cancer, suggesting an improved survival. Nonlinear optical methods based on two-photon excited fluorescence (TPEF and second harmonic generation (SHG of intrinsic optical biomarkers show the ability to visualize the morphology of fresh tissues associated with histology, which is promising for real-time intraoperative evaluation of pancreatic cancer. METHODOLOGY/PRINCIPAL FINDINGS: In order to investigate whether the nonlinear optical imaging methods have the ability to characterize pancreatic histology at cellular resolution, we studied different types of pancreatic tissues by using label-free TPEF and SHG. Compared with other routine methods for the preparation of specimens, fresh tissues without processing were found to be most suitable for nonlinear optical imaging of pancreatic tissues. The detailed morphology of the normal rat pancreas was observed and related with the standard histological images. Comparatively speaking, the preliminary images of a small number of chemical-induced pancreatic cancer tissues showed visible neoplastic differences in the morphology of cells and extracellular matrix. The subcutaneous pancreatic tumor xenografts were further observed using the nonlinear optical microscopy, showing that most cells are leucocytes at 5 days after implantation, the tumor cells begin to proliferate at 10 days after implantation, and the extracellular collagen fibers become disordered as the xenografts grow. CONCLUSIONS/SIGNIFICANCE: In this study, nonlinear optical imaging was used to characterize the morphological details of fresh pancreatic tissues for the first time. We demonstrate that it is possible to provide real-time histological evaluation of pancreatic cancer by the nonlinear optical methods, which present an
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Normal mode splitting and mechanical effects of an optical lattice in a ring cavity
Klinner, J; Lindholdt, M; Nagorny, B; Hemmerich, Andreas; Klinner, Julian; Lindholdt, Malik; Nagorny, Boris
2005-01-01
A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detunedby about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.
Normal Mode Splitting and Mechanical Effects of an Optical Lattice in a Ring Cavity
Klinner, Julian; Lindholdt, Malik; Nagorny, Boris; Hemmerich, Andreas
2006-01-01
A novel regime of atom-cavity physics is explored, arising when large atom samples dispersively interact with high-finesse optical cavities. A stable far-detuned optical lattice of several million rubidium atoms is formed inside an optical ring resonator by coupling equal amounts of laser light to each propagation direction of a longitudinal cavity mode. An adjacent longitudinal mode, detuned by about 3 GHz, is used to perform probe transmission spectroscopy of the system. The atom-cavity coupling for the lattice beams and the probe is dispersive and dissipation results only from the finite photon-storage time. The observation of two well-resolved normal modes demonstrates the regime of strong cooperative coupling. The details of the normal mode spectrum reveal mechanical effects associated with the retroaction of the probe upon the optical lattice.
Isotope effect in normal-to-local transition of acetylene bending modes.
Ma, Jianyi; Xu, Dingguo; Guo, Hua; Tyng, Vivian; Kellman, Michael E
2012-01-07
The normal-to-local transition for the bending modes of acetylene is considered a prelude to its isomerization to vinylidene. Here, such a transition in fully deuterated acetylene is investigated using a full-dimensional quantum model. It is found that the local benders emerge at much lower energies and bending quantum numbers than in the hydrogen isotopomer HCCH. This is accompanied by a transition to a second kind of bending mode called counter-rotator, again at lower energies and quantum numbers than in HCCH. These transitions are also investigated using bifurcation analysis of two empirical spectroscopic fitting Hamiltonians for pure bending modes, which helps to understand the origin of the transitions semiclassically as branchings or bifurcations out of the trans- and cis-normal bend modes when the latter become dynamically unstable. The results of the quantum model and the empirical bifurcation analysis are in very good agreement.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Breton, N
2016-01-01
The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNMs of four nonlinear electromagnetic black holes, two singular and two regular, namely from Euler-Heisenberg and Born-Infeld theories, for singular, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparison is shown with the QNMs of the linear electromagnetic counterpart, their Reissner-Nordstr\\"{o}m black hole.
Chattering free adaptive fuzzy terminal sliding mode control for second order nonlinear system
Institute of Scientific and Technical Information of China (English)
Jinkun LIU; Fuchun SUN
2006-01-01
A novel fuzzy terminal sliding mode control (FTSMC) scheme is proposed for position tracking of a class of second-order nonlinear uncertain system. In the proposed scheme, we integrate input-output linearization technique to cancel the nonlinearities. By using a function-augmented sliding hyperplane, it is guaranteed that the output tracking error converges to zero in finite time which can be set arbitrarily. The proposed scheme eliminates reaching phase problem, so that the closed-loop system always shows invariance property to parameter uncertainties. Fuzzy logic systems are used to approximate the unknown system functions and switch item. Robust adaptive law is proposed to reduce approximation errors between true nonlinear functions and fuzzy systems, thus chattering phenomenon can be eliminated. Stability of the proposed control scheme is proved and the scheme is applied to an inverted pendulum system. Simulation studies are provided to confirm performance and effectiveness of the proposed control approach.
Quasinormal modes of nonlinear electromagnetic black holes from unstable null geodesics
Bretón, Nora; López, L. A.
2016-11-01
The expressions for the quasinormal modes (QNM) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNM of black holes are determined by the parameters of the circular null geodesics. The unstable circular null orbits are derived from the effective metric that is the one obeyed by light rays under the influence of a nonlinear electromagnetic field. As an illustration we calculate the QNM of four nonlinear electromagnetic black holes, two singular and two regular, namely, from Euler-Heisenberg and Born-Infeld theories, for singular ones, and the magnetic Bardeen black hole and the one derived by Bronnikov for regular ones. Comparing with the QNM of the linear electromagnetic counterpart, their Reissner-Nordström black hole is done.
Nonlinear and Perturbative Evolution of Distorted Black Holes; 2, Odd-parity Modes
Baker, J; Campanelli, M; Loustó, C O; Seidel, E; Takahashi, R
2000-01-01
We compare the fully nonlinear and perturbative evolution of nonrotating black holes with odd-parity distortions utilizing the perturbative results to interpret the nonlinear results. This introduction of the second polarization (odd-parity) mode of the system, and the systematic use of combined techniques brings us closer to the goal of studying more complicated systems like distorted, rotating black holes, such as those formed in the final inspiral stage of two black holes. The nonlinear evolutions are performed with the 3D parallel code for Numerical Relativity, {Cactus}, and an independent axisymmetric code, {Magor}. The linearized calculation is performed in two ways: (a) We treat the system as a metric perturbation on Schwarzschild, using the Regge-Wheeler equation to obtain the waveforms produced. (b) We treat the system as a curvature perturbation of a Kerr black hole (but here restricted to the case of vanishing rotation parameter a) and evolve it with the Teukolsky equation The comparisons of the wa...
Orain, François; Bécoulet, M.; Morales, J.; Huijsmans, G. T. A.; Dif-Pradalier, G.; Hoelzl, M.; Garbet, X.; Pamela, S.; Nardon, E.; Passeron, C.; Latu, G.; Fil, A.; Cahyna, P.
2015-01-01
The dynamics of a multi-edge localized mode (ELM) cycle as well as the ELM mitigation by resonant magnetic perturbations (RMPs) are modeled in realistic tokamak X-point geometry with the non-linear reduced MHD code JOREK. The diamagnetic rotation is found to be a key parameter enabling us to reproduce the cyclical dynamics of the plasma relaxations and to model the near-symmetric ELM power deposition on the inner and outer divertor target plates consistently with experimental measurements. Moreover, the non-linear coupling of the RMPs with unstable modes are found to modify the edge magnetic topology and induce a continuous MHD activity in place of a large ELM crash, resulting in the mitigation of the ELMs. At larger diamagnetic rotation, a bifurcation from unmitigated ELMs—at low RMP current—towards fully suppressed ELMs—at large RMP current—is obtained.
Variable structure control with sliding mode prediction for discrete-time nonlinear systems
Institute of Scientific and Technical Information of China (English)
Lingfei XIAO; Hongye SU; Xiaoyu ZHANG; Jian CHU
2006-01-01
A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.
Kong, Lingjie; Xiao, Xiaosheng; Yang, Changxi
2011-09-12
We numerically studied the polarization dynamics in dissipative soliton lasers mode-locked by nonlinear polarization rotation (NPR). It was found that the polarization states of the intracavity dissipative soliton vary with time across the pulse. Depending on output coupling ratios, the polarization states of the pulse peak before the polarizer can be either nearly circular or nearly linear polarizations. The polarization dependent component in NPR is found to play a role of spectral filter under high and medium output coupling. However, NPR may work as a weak optical limiter under low output coupling, when additional spectral filtering is necessary to maintain steady mode-locking state.
Dielectric normal and segmental relaxation modes by extended irreversible thermodynamics (EIT)
Energy Technology Data Exchange (ETDEWEB)
Diaz-Calleja, Ricardo; Compan, Vicente; Riande, E
2004-06-15
The time rate change of the polarization vector of an isotropic polymer containing dipoles along the chain contour under an electric field is studied using the extended irreversible thermodynamics formalism. The analysis leads to the formulation of phenomenological equations of Havriliak-Negami for the dielectric permittivity that give a good account of the dielectric {alpha} and normal mode peaks associated, respectively, with the segmental modes and the motion of the whole chain.
Circuits and systems based on delta modulation linear, nonlinear and mixed mode processing
Zrilic, Djuro G
2005-01-01
This book is intended for students and professionals who are interested in the field of digital signal processing of delta-sigma modulated sequences. The overall focus is on the development of algorithms and circuits for linear, non-linear, and mixed mode processing of delta-sigma modulated pulse streams. The material presented here is directly relevant to applications in digital communication, DSP, instrumentation, and control.
Nonlinear Control Strategies for Bioprocesses: Sliding Mode Control versus Vibrational Control
Selisteanu, Dan; Petre, Emil; Popescu, Dorin; Bobasu, Eugen
2008-01-01
In this work, two nonlinear high-frequency control strategies for bioprocesses are proposed: a feedback sliding mode control law and a vibrational control strategy. In order to implement these strategies, a prototype bioprocess that is carried out in a Continuous Stirred Tank Bioreactor was considered. First, a discontinuous feedback law was designed using the exact linearization and by imposing a SMC that stabilizes the output of the bioprocess. When some state variables used in the control ...
Dynamic Sliding Mode Control Design Based on an Integral Manifold for Nonlinear Uncertain Systems
Qudrat Khan; Aamer Iqbal Bhatti; Antonella Ferrara
2014-01-01
An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In c...
MODES: open-access software for the normal-mode representation of the global 3D circulation
Zagar, Nedjeljka
2015-04-01
The goal of the talk is to present MODES, software for the normal-mode function representation of the 3D global datasets. The software, developed within the ERC project MODES, is now available to atmospheric research community as an open-access tool. MODES allows one to diagnose properties of balanced and inertio-gravity (IG) circulation across many scales by considering both mass and wind field and the whole model depth. In particular, the IG spectrum, which has only recently become observable in global datasets, can be studied simultaneously in the mass field and wind field and considering the whole model depth. The software can be used for the comparison of climate model outputs with the reanalysis datasets. The presentation will include theoretical background and basic technical details of the software that can be installed and used with a relatively modest effort. Example of the software outputs are available in real-time at http://meteo.fmf.uni-lj.si/MODES. Results from the modal analysis of the ERA Interim dataset as well as the ensemble prediction system of ECMWF are presented.
Ishioka, Tsutomu; Yan, Wenhong; Strauss, Herbert L; Snyder, Robert G
2003-03-01
Normal mode analyses are made for methyl palmitate molecule having all-trans or conformational disorders around the ester head group, in order to explain characteristic observed frequency shifts in the wagging progressive region between all-trans and disorder chains in triglyceride molecules. It was found that one gauche conformation at C(alpha)-C(beta) position and 90 degrees rotation of the ester head group in an alkyl chain produce frequency shifts for twisting mode as observed. For wagging modes, contamination of the disorders around the head group makes assignments change and apparent frequency shifts occur.
Hou, Huazhou; Zhang, Qingling
2016-11-01
In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method.
Nazemosadat, Elham; Mafi, Arash
2014-08-15
We propose an all-fiber mode-locking device, which operates based on nonlinear switching in a novel two-concentric-core fiber structure. The design is particularly attractive given the ease of fabrication and coupling to other components in a mode-locked fiber laser cavity. The nonlinear switching in this coupler is studied, and the relative power transmission is obtained. The analysis shows that this nonlinear switch is practical for mode-locking fiber lasers and is forgiving to fabrication errors.
Institute of Scientific and Technical Information of China (English)
WANG Huanlei; ZHU Xiaofeng; GONG Xiufen; ZHANG Dong
2003-01-01
Based on the finite amplitude insert-substitu- tion method, a novel technique to reconstruct the acoustic nonlinear parameter B/A tomography for biological tissues in reflection mode via the difference frequency wave generated by a parametric array is developed in this paper. An experimental system is established, and the beam pattern of the difference frequency wave is measured and compared with that excited directly from a transmitter at the same frequency. B/A tomography for several biological tissues including normal and pathological tissues, is experimentally obtained with satisfying quality. Results indicate that B/A imaging using this mode may become a novel modality in ultrasonic diagnosis.
Mode Coupling and Nonlinear Resonances of MEMS Arch Resonators for Bandpass Filters
Hajjaj, Amal Z.
2017-01-30
We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.
Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion
Wabnitz, Stefan
2013-01-01
In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schr\\"odinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.
Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions.
Lachos, Victor H; Bandyopadhyay, Dipankar; Garay, Aldo M
2011-08-01
An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.
Flat super-continuum generation based on normal dispersion nonlinear photonic crystal fibre
DEFF Research Database (Denmark)
Chow, K.K.; Takushima, Y.; Lin, C.
2006-01-01
Flat super-continuum generation spanning over the whole telecommunication band using a passively modelocked fibre laser source at 1550 nm together with a dispersion-flattened nonlinear photoinc crystal fibre is demonstrated. Since the pulses propagate in the normal dispersion regime of the fibre...... only, linear frequency chirp is induced by self-phase modulation which leads to a flat super-continuum. By launching the compressed 170 fs modelocked pulses with an average power of 10 mW into the fibre, super-continuum over 185 nm with less than 5 dB fluctuation is obtained from the all...
Laser ultrasonic analysis of normal modes generated by a voltage pulse on an AT quartz sensor.
Goossens, Jozefien; Martinez, Loïc; Glorieux, Christ; Wilkie-Chancellier, Nicolas; Ehssein, Chighali Ould; Serfaty, Stéphane
2006-12-22
Laser ultrasonic detection is a versatile and highly sensitive tool for the observation of surface waves. In the following study, laser ultrasonic detection is used for the experimental study of spurious normal vibration modes of a disk quartz sensor excited by a voltage pulse. The AT cut crystal (cut of the crystal relative to the the main crystallographic axis is 35.25 degrees) is optimal for generating mainly thickness-shear vibrations (central frequency 6 MHz) on the quartz surface. However, resulting from shear-to-longitudinal and shear-to-surface mode conversion, and from the weak coupling with the other crystallographic axes, other modes (thickness-compressional and bending modes) are always present in the plate response. Since the laser vibrometer is sensitive to normal displacements, the laser investigation shows waves that can be considered as unwanted for the AT quartz used as a shear sensor. The scanned three dimensional (3D) amplitude-space-time signals are carefully analysed using their representation in three dual Fourier domains (space-time, wave number-frequency). Results on the transient analysis of the waves, the normal bending modes and the dispersion curves are shown.
Xiao, Jianyuan; Qin, Hong; Yu, Zhi; Xiang, Nong
2015-01-01
In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and cur...
Gil, Victor A; Lecina, Daniel; Grebner, Christoph; Guallar, Victor
2016-10-15
Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5-7×), making it a good candidate for future normal mode implementations in Monte Carlo methods. Copyright © 2016 Elsevier Ltd. All rights reserved.
Calculation and measurement of terahertz active normal modes in crystalline PETN.
Burnett, Andrew D; Kendrick, John; Cunningham, John E; Hargreaves, Michael D; Munshi, Tasmin; Edwards, Howell G M; Linfield, Edmund H; Davies, A Giles
2010-02-01
The terahertz frequency spectrum of pentaerythritol tetranitrate (PETN) is calculated using Discover with the COMPASS force field, CASTEP and PWscf. The calculations are compared to each other and to terahertz spectra (0.3-3 THz) of crystalline PETN recorded at 4 K. A number of analysis methods are used to characterise the calculated normal modes.
Anisotropy of Earth's inner core intrinsic attenuation from seismic normal mode models
Mäkinen, Anna M.; Deuss, Arwen; Redfern, Simon A T
2014-01-01
The Earth's inner core, the slowly growing sphere of solid iron alloy at the centre of our planet, is known to exhibit seismic anisotropy. Both normal mode and body wave studies have established that, when the global average is taken, compressional waves propagate faster in the North-South direction
Anisotropy of Earth's inner core intrinsic attenuation from seismic normal mode models
Mäkinen, Anna M.; Deuss, Arwen; Redfern, Simon A T
2014-01-01
The Earth's inner core, the slowly growing sphere of solid iron alloy at the centre of our planet, is known to exhibit seismic anisotropy. Both normal mode and body wave studies have established that, when the global average is taken, compressional waves propagate faster in the North-South direction
Maksimovic, Milan; Lohmeyer, Manfred; van Groesen, Embrecht W.C.
Quasi-Normal Modes are used to characterize transmission resonances in 1D optical defect cavities and the related field approximations. Using a mirror field and the relevant QNM, a variational principle permits to represent the field and the spectral transmission close to resonances.
Maksimovic, Milan; Lohmeyer, Manfred; van Groesen, Embrecht W.C.
2008-01-01
Quasi-normal modes are used to characterize transmission resonances in 1D optical defect cavities and the related field approximations. We specialize to resonances inside the bandgap of the periodic multilayer mirrors that enclose the defect cavities. Using a template with the most relevant QNMs a
Coupled optical defect microcavities in one-dimensional photonic crystals and quasi-normal modes
Maksimovic, Milan; Lohmeyer, Manfred; van Groesen, Embrecht W.C.
2008-01-01
We analyze coupled optical defect cavities realized in finite one-dimensional photonic crystals (PC). Viewing these as open systems, where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and quasi-normal modes (QNM) (eigenfunctions).
Coupled optical defect microcavities in 1D photonic crystals and quasi-normal modes
Maksimovic, Milan; Lohmeyer, Manfred; van Groesen, Embrecht W.C.; Greiner, C.M.; Waechter, C.A.
2008-01-01
We analyze coupled optical defect cavities realized in finite one-dimensional Photonic Crystals. Viewing these as open systems where waves are permitted to leave the structures, one obtains eigenvalue problems for complex frequencies (eigenvalues) and Quasi-Normal-Modes (eigenfunctions). Single
Song, Yong-Won; Yamashita, Shinji; Goh, Chee S.; Set, Sze Y.
2007-01-01
We demonstrate a novel passive mode-locking scheme for pulsed lasers enhanced by the interaction of carbon nanotubes (CNTs) with the evanescent field of propagating light in a D-shaped optical fiber. The scheme features all-fiber operation as well as a long lateral interaction length, which guarantees a strong nonlinear effect from the nanotubes. Mode locking is achieved with less than 30% of the CNTs compared with the amount of nanotubes used for conventional schemes. Our method also ensures the preservation of the original morphology of the individual CNTs. The demonstrated pulsed laser with our CNT mode locker has a repetition rate of 5.88 MHz and a temporal pulse width of 470 fs.
Song, Yong-Won; Yamashita, Shinji; Goh, Chee S; Set, Sze Y
2007-01-15
We demonstrate a novel passive mode-locking scheme for pulsed lasers enhanced by the interaction of carbon nanotubes (CNTs) with the evanescent field of propagating light in a D-shaped optical fiber. The scheme features all-fiber operation as well as a long lateral interaction length, which guarantees a strong nonlinear effect from the nanotubes. Mode locking is achieved with less than 30% of the CNTs compared with the amount of nanotubes used for conventional schemes. Our method also ensures the preservation of the original morphology of the individual CNTs. The demonstrated pulsed laser with our CNT mode locker has a repetition rate of 5.88 MHz and a temporal pulse width of 470 fs.
Sliding-mode control design for nonlinear systems using probability density function shaping.
Liu, Yu; Wang, Hong; Hou, Chaohuan
2014-02-01
In this paper, we propose a sliding-mode-based stochastic distribution control algorithm for nonlinear systems, where the sliding-mode controller is designed to stabilize the stochastic system and stochastic distribution control tries to shape the sliding surface as close as possible to the desired probability density function. Kullback-Leibler divergence is introduced to the stochastic distribution control, and the parameter of the stochastic distribution controller is updated at each sample interval rather than using a batch mode. It is shown that the estimated weight vector will converge to its ideal value and the system will be asymptotically stable under the rank-condition, which is much weaker than the persistent excitation condition. The effectiveness of the proposed algorithm is illustrated by simulation.
Uncertain Unified Chaotic Systems Control with Input Nonlinearity via Sliding Mode Control
Directory of Open Access Journals (Sweden)
Zhi-ping Shen
2016-01-01
Full Text Available This paper studies the stabilization problem for a class of unified chaotic systems subject to uncertainties and input nonlinearity. Based on the sliding mode control theory, we present a new method for the sliding mode controller design and the control law algorithm for such systems. In order to achieve the goal of stabilization unified chaotic systems, the presented controller can make the movement starting from any point in the state space reach the sliding mode in limited time and asymptotically reach the origin along the switching surface. Compared with the existing literature, the controller designed in this paper has many advantages, such as small chattering, good stability, and less conservative. The analysis of the motion equation and the simulation results all demonstrate that the method is effective.
Electronic control of nonlinear-polarization-rotation mode locking in Yb-doped fiber lasers.
Shen, Xuling; Li, Wenxue; Yan, Ming; Zeng, Heping
2012-08-15
We demonstrate a convenient approach to precisely tune the polarization state of a nonlinear-polarization-rotation mode-locked Yb-doped fiber laser by using an electronic polarization controller. It is shown to benefit self-starting of mode-locking states, with precise tuning of the spectral profile, pulse width, and carrier-envelope offset frequency. The pulse width changed linearly by 0.78 ps in the time domain, and the carrier-envelope offset frequency shifted ~77.5 MHz in the frequency domain with a slight change of the driving voltage of 30.7 mV applied on the controller, corresponding to a polarization rotation of 0.0135π. This facilitated precise and automatic regeneration of a particular mode-locking state by setting an accurate voltage at the polarization controller with a programmed microprocessor control unit.
Normal Mode Analysis on the Relaxation of AN Excited Nitromethane Molecule in Argon Bath
Rivera-Rivera, Luis A.; Wagner, Albert F.
2017-06-01
In our previous work [Rivera-Rivera et al. J. Chem. Phys. 142, 014303 (2015).] classical molecular dynamics simulations followed, in an Ar bath, the relaxation of nitromethane (CH_3NO_2) instantaneously excited by statistically distributing 50 kcal/mol among all its internal degrees of freedom. The 300 K Ar bath was at pressures of 10 to 400 atm. Both rotational and vibrational energies exhibited multi-exponential decay. This study explores mode-specific mechanisms at work in the decay process. With the separation of rotation and vibration developed by Rhee and Kim [J. Chem. Phys. 107, 1394 (1997).], one can show that the vibrational kinetic energy decomposes only into vibrational normal modes while the rotational and Coriolis energies decompose into both vibrational and rotational normal modes. Then the saved CH_3NO_2 positions and momenta can be converted into mode-specific energies whose decay over 1000 ps can be monitored. The results identify vibrational and rotational modes that promote/resist energy lost and drive multi-exponential behavior. In addition to mode-specificity, the results show disruption of IVR with increasing pressure.
Energy Technology Data Exchange (ETDEWEB)
Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)
2011-01-15
The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.
A coupling model for quasi-normal modes of photonic resonators
Vial, Benjamin; Hao, Yang
2016-11-01
We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a generalized eigenvalue problem involving small size dense matrices. We apply this technique to dielectric rod dimmer of rectangular cross section for transverse electric polarization in a two-dimensional setup. The results of our model show excellent agreement with full wave finite element simulations. We provide a convergence analysis, and a simplified model with a few modes to study the influence of the relative position of the two resonators. This model provides interesting physical insights on the coupling scheme at stake in such systems and pave the way for systematic and efficient design and optimization of resonances in more complicated systems, for applications including sensing, antennae and spectral filtering.
Normal modes and quality factors of spherical dielectric resonators: I — Shielded dielectric sphere
Indian Academy of Sciences (India)
R A Yadav; I D Singh
2004-06-01
Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of $$m size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.
Institute of Scientific and Technical Information of China (English)
Liu Yang; Tang Yi
2008-01-01
By means of the Glauber's coherent state method combined with multiple-scale method,this paper investigates the localized modes in a quantum one-dimensional Klein-Gordon chain and finds that the equation of motion of annihilation operator is reduced to the nonlinear Schr(o)dinger equation.Interestingly,the model can support both bright and dark small amplitude travelling and non-travelling nonlinear localized modes in different parameter spaces.
Yi-You Hou; Zhang-Lin Wan
2014-01-01
This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI) optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance). The effectiveness and accura...
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
A Nonlinear Coupled-Mode System for Water Waves over a General Bathymetry
Athanassoulis, G. A.; Belibassakis, K. A.
2003-04-01
In the present work we consider the problem of non-linear gravity waves propagating over a general bathymetry. The simpler two dimensional problem (one horizontal dimension) is first examined. An essential feature of this problem is that the wave field is not spatially periodic. Extra difficulties are introduced by the fact that we wish to drop the assumptions of smallness of the free-surface and bottom slope. The interaction of free-surface gravity waves with uneven bottom topography requires, in principle, the solution of a complicated nonlinear boundary value problem. Under the assumptions of incompressibility and irrotationality, the problem of evolution of water waves, over a variable bathymetry region, admits of at least two different varia-tional formulations: A Hamiltonian one, proposed by Petrov (1964) and exploited further by Zakharov (1968) and various other authors thenceforth, and an unconstrained one, proposed by Luke (1967). Our main concern herewith is to develop a non-linear theory for the case of a smooth, generally shaped bathymetry, without imposing any mild-slope type assumptions neither on the free-surface nor on the bottom boundary. The present development is based on Luke's variational principle, in which the admissible fields are free of essential conditions, except, of course, for the smoothness and completeness (compatibility) prerequisites. The vertical structure of the wave field is exactly represented by means of a modal-type series expansion of the wave potential (Athanassoulis and Belibassakis 2000). This series expansion contains the usual propagating and evanescent modes, plus two additional modes, called the free-surface mode and the sloping-bottom mode, introduced in order to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. A similar technique has been successfully applied to the solution of the linearised (Athanassoulis and Belibassakis 1999) and the second-order (Belibassakis and
Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line
Sato, M.; Mukaide, T.; Nakaguchi, T.; Sievers, A. J.
2016-07-01
The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.
Indian Academy of Sciences (India)
Shyamal Mondal; Satya Pratap Singh; Sourabh Mukhopadhyay; Aditya Date; Kamal Hussain; Shouvik Mukherjee; Prasanta Kumar Datta
2014-02-01
A comparative study in terms of optimized output power and stability is made on cascaded second-order nonlinear optical mode-locking with KTP, BBO and LBO crystals for both 1064 nm and 532 nm. Large nonlinear optical phase shift achieved in a non-phase-matched second harmonic generating crystal, is transformed into amplitude modulation through soft aperturing the nonlinear cavity mode variation at the laser gain medium to mode-lock a Nd:YVO4 laser. The laser delivers stable dual wavelength cw mode-locked pulse train with pulse duration 10.3 ps and average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively for the optimum performance in type-II KTP crystal. The exceptional stability achieved with KTP is accounted by simulating the mode-size variation with phase mismatch.
Excitation of travelling torsional normal modes in an Earth's core model
Gillet, N.; Jault, D.; Canet, E.
2017-09-01
The proximity between the 6 yr recurrence time of the torsional Alfvén waves that have been inferred in the Earth's outer core over 1940-2010 and their 4 yr traveltime across the fluid core is nicely explained if these travelling waves are to be considered as normal modes. We discuss to what extent the emergence of free torsional modes from a stochastic forcing in the fluid core is compatible with some dissipation, specifically with an electromagnetic torque strong enough to account for the observed length of day variations of 6 yr period. In a spherical cavity enclosed by an insulating mantle, torsional normal modes consist of standing waves. In the presence of a conducting mantle, they transform into outward travelling waves very similar to the torsional waves that have been detected in the Earth's outer core. With such a resonant response a periodic forcing is not required to explain the regular recurrence of torsional waves; neither is the search for a source of motions in the vicinity of the cylindrical surface tangent to the inner core, where travelling waves seem to emerge. We discuss these results in the light of the reflection properties of torsional waves at the equator. We are able to reproduce the properties found for geophysical time-series of geostrophic flows (detection of a normal mode, almost total absorption at the equator) if the conductance of the lowermost mantle is 3 × 107 to 108 S.
Adaptive terminal sliding mode control for high-order nonlinear dynamic systems
Institute of Scientific and Technical Information of China (English)
庄开宇; 苏宏业; 张克勤; 褚健
2003-01-01
An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.
Nonlinear adaptive control based on fuzzy sliding mode technique and fuzzy-based compensator.
Nguyen, Sy Dzung; Vo, Hoang Duy; Seo, Tae-Il
2017-09-01
It is difficult to efficiently control nonlinear systems in the presence of uncertainty and disturbance (UAD). One of the main reasons derives from the negative impact of the unknown features of UAD as well as the response delay of the control system on the accuracy rate in the real time of the control signal. In order to deal with this, we propose a new controller named CO-FSMC for a class of nonlinear control systems subjected to UAD, which is constituted of a fuzzy sliding mode controller (FSMC) and a fuzzy-based compensator (CO). Firstly, the FSMC and CO are designed independently, and then an adaptive fuzzy structure is discovered to combine them. Solutions for avoiding the singular cases of the fuzzy-based function approximation and reducing the calculating cost are proposed. Based on the solutions, fuzzy sliding mode technique, lumped disturbance observer and Lyapunov stability analysis, a closed-loop adaptive control law is formulated. Simulations along with a real application based on a semi-active train-car suspension are performed to fully evaluate the method. The obtained results reflected that vibration of the chassis mass is insensitive to UAD. Compared with the other fuzzy sliding mode control strategies, the CO-FSMC can provide the best control ability to reduce unwanted vibrations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Taochang Li
2014-01-01
Full Text Available Automatic steering control is the key factor and essential condition in the realization of the automatic navigation control of agricultural vehicles. In order to get satisfactory steering control performance, an adaptive sliding mode control method based on a nonlinear integral sliding surface is proposed in this paper for agricultural vehicle steering control. First, the vehicle steering system is modeled as a second-order mathematic model; the system uncertainties and unmodeled dynamics as well as the external disturbances are regarded as the equivalent disturbances satisfying a certain boundary. Second, a transient process of the desired system response is constructed in each navigation control period. Based on the transient process, a nonlinear integral sliding surface is designed. Then the corresponding sliding mode control law is proposed to guarantee the fast response characteristics with no overshoot in the closed-loop steering control system. Meanwhile, the switching gain of sliding mode control is adaptively adjusted to alleviate the control input chattering by using the fuzzy control method. Finally, the effectiveness and the superiority of the proposed method are verified by a series of simulation and actual steering control experiments.
Multi-input sliding mode control of nonlinear uncertain affine systems
Bartolini, Giorgio; Punta, Elisabetta; Zolezzi, Tullio
2011-05-01
In the extension to multi-input nonlinear uncertain systems of the sliding mode methodology, a crucial role is played by the matrix pre-multiplying the control in the dynamic equation of the sliding output. If this matrix is perfectly known and invertible, it is possible to transform a multi-input sliding mode control problem in an almost decoupled set of single-input problems. If this matrix is uncertain then nothing can be done in general, and the investigation is oriented to find conditions ensuring the feasibility of control strategies in a progressively more general set of uncertain matrices. In the case of uncertain and constant matrices, it is possible, in principle, to manage the case in which the matrix in question is invertible. The corresponding adaptive or switching strategy suffers from the curse of dimensionality of the so-called unmixing set. In this article the case of time- and state-varying uncertain matrix is dealt with. A more general class of such a matrices for which there is, at least locally, a solution of the problem is found. The introduction of artificial integrators in the output channel (the integral sliding mode control methodology) allows the practical implementation of the control law without requiring the a priori knowledge of parameters featured by the solution of a relevant nonlinear Lyapunov equation.
M-mode echocardiography in normal children and adolescents: some new perspectives.
Lester, L A; Sodt, P C; Hutcheon, N; Arcilla, R A
1987-01-01
Normal M-mode echocardiography values were determined using computer-assisted measurements of echocardiograms (ECHO) in 202 children and young adults 25 days to 23 years of age: 77 were female, and 125 were male and, reflecting the population served by our Center, 99 were black and 103 were white children. The values for left and right heart wall thicknesses and chamber sizes were graphically displayed as a function of body surface area, and with an illustration of the regression line and 2 standard deviation (SD) range of normal for each parameter. In addition, normal ECHO predicting equations for dimension and function parameters were derived using multiple linear regression analysis with age, height, weight, sex, race, and heart rate as independent variables. A comparison was made between the observed data and the data derived from the normal predicting equations for each of the parameters. Also, values obtained from these equations were compared to data generated from other published normal predicting equations. A description of the digitizer measurements, computer interfacing, and a sample ECHO report form utilizing the predicted normal ranges for each of the parameters is presented. We propose that quantitative M-mode echocardiographic reporting should be easily accessible to all pediatric cardiology laboratories.
Microwave emission by nonlinear crystals irradiated with a high-intensity, mode-locked laser
Borghesani, A F; Guarise, M
2016-01-01
We report on the experimental investigation of the efficiency of some nonlinear crystals to generate microwave (RF) radiation as a result of optical rectification (OR) when irradiated with intense pulse trains delivered by a mode-locked laser at $1064\\,$nm. We have investigated lithium triborate (LBO), lithium niobate (LiNbO$_3$), zinc selenide (ZnSe), and also potassium titanyl orthophosphate (KTP) for comparison with previous measurements. The results are in good agreement with the theoretical predictions based on the form of the second-order nonlinear susceptibility tensor. For some crystals we investigated also the second harmonic generation (SHG) to cross check the theoretical model. We confirm the theoretical prediction that OR leads to the production of higher order RF harmonics that are overtones of the laser repetition rate.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven By Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G.Y. Fu
2010-10-01
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
On Nonlinear Self-interaction of Geodesic Acoustic Mode Driven by Energetic Particles
Energy Technology Data Exchange (ETDEWEB)
G. Y. Fu
2010-06-04
It is shown that nonlinear self-interaction of energetic particle-driven Geodesic Acoustic Mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low uctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.
Mukamel, Shaul
2003-08-01
Computing response functions by following the time evolution of superoperators in Liouville space (whose vectors are ordinary Hilbert space operators) offers an attractive alternative to the diagrammatic perturbative expansion of many-body equilibrium and nonequilibrium Green's functions. The bookkeeping of time ordering is naturally maintained in real (physical) time, allowing the formulation of Wick's theorem for superoperators, giving a factorization of higher order response functions in terms of two fundamental Green's functions. Backward propagations and analytic continuations using artificial times (Keldysh loops and Matsubara contours) are avoided. A generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions. Classical response functions are obtained without the explicit computation of stability matrices.
Villanueva, Guillermo E; Jakubinek, Michael B; Simard, Benoit; Oton, Claudio J; Matres, Joaquín; Shao, Li-Yang; Pérez-Millán, Pere; Albert, Jacques
2011-06-01
Single-wall carbon nanotube deposition on the cladding of optical fibers has been carried out to fabricate an all-fiber nonlinear device. Two different nanotube deposition techniques were studied. The first consisted of repeatedly immersing the optical fiber into a nanotube supension, increasing the thickness of the coating in each step. The second deposition involved wrapping a thin film of nanotubes around the optical fiber. For both cases, interaction of transmitted light through the fiber core with the external coating was assisted by the cladding mode resonances of a tilted fiber Bragg grating. Ultrafast nonlinear effects of the nanotube-coated fiber were measured by means of a pump-probe pulses experiment. © 2011 Optical Society of America
Nonlinear Dynamic Study on Geomagnetic Polarity Reversal and Cretaceous Normal Superchron
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is generally acknowledged that geomagnetic polarity has reversed many times in geological history and an abnormal geologic phenomenon is the Cretaceous normal superchron. However, the causes have been unknown up to now. The nonlinear theory has been applied to analyze the phenomenon in geomagnetic polarity reversal and the Cretaceous normal superchron. The Cretaceous normal superchron implies that interaction of the Earth's core-mantle and liquid movement in the outer core may be the lowest energy state and the system of Earth magnetic field maintains a sort of temporal or spatial order structure by exchanging substance and energy in the outside continuously.During 121-83 Ma, there was no impact of a celestial body that would result in a geomagnetic polarity reversal, which may be a cause for occurrence of the Cretaceous normal superchron. The randomness of geomagnetic polarity reversal has the self-reversion characteristic of chaos and the chaos theory gives a simple and clear explanation for the dynamic cause of the geomagnetic polarity reversal.
Theory and praxis of map analsys in CHEF part 2: Nonlinear normal form
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /FERMILAB
2009-04-01
This is the second of three memos describing how normal form map analysis is implemented in CHEF. The first [1] explained the manipulations required to assure that initial, linear transformations preserved Poincare invariants, thereby confirming correct normalization of action-angle coordinates. In this one, the transformation will be extended to nonlinear terms. The third, describing how the algorithms were implemented within the software of CHEF's libraries, most likely will never be written. The first section, Section 2, quickly lays out preliminary concepts and relationships. In Section 3, we shall review the perturbation theory - an iterative sequence of transformations that converts a nonlinear mapping into its normal form - and examine the equation which moves calculations from one step to the next. Following that is a section titled 'Interpretation', which identifies connections between the normalized mappings and idealized, integrable, fictitious Hamiltonian models. A final section contains closing comments, some of which may - but probably will not - preview work to be done later. My reasons for writing this memo and its predecessor have already been expressed. [1] To them can be added this: 'black box code' encourages users to proceed with little or no understanding of what it does or how it operates. So far, CHEF has avoided this trap admirably by failing to attract potential users. However, we reached a watershed last year: even I now have difficulty following the software through its maze of operations. Extensions to CHEF's physics functionalities, software upgrades, and even simple maintenance are becoming more difficult than they should. I hope these memos will mark parts of the maze for easier navigation in the future. Despite appearances to the contrary, I tried to include no (or very little) more than the minimum needed to understand what CHEF's nonlinear analysis modules do.1 As with the first memo, material
Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems
Institute of Scientific and Technical Information of China (English)
Wu Ligang; Wang Changhong; Gao Huijun; Zhang Lixian
2006-01-01
A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H∞ control problem by designing a memoryless H∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.
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 ...
Normal incidence filters using symmetry-protected modes in dielectric subwavelength gratings
Cui, Xuan; Tian, Hao; Du, Yan; Shi, Guang; Zhou, Zhongxiang
2016-11-01
We investigate narrowband transmission filters based on subwavelength-grating reflectors at normal incidence. Computational results show that the filtering is realized through symmetry-protected mode coupling. The guided mode resonances introduced by the slab layer allow flexible control of the filter frequencies. The quality factor of the filters could exceed 106. Dielectric gratings can be used over the entire range of electromagnetic waves, owing to their scale-invariant operations. Owing to the high refraction index and low index dispersion of semiconductors in the infrared range, these filters can be applied over a broad range from near infrared to terahertz frequencies.
Joannin, Colas; Chouvion, Benjamin; Thouverez, Fabrice; Ousty, Jean-Philippe; Mbaye, Moustapha
2017-01-01
This paper presents an extension to classic component mode synthesis methods to compute the steady-state forced response of nonlinear and dissipative structures. The procedure makes use of the nonlinear complex modes of each substructure, computed by means of a modified harmonic balance method, in order to build a reduced-order model easily solved by standard iterative solvers. The proposed method is applied to a mistuned cyclic structure subjected to dry friction forces, and proves particularly suitable for the study of such systems with high modal density and non-conservative nonlinearities.
Autoresonant control of nonlinear mode in ultrasonic transducer for machining applications.
Babitsky, V I; Astashev, V K; Kalashnikov, A N
2004-04-01
Experiments conducted in several countries have shown that the improvement of machining quality can be promoted through conversion of the cutting process into one involving controllable high-frequency vibration at the cutting zone. This is achieved through the generation and maintenance of ultrasonic vibration of the cutting tool to alter the fracture process of work-piece material cutting to one in which loading of the materials at the tool tip is incremental, repetitive and controlled. It was shown that excitation of the high-frequency vibro-impact mode of the tool-workpiece interaction is the most effective way of ultrasonic influence on the dynamic characteristics of machining. The exploitation of this nonlinear mode needs a new method of adaptive control for excitation and stabilisation of ultrasonic vibration known as autoresonance. An approach has been developed to design an autoresonant ultrasonic cutting unit as an oscillating system with an intelligent electronic feedback controlling self-excitation in the entire mechatronic system. The feedback produces the exciting force by means of transformation and amplification of the motion signal. This allows realisation for robust control of fine resonant tuning to bring the nonlinear high Q-factor systems into technological application. The autoresonant control provides the possibility of self-tuning and self-adaptation mechanisms for the system to keep the nonlinear resonant mode of oscillation under unpredictable variation of load, structure and parameters. This allows simple regulation of intensity of the process whilst keeping maximum efficiency at all times. An autoresonant system with supervisory computer control was developed, tested and used for the control of the piezoelectric transducer during ultrasonically assisted cutting. The system has been developed as combined analog-digital, where analog devices process the control signal, and parameters of the devices are controlled digitally by computer. The
Fuzzy Sliding Mode Controller Design Using Takagi-Sugeno Modelled Nonlinear Systems
Directory of Open Access Journals (Sweden)
S. Bououden
2013-01-01
Full Text Available Adaptive fuzzy sliding mode controller for a class of uncertain nonlinear systems is proposed in this paper. The unknown system dynamics and upper bounds of the minimum approximation errors are adaptively updated with stabilizing adaptive laws. The closed-loop system driven by the proposed controllers is shown to be stable with all the adaptation parameters being bounded. The performance and stability of the proposed control system are achieved analytically using the Lyapunov stability theory. Simulations show that the proposed controller performs well and exhibits good performance.
Terminal Sliding Mode Control with Adaptive Law for Uncertain Nonlinear System
Directory of Open Access Journals (Sweden)
Zhanshan Zhao
2015-01-01
Full Text Available A novel nonsingular terminal sliding mode controller is proposed for a second-order system with unmodeled dynamics uncertainties and external disturbances. We need not achieve the knowledge for boundaries of uncertainties and external disturbances in advance. The adaptive control gains are obtained to estimate the uncertain parameters and external disturbances which are unknown but bounded. The closed loop system stability is ensured with robustness and adaptation by the Lyapunov stability theorem in finite time. An illustrative example of second-order nonlinear system with unmodeled dynamics and external disturbances is given to demonstrate the effectiveness of the presented scheme.
Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides
DEFF Research Database (Denmark)
Reddy, D. V.; Raymer, M. G.; McKinstrie, C. J.;
2013-01-01
in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process...... in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion....
Effects of nonlinear forces on dynamic mode atomic force microscopy and spectroscopy.
Das, Soma; Sreeram, P A; Raychaudhuri, A K
2007-06-01
In this paper, we describe the effects of nonlinear tip-sample forces on dynamic mode atomic force microscopy and spectroscopy. The jumps and hysteresis observed in the vibration amplitude (A) versus tip-sample distance (h) curves have been traced to bistability in the resonance curve. A numerical analysis of the basic dynamic equation was used to explain the hysteresis in the experimental curve. It has been found that the location of the hysteresis in the A-h curve depends on the frequency of the forced oscillation relative to the natural frequency of the cantilever.
Gusev, Vitalyi E; Lomonosov, Alexey M; Ni, Chenyin; Shen, Zhonghua
2017-09-01
An analytical theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous plate material on the Lamb waves near the S1 zero group velocity point is developed. The theory predicts that the main effect of the hysteretic quadratic nonlinearity consists in the modification of the frequency and the induced absorption of the Lamb modes. The effects of the nonlinear self-action in the propagating and standing Lamb waves are expected to be, respectively, nearly twice and three times stronger than those in the plane propagating acoustic waves. The theory is restricted to the simplest hysteretic nonlinearity, which is influencing only one of the Lamé moduli of the materials. However, possible extensions of the theory to the cases of more general hysteretic nonlinearities are discussed as well as the perspectives of its experimental testing. Applications include nondestructive evaluation of micro-inhomogeneous and cracked plates. Copyright © 2017 Elsevier B.V. All rights reserved.
Guo, Z. B.; Hahm, T. S.
2016-06-01
We investigate zonal flow (ZF) generation in ion temperature gradient driven trapped-electron-mode (ITG-driven TEM) turbulence via modulational instability analysis. We show that the acceleration of a seed ZF is a consequence of the competition of negative radiation pressure (NRP, acting as a driving force) and positive radiation pressure (PRP, acting as a retarding force) of the ITG-driven TEM turbulence. A critical dimensionless ion temperature logarithmic gradient (R/{{L}{{T\\text{i}},\\text{c}}} ) normalized to the major radius is obtained by balancing the NRP- and PRP effects. For \\frac{R}{{{L}{{T\\text{i}}}}}text{i}},\\text{c}}}} , the NRP effect is dominant and the seed ZF is accelerated. Otherwise, the PRP effect is dominant and the seed ZF is decelerated. In addition, a new nonlinear evolution mechanism of the ZF is also proposed. It is shown that the turbulence energy intensity spectrum gets steepened in k-space due to the ZF shearing, which in turn induces nonlinear growth of the ZF.
Zero, Normal and Super-radiant Modes for Scalar and Spinor Fields in Kerr-anti de Sitter Spacetime
Kenmoku, Masakatsu; Shigemoto, Kazuyasu; Yoon, Jong Hyuk
2016-01-01
Zero and normal modes for scalar and spinor fields in Kerr-anti de Sitter spacetime are studied as bound state problem with Dirichlet and Neumann boundary conditions. Zero mode is defined as the momentum near the horizon to be zero: $p_{\\rm H}=\\omega-\\Omega_{\\rm H}m=0$, and is shown not to exist as physical state for both scalar and spinor fields. Physical normal modes satisfy the spectrum condition $p_{\\rm H}>0$ as a result of non-existence of zero mode and the analyticity with respect to rotation parameter $a$ of Kerr-anti de Sitter black hole. Comments on the super-radiant modes and the thermodynamics of black hole are given in relation to the spectrum condition for normal modes. Preliminary numerical analysis on normal modes is presented.
McDonald, Alison C; Sanei, Kia; Keir, Peter J
2013-06-01
Muscle force estimates are important for full understanding of the musculoskeletal system and EMG is a modeling method used to estimate muscle force. The purpose of this investigation was to examine the effect of high pass filtering and non-linear normalization on the EMG-force relationship of sub-maximal finger exertions. Sub-maximal isometric ramp exertions were performed under three conditions (i) extension with restraint at the mid-proximal phalanx, (ii) flexion at the proximal phalanx and (iii) flexion at the distal phalanx. Thirty high pass filter designs were compared to a standardized processing procedure and an exponential fit equation was used for non-linear normalization. High pass filtering significantly reduced the %RMS error and increased the peak cross correlation between EMG and force in the distal flexion condition and in the other two conditions there was a trend towards improving force predictions with high pass filtering. The degree of linearity differed between the three contraction conditions and high pass filtering improved the linearity in all conditions. Non-linear normalization had greater impact on the EMG-force relationship than high pass filtering. The difference in optimal processing parameters suggests that high pass filtering and linearity are dependent on contraction mode as well as the muscle analyzed.
Robust stabilization of underactuated nonlinear systems: A fast terminal sliding mode approach.
Khan, Qudrat; Akmeliawati, Rini; Bhatti, Aamer Iqbal; Khan, Mahmood Ashraf
2017-01-01
This paper presents a fast terminal sliding mode based control design strategy for a class of uncertain underactuated nonlinear systems. Strategically, this development encompasses those electro-mechanical underactuated systems which can be transformed into the so-called regular form. The novelty of the proposed technique lies in the hierarchical development of a fast terminal sliding attractor design for the considered class. Having established sliding mode along the designed manifold, the close loop dynamics become finite time stable which, consequently, result in high precision. In addition, the adverse effects of the chattering phenomenon are reduced via strong reachability condition and the robustness of the system against uncertainties is confirmed theoretically. A simulation as well as experimental study of an inverted pendulum is presented to demonstrate the applicability of the proposed technique.
Directory of Open Access Journals (Sweden)
Faten Baklouti
2016-01-01
Full Text Available The trajectory tracking of underactuated nonlinear system with two degrees of freedom is tackled by an adaptive fuzzy hierarchical sliding mode controller. The proposed control law solves the problem of coupling using a hierarchical structure of the sliding surfaces and chattering by adopting different reaching laws. The unknown system functions are approximated by fuzzy logic systems and free parameters can be updated online by adaptive laws based on Lyapunov theory. Two comparative studies are made in this paper. The first comparison is between three different expressions of reaching laws to compare their abilities to reduce the chattering phenomenon. The second comparison is made between the proposed adaptive fuzzy hierarchical sliding mode controller and two other control laws which keep the coupling in the underactuated system. The tracking performances of each control law are evaluated. Simulation examples including different amplitudes of external disturbances are made.
A novel dynamic terminal sliding mode control of uncertain nonlinear systems
Institute of Scientific and Technical Information of China (English)
Jinkun LIU; Fuchun SUN
2007-01-01
A new dynamic terminal sliding mode control (DTSMC) technique is proposed for a class of single-input and single-output (SISO) uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized.Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.
Fang, Xiaohui; Wai, P K A; Lu, Chao; Chen, Jinhua
2014-02-10
A pulse-width-tunable 10 GHz flattop pulse (FTP) train is generated based on the combined action of active mode locking and nonlinear polarization rotation pulse shaping. Although the setup was previously used for other applications, the mechanism of FTP generation based on it is first analyzed and confirmed in the experiment. An FTP with pulse width tunable from 12 to 20 ps by changing polarization controllers is generated within the wavelength tuning range of 20 nm. The generated pulse reveals good stability, with the side mode suppression ratio of 65 dB, timing jitter of 92 fs, and amplitude fluctuation of 0.36%.
Theoretical and experimental study of the normal modes in a coupled two-dimensional system
Giménez, Marcos H; Gómez-Tejedor, José Antonio; Velazquez, Luisberis; Monsoriu, Juan A
2016-01-01
In this work, the normal modes of a two-dimensional oscillating system have been studied from a theoretical and experimental point of view. The normal frequencies predicted by the Hessian matrix for a coupled two-dimensional particle system are compared to those obtained for a real system consisting of two oscillating smartphones coupled one to the other by springs. Experiments are performed on an air table in order to remove the friction forces. The oscillation data are captured by the acceleration sensor of the smartphones and exported to file for further analysis. The experimental frequencies compare reasonably well with the theoretical predictions, namely, within 1.7 % of discrepancy.
Optimization of force constants with an Urey-Bradley force field avoiding normal mode crossings.
Vivoni, A; Birke, R; Lombardi, J
2001-03-01
We present a method that simplifies the refinement of force constants in normal mode calculations and makes the results more reliable. The method avoids normal mode crossings by constraining the force constants during refinement. It was tested with pyrrole, imidazole, benzene, pyridine, pyrimidine, aniline and adenine using a Urey-Bradley force field. The global error of the frequency fit for these molecules was 0.61%. The method reproduced with fewer parameters the accuracy of similar calculations of the single ring aromatic compounds. It improved the accuracy and isotopic shifts of previous empirical calculations of adenine by 40%. The C-C and C-N stretchings differed by less than 7% from the values of force constant-bond length empirical relations.
Hanasoge, Shravan M.; Woodard, Martin; Antia, H. M.; Gizon, Laurent; Sreenivasan, Katepalli R.
2017-09-01
In this article, we derive and compute the sensitivity of measurements of coupling between normal modes of oscillation in the Sun to underlying flows. The theory is based on first-born perturbation theory, and the analysis is carried out using the formalism described by Lavely & Ritzwoller (1992). Albeit tedious, we detail the derivation and compute the sensitivity of specific pairs of coupled normal modes to anomalies in the interior. Indeed, these kernels are critical for the accurate inference of convective flow amplitudes and large-scale circulations in the solar interior. We resolve some inconsistencies in the derivation of Lavely & Ritzwoller (1992) and reformulate the fluid-continuity condition. We also derive and compute sound-speed kernels, paving the way for inverting for thermal anomalies alongside flows.
High-frequency Born synthetic seismograms based on coupled normal modes
Pollitz, Fred F.
2011-01-01
High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ∼4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD).
Unstable normal modes of low T/W dynamical instabilities in differentially rotating stars
Saijo, Motoyuki
2016-01-01
We investigate the nature of low T/W dynamical instabilities in differentially rotating stars by means of linear perturbation. Here, T and W represent rotational kinetic energy and the gravitational binding energy of the star. This is the first attempt to investigate low T/W dynamical instabilities as a complete set of the eigenvalue problem. Our equilibrium configuration has "constant" specific angular momentum distribution, which potentially contains a singular solution in the perturbed enthalpy at corotation radius in linear perturbation. We find the unstable normal modes of differentially rotating stars by solving the eigenvalue problem along the equatorial plane of the star, imposing the regularity condition on the center and the vanished enthalpy at the oscillating equatorial surface. We find that the existing pulsation modes become unstable due to the existence of the corotation radius inside the star. The feature of the unstable mode eigenfrequency and its eigenfunction in the linear analysis roughly ...
Axial quasi-normal modes of Einstein-Gauss-Bonnet-dilaton neutron stars
Blázquez-Salcedo, Jose Luis; Kunz, Jutta; Mojica, Sindy; Navarro-Lérida, Francisco
2015-01-01
We investigate axial quasi-normal modes of realistic neutron stars in Einstein-Gauss-Bonnet-dilaton gravity. We consider 8 realistic equations of state containing nuclear, hyperonic, and hybrid matter. We focus on the fundamental curvature mode and compare the results with those of pure Einstein theory. We observe that the frequency of the modes is increased by the presence of the Gauss-Bonnet-dilaton, while the impact on the damping time is typically smaller. Interestingly, we obtain that universal relations valid in pure Einstein theory still hold for Einstein-Gauss-Bonnet-dilaton gravity, and we propose a method to use these phenomenological relations to constrain the value of the Gauss-Bonnet coupling.
A coupling model for quasi-normal modes of photonic resonators
Vial, Benjamin
2016-01-01
We develop a model for the coupling of quasi-normal modes in open photonic systems consisting of two resonators. By expressing the modes of the coupled system as a linear combination of the modes of the individual particles, we obtain a generalized eigenvalue problem involving small size dense matrices. We apply this technique to a 2D problem of a high index rod dimmer of rectangular cross section for Transverse Electric (TE) polarization. The results of our model are compared with full-wave finite element simulations and show a good agreement for the four lowest eigenvalues by taking into account the two lowest eigenfrequencies of the isolated rods. This model provides interesting physical insights on the coupling scheme at stake in such systems and pave the way for the design and optimization of resonances in more complicated systems, including the engineering of metamaterial unit cells.
Mixing induced by a propagating normal mode in long term experiments
Dossmann, Yvan; Pollet, Florence; Odier, Philippe; Dauxois, Thierry
2017-04-01
The energy pathways from propagating internal waves to the scales of irreversible mixing in the ocean are numerous. The triadic resonant instability (TRI) is an intrinsic destabilization process that can lead to mixing away from topographies. It consists in the destabilization of a primary internal wave generation leading to the radiation of two secondary waves of lower frequencies and different wave vectors. In the process, internal wave energy is carried down to smaller scales. A previous study focused on the assessment of instantaneous turbulent fluxes fields associated with the TRI process in laboratory experiments [1]. The present study investigates the integrated impact of mixing processes induced by a propagative normal mode over long term experiments using a similar setup. Configurations for which the TRI process is either favored or inhibited are tackled. Optical measurements using the light attenuation technique allow to follow the internal waves dynamics and the evolution of the density profile between two runs of one hour typical duration. The horizontally averaged turbulent diffusivity Kt(z) and the mixing efficiency Γ are assessed. One finds values up to Kt = 10-6 m2/s and Γ = 11 %, with slightly larger values in the presence of TRI. The maximum value for Kt is measured at the position(s) of the maximum shear normal mode shear for both normal modes 1 and 2. The development of staircases in the density profile is observed after several hours of forcing. This mechanism can be explained by Phillips' argument by which sharp interfaces can form due to vertical variations of the buoyancy flux. The staircases are responsible for large variations in the vertical distribution of turbulent diffusivity. These results could help to refine parameterizations of the impact of low order normal modes in ocean mixing. Reference : [1] Dossmann et al. 2016, Mixing by internal waves quantified using combined PIV/PLIF technique, Experiments in Fluids, 57, 132.
Black Boles in the 3D Higher Spin Theory and Their Quasi Normal Modes
Cabo-Bizet, Alejandro; Giraldo-Rivera, V I; Narain, K S
2014-01-01
We present a class of 3D Black Holes based on flat connections which are polynomials in the BTZ $hs(\\lambda)\\times hs(\\lambda)$-valued connection. We solve analytically the fluctuation equations of matter in their background and find the spectrum of their Quasi Normal Modes. We analyze the bulk to boundary two-point functions. We also relate our results and those arising in other backgrounds discussed recently in the literature on the subject.
Nonlinear dynamics in pulsatile secretion of parathyroid hormone in normal human subjects
Prank, Klaus; Harms, Heio; Brabant, Georg; Hesch, Rolf-Dieter; Dämmig, Matthias; Mitschke, Fedor
1995-03-01
In many biological systems, information is transferred by hormonal ligands, and it is assumed that these hormonal signals encode developmental and regulatory programs in mammalian organisms. In contrast to the dogma of endocrine homeostasis, it could be shown that the biological information in hormonal networks is not only present as a constant hormone concentration in the circulation pool. Recently, it has become apparent that hormone pulses contribute to this hormonal pool, which modulates the responsiveness of receptors within the cell membrane by regulation of the receptor synthesis, movement within the membrane layer, coupling to signal transduction proteins and internalization. Phase space analysis of dynamic parathyroid hormone (PTH) secretion allowed the definition of a (in comparison to normal subjects) relatively quiet ``low dynamic'' secretory pattern in osteoporosis, and a ``high dynamic'' state in hyperparathyroidism. We now investigate whether this pulsatile secretion of PTH in healthy men exhibits characteristics of nonlinear determinism. Our findings suggest that this is conceivable, although on the basis of presently available data and techniques, no proof can be established. Nevertheless, pulsatile secretion of PTH might be a first example of nonlinear deterministic dynamics in an apparently irregular hormonal rhythm in human physiology.
Skin pigmentation and texture changes after hair removal with the normal-mode ruby laser.
Haedersdal, M; Egekvist, H; Efsen, J; Bjerring, P
1999-11-01
Promising clinical results have been obtained with the normal mode ruby laser for removal of unwanted hair. Melanin within the hair follicles is thought to act as target for the ruby laser pulses, whereas epidermal melanin is thought to be a competitive chromophore, responsible for potential side effects. This study aimed (i) to objectify postoperative changes in skin pigmentation and texture and (ii) to evaluate the importance of variations in preoperative skin pigmentation for the development of side effects 12 weeks after 1 treatment with the normal-mode ruby laser. A total of 17 volunteers (skin types I-IV) were laser-treated in the hairy pubic region (n = 51 test areas). A shaved test area served as control. Skin reflectance spectroscopical measurements, 3-dimensional surface contour analysis and ultrasonography objectified postoperative changes in skin pigmentation and texture. Blinded clinical assessments revealed postoperative hyperpigmentation (2% of test areas) and hypopigmentation (10%), whereas no textural changes were seen. Reflectance spectroscopically-determined pigmentary changes depended on the degree of preoperative skin pigmentation, fairly pigmented skin types experiencing subclinical hyperpigmentation and darkly pigmented skin types experiencing subclinical hypopigmentation. Three-dimensional surface profilometry documented similar pre- and postoperative surface contour parameters, indicating that the skin surface texture is preserved after laser exposure. Ultrasonography revealed similar skin thicknesses in laser-exposed and untreated control areas. It is concluded that normal-mode ruby laser treatment is safe for hair removal in skin types I-IV.
Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice
Energy Technology Data Exchange (ETDEWEB)
Kavitha, L., E-mail: louiskavitha@yahoo.co.in [Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu (CUTN), Thiruvarur 610 101, Tamil Nadu (India); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany); The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Parasuraman, E. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Gopi, D. [Department of Chemistry, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Prabhu, A. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Vicencio, Rodrigo A. [Departamento de Física and MSI-Nucleus on Advanced Optics, Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago 7800003 (Chile); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-03-01
We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.
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.
Wave-particle interaction and the nonlinear saturation of the electron temperature gradient mode
Vadlamani, Srinath; Parker, Scott E.; Chen, Yang; Howard, James E.
2004-11-01
It has been proposed that the electron temperature gradient (ETG) driven turbulence is responsible for experimentally relevant electron thermal transport in tokamak plasmas. Significant transport levels are possible by the creation of radially elongated vortices or ``streamers" [1,2], which are sustained by the nonlinear saturation of the instability and are not susceptible to shear flow destruction, as is the case with the ion temperature gradient (ITG) mode. We present a dynamical system to explore the dependence of saturation level due to E × B and E_\\| motion, as well as the effect of radial elongation. With this model, we can predict the nonlinear saturation level of the ETG streamers. We compare our theoretical predictions with a 2D shear-less slab gyrokinetic electron code that includes the E_\\| nonlinearity. [1]F. Jenko, W. Dorland, M Kotschenreuther, and B.N. Rogers, Phys. Plasmas 7, 1904 (2000). [2]C. Holland, and P.H. Diamond, Phys. Plasmas 9, 3857 (2002). [3]W. M. Manheimer, Phys. Fluids 14, 579 (1971). [4]R. A. Smith, John A. Krommes, and W. W. Lee, Phys. Fluids 28, 1069 (1985).
Nonlinear TeraHertz Coherent Excitation of Vibrational Modes of Liquids
Allodi, Marco A; Blake, Geoffrey A
2015-01-01
We report the first coherent excitation of intramolecular vibrational modes via the nonlinear interaction of a TeraHertz (THz) light field with molecular liquids. A TeraHertz-TeraHertz-Raman pulse sequence prepares the coherences with a broadband, high-energy, (sub)picosecond TeraHertz pulse, that are then measured in a TeraHertz Kerr effect spectrometer via phase-sensitive, heterodyne detection with an optical pulse. The spectrometer reported here has broader TeraHertz frequency coverage and an increased sensitivity relative to previously reported TeraHertz Kerr effect experiments. Vibrational coherences are observed in liquid diiodomethane at 3.66 THz (122 cm$^{-1}$), and in carbon tetrachloride at 6.50 THz (217 cm$^{-1}$), in exact agreement with literature values of those intramolecular modes. This work opens the door to 2D spectroscopies, nonlinear in TeraHertz field, that can study the dynamics of condensed-phase molecular systems, as well as coherent control at TeraHertz frequencies.
Huang, Norden E.
2000-04-01
A new method for analyzing nonlinear and nonstationary data has been developed. The key pat of the method is the Empirical Mode Decomposition method with which any complicated data set can be decomposed into a finite and often small number of Intrinsic Mode Functions (IMF). An IMF is define das any function having the same numbers of zero- crossing and extrema, and also having symmetric envelopes defined by the local maxima and minima respectively. The IMF also admits well-behaved Hilbert transform. This decomposition method is adaptive, and therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of het data, it is applicable to nonlinear and nonstationary processes. With the Hilbert transform, the IMF yield instantaneous frequencies as functions of time that give sharp identifications of embedded structures. The final presentation of the result is an energy-frequency-time distribution, designated as the Hilbert Spectrum. Comparisons with Wavelet and window Fourier analysis show the new method offers much better temporal and frequency resolutions.
Deguchi, K.; Altmeyer, S.
2013-04-01
Interactions between nearly bicritical modes in Taylor-Couette flow, which have been concerned with the framework of weakly nonlinear theory, are extended to fully nonlinear Navier-Stokes computation. For this purpose, a standard Newton solver for axially periodic flows is generalized to compute any mixed solutions having up to two phases, which typically arise from interactions of two spiral or Taylor vortex modes. Also, a simple theory is developed in order to classify the mixed solutions. With these methods, we elucidate pattern formation phenomena, which have been observed in a Taylor-Couette flow experiment. Focusing on the counter-rotating parameter range, all possible classes of interaction of various solutions with different azimuthal and axial wave numbers are considered within our computational restriction, and we observe numerous connection branches, e.g., footbridge solutions. Some of the mixed solutions result in a three-dimensional wavy spiral solution with axial relative periodicity or an axially doubly periodic toroidally closed vortex solution. The possible connection of the former solution family to spiral turbulence, which has been observed in highly counter-rotating Taylor-Couette flow, is discussed.
Identification of surface species by vibrational normal mode analysis. A DFT study
Zhao, Zhi-Jian; Genest, Alexander; Rösch, Notker
2017-10-01
Infrared spectroscopy is an important experimental tool for identifying molecular species adsorbed on a metal surface that can be used in situ. Often vibrational modes in such IR spectra of surface species are assigned and identified by comparison with vibrational spectra of related (molecular) compounds of known structure, e. g., an organometallic cluster analogue. To check the validity of this strategy, we carried out a computational study where we compared the normal modes of three C2Hx species (x = 3, 4) in two types of systems, as adsorbates on the Pt(111) surface and as ligands in an organometallic cluster compound. The results of our DFT calculations reproduce the experimental observed frequencies with deviations of at most 50 cm-1. However, the frequencies of the C2Hx species in both types of systems have to be interpreted with due caution if the coordination mode is unknown. The comparative identification strategy works satisfactorily when the coordination mode of the molecular species (ethylidyne) is similar on the surface and in the metal cluster. However, large shifts are encountered when the molecular species (vinyl) exhibits different coordination modes on both types of substrates.
Energy Technology Data Exchange (ETDEWEB)
Nagy, Tibor; Vikár, Anna; Lendvay, György, E-mail: lendvay.gyorgy@ttk.mta.hu [Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2., H-1117 Budapest (Hungary)
2016-01-07
The quasiclassical trajectory (QCT) method is an efficient and important tool for studying the dynamics of bimolecular reactions. In this method, the motion of the atoms is simulated classically, and the only quantum effect considered is that the initial vibrational states of reactant molecules are semiclassically quantized. A sensible expectation is that the initial ensemble of classical molecular states generated this way should be stationary, similarly to the quantum state it is supposed to represent. The most widely used method for sampling the vibrational phase space of polyatomic molecules is based on the normal mode approximation. In the present work, it is demonstrated that normal mode sampling provides a nonstationary ensemble even for a simple molecule like methane, because real potential energy surfaces are anharmonic in the reactant domain. The consequences were investigated for reaction CH{sub 4} + H → CH{sub 3} + H{sub 2} and its various isotopologs and were found to be dramatic. Reaction probabilities and cross sections obtained from QCT calculations oscillate periodically as a function of the initial distance of the colliding partners and the excitation functions are erratic. The reason is that in the nonstationary ensemble of initial states, the mean bond length of the breaking C–H bond oscillates in time with the frequency of the symmetric stretch mode. We propose a simple method, one-period averaging, in which reactivity parameters are calculated by averaging over an entire period of the mean C–H bond length oscillation, which removes the observed artifacts and provides the physically most reasonable reaction probabilities and cross sections when the initial conditions for QCT calculations are generated by normal mode sampling.
Tiwari, Nivedan; Chabra, Sanjay; Mehdi, Sheherbano; Sweet, Paula; Krasieva, Tatiana B.; Pool, Roy; Andrews, Brian; Peavy, George M.
2010-09-01
An estimated 1.3 million people in the United States suffer from rheumatoid arthritis (RA). RA causes profound changes in the synovial membrane of joints, and without early diagnosis and intervention, progresses to permanent alterations in joint structure and function. The purpose of this study is to determine if nonlinear optical microscopy (NLOM) can utilize the natural intrinsic fluorescence properties of tissue to generate images that would allow visualization of the structural and cellular composition of fresh, unfixed normal and pathologic synovial tissue. NLOM is performed on rabbit knee joint synovial samples using 730- and 800-nm excitation wavelengths. Less than 30 mW of excitation power delivered with a 40×, 0.8-NA water immersion objective is sufficient for the visualization of synovial structures to a maximum depth of 70 μm without tissue damage. NLOM imaging of normal and pathologic synovial tissue reveals the cellular structure, synoviocytes, adipocytes, collagen, vascular structures, and differential characteristics of inflammatory infiltrates without requiring tissue processing or staining. Further study to evaluate the ability of NLOM to assess the characteristics of pathologic synovial tissue and its potential role for the management of disease is warranted.
A global shear velocity model of the mantle from normal modes and surface waves
durand, S.; Debayle, E.; Ricard, Y. R.; Lambotte, S.
2013-12-01
We present a new global shear wave velocity model of the mantle based on the inversion of all published normal mode splitting functions and the large surface wave dataset measured by Debayle & Ricard (2012). Normal mode splitting functions and surface wave phase velocity maps are sensitive to lateral heterogeneities of elastic parameters (Vs, Vp, xi, phi, eta) and density. We first only consider spheroidal modes and Rayleigh waves and restrict the inversion to Vs, Vp and the density. Although it is well known that Vs is the best resolved parameter, we also investigate whether our dataset allows to extract additional information on density and/or Vp. We check whether the determination of the shear wave velocity is affected by the a priori choice of the crustal model (CRUST2.0 or 3SMAC) or by neglecting/coupling poorly resolved parameters. We include the major discontinuities, at 400 and 670 km. Vertical smoothing is imposed through an a priori gaussian covariance matrix on the model and we discuss the effect of coupling/decoupling the inverted structure above and below the discontinuities. We finally discuss the large scale structure of our model and its geodynamical implications regarding the amount of mass exchange between the upper and lower mantle.
Hudecová, Jana; Hopmann, Kathrin H; Bouř, Petr
2012-01-12
Vibrational properties of solutions are frequently simulated with clusters of a solute and a few solvent molecules obtained during molecular dynamics (MD) simulations. The raw cluster geometries, however, often provide unrealistic vibrational band broadening, for both ab initio and empirical force fields. In this work, partial optimization in normal-mode coordinates is used on empirical basis to reduce the broadening. The origin of the error is discussed on a simplified two-dimensional system, which indicates that the problem is caused by the anharmonic MD potential, mode coupling, and neglect of quantum effects. Then the procedure of partial geometry optimization on Raman and Raman optical activity (ROA) spectra is applied and analyzed for the solvated lactamide molecule. Comparison to experiment demonstrates that the normal-mode partial optimization technique with a suitable frequency limit can significantly reduce the broadening error. For lactamide, experimental and simulated vibrational bandwidths are compared; the most realistic theoretical spectra are obtained for partially optimized clusters with the vibrational wavenumber cutoff of about 200 cm(-1).
Plantar fascia softening in plantar fasciitis with normal B-mode sonography.
Wu, Chueh-Hung; Chen, Wen-Shiang; Wang, Tyng-Guey
2015-11-01
To investigate plantar fascia elasticity in patients with typical clinical manifestations of plantar fasciitis but normal plantar fascia morphology on B-mode sonography. Twenty patients with plantar fasciitis (10 unilateral and 10 bilateral) and 30 healthy volunteers, all with normal plantar fascia morphology on B-mode sonography, were included in the study. Plantar fascia elasticity was evaluated by sonoelastographic examination. All sonoelastograms were quantitatively analyzed, and less red pixel intensity was representative of softer tissue. Pixel intensity was compared among unilateral plantar fasciitis patients, bilateral plantar fasciitis patients, and healthy volunteers by one-way ANOVA. A post hoc Scheffé's test was used to identify where the differences occurred. Compared to healthy participants (red pixel intensity: 146.9 ± 9.1), there was significantly less red pixel intensity in the asymptomatic sides of unilateral plantar fasciitis (140.4 ± 7.3, p = 0.01), symptomatic sides of unilateral plantar fasciitis (127.1 ± 7.4, p fascia thickness or green or blue pixel intensity among these groups. Sonoelastography revealed that the plantar fascia is softer in patients with typical clinical manifestations of plantar fasciitis, even if they exhibit no abnormalities on B-mode sonography.
Signatures of nonlinear mode interactions in the pulsating hot B subdwarf star KIC 10139564
Zong, Weikai; Vauclair, Gérard
2016-01-01
We analyse 38-month of contiguous short-cadence data, concentrating on mode multiplets induced by the star rotation and on frequencies forming linear combinations that show intriguing behaviors during the course of the observations. We find clear signatures that point toward nonlinear effects predicted by resonant mode coupling mechanisms. These couplings can induce various mode behaviors for the components of multiplets and for frequencies related by linear relationships. We find that a triplet at 5760\\,$\\mu$Hz, a quintuplet at 5287\\,$\\mu$Hz and a ($\\ell>2$) multiplet at 5412\\,$\\mu$Hz, all induced by rotation, show clear frequency and amplitude modulations which are typical of the so-called intermediate regime of a resonance between the components. One triplet at 316\\,$\\mu$Hz and a doublet at 394\\,$\\mu$Hz show modulated amplitude and constant frequency which can be associated with a narrow transitory regime of the resonance. Another triplet at 519\\,$\\mu$Hz appears to be in a frequency lock regime where both ...
Nonlinear evolution of multi-helicity neo-classical tearing modes in rotating tokamak plasmas
Wei, Lai; Wang, Zheng-Xiong; Wang, Jialei; Yang, Xuefeng
2016-10-01
Plasma perturbations from the core and/or boundary regions of tokamaks can provide seed islands for the excitation of neo-classical tearing modes (NTMs) with negative {{ Δ }\\prime} , where {{ Δ }\\prime} is the linear instability parameter of the classical tearing mode. In this work, by means of reduced magnetohydrodynamic simulations, we numerically investigate the nonlinear evolution of multi-helicity NTMs in rotating tokamak plasmas with these two types of plasma perturbations with different boundary conditions. In the first case of initial plasma perturbations from the core region with a zero boundary condition, the meta-stable property of seed-island triggered NTM with negative {{ Δ }\\prime} is verified in the single helicity simulation. Nevertheless in the multiple helicity simulation, this seed-island triggered NTM with negative {{ Δ }\\prime} can be suppressed by a spontaneous NTM with positive {{ Δ }\\prime} through the competitive interaction between NTMs with different helicities. If a fixed poloidal rotation is taken into account in the first case, two different helicity NTMs could coexist in the saturation stage, which is different qualitatively from the process without plasma rotation. In the second case of initial plasma perturbations from the boundary region with a nonzero boundary condition, as the amplitude of plasma perturbations on the boundary increases, the mode with negative {{ Δ }\\prime} gradually changes from the driven-reconnection state to the NTM state, accompanied by an enhancement of magnetic island width in the single helicity simulation. Nevertheless in the multi-helicity simulation, the spontaneous NTM with positive {{ Δ }\\prime} can make the driven-reconnection triggered NTM with negative {{ Δ }\\prime} transfer from the NTM state back to the driven-reconnection state again. The underlying mechanism behind these transitions is analyzed step by step. Effects of fixed and unfixed poloidal rotations on the nonlinear
Institute of Scientific and Technical Information of China (English)
CHENMou; JIANGChang-sheng; CHENWen-hua
2004-01-01
A new decentralized robust control method is discussed for a class of nonlinear interconnected largescale system with unknown bounded disturbance and unknown nonlinear function term. A decentralized control law is proposed which combines the approximation method of neural network with sliding mode control. The decentralized controller consists of an equivalent controller and an adaptive sliding mode controller. The sliding mode controller is a robust controller used to reduce the track error of the control system. The neural networks are used to approximate the unknown nonlinear functions, meanwhile the approximation errors of the neural networks are applied to the weight value updated law to improve performance of the system. Finally, an example demonstrates the availability of the decentralized control method.
Measurement of Quasi Normal Modes for a population of Binary Black Hole Mergers
da Silva Costa, Carlos Filipe; Klimenko, Sergey; Tiwari, Shubhanshu
2017-01-01
Perturbed solutions of the Kerr Black Hole (BH) are superimposition of damped sinusoids, named Quasi Normal Modes (QNM). These modes are completely defined by the final black hole parameters, mass and spin. Numerical simulations support that Binary BHs (BBH), after merging, produce a final BH emitting gravitational waves as described by the QNMs. This signal is very weak and hence the extraction of a QNM is quite challenging for the current generation of the ground based detectors. I will present a method for extraction of superimposed QNMs from future multiple observations of BBH merger signals in the advanced interferometers. We show that we can coherently sum up QNMs from the different signals and measure QNM parameters to prove the Kerr nature of a detected BHs population. NSF grant PHY 1505308.
On quasi-normal modes, area quantization and Bohr correspondence principle
Corda, Christian
2015-01-01
In Int. Journ. Mod. Phys. D 14, 181 (2005) Khriplovich verbatim claims that "the correspondence principle does not dictate any relation between the asymptotics of quasinormal modes and the spectrum of quantized black holes" and that "this belief is in conflict with simple physical arguments". In this paper we analyze Khriplovich's criticisms and realize that they work only for the original proposal by Hod, while they do not work for the improvements suggested by Maggiore and recently finalized by the author and collaborators through a connection between Hawking radiation and black hole (BH) quasi-normal modes (QNMs). This is a model of quantum BH somewhat similar to the historical semi-classical model of the structure of a hydrogen atom introduced by Bohr in 1913. Thus, QNMs can be really interpreted as BH quantum levels (the "electrons" of the "Bohr-like BH model"). Our results have also important implications on the BH information puzzle.
Dynamical analysis of tRNA Gln-GlnRS complex using normal mode calculation
Nakamura, Shugo; Ikeguchi, Mitsunori; Shimizu, Kentaro
2003-04-01
We applied normal mode calculation in internal coordinates to a complex of glutamine transfer RNA (tRNA Gln) and glutaminyl-tRNA synthetase (GlnRS). Calculated deviations of atoms agreed well with those obtained from X-ray data. The differences of motions corresponding to low mode frequencies between the free state and the complex state were analyzed. For GlnRS, many motions in the free state were conserved in the complex state, while the dynamics of tRNA Gln was largely affected by the complex formation. Superimposed images of the conserved and non-conserved motions of tRNA Gln clearly indicated the restricted direction of motions in the complex.
Olivier, Michel; Gagnon, Marc-Daniel; Piché, Michel
2015-03-09
A strategy to align a mode-locked fiber laser with nonlinear polarization rotation is presented. This strategy is based on measurements of the output polarization state. It is shown that, as the angle of a motorized polarization controller inside the cavity is swept, the laser eventually reaches a mode-locked regime and the values of the Stokes parameters undergo an abrupt change. The sensing of this sudden variation is thus used to detect the mode-locking condition and a feedback mechanism drives the alignment of the polarization controller to force mode locking.
Yan, Zhiyu; Li, Xiaohui; Tang, Yulong; Shum, Perry Ping; Yu, Xia; Zhang, Ying; Wang, Qi Jie
2015-02-23
We propose and demonstrate a tunable and switchable dual-wavelength ultra-fast Tm-doped fiber laser. The tunability is based on nonlinear polarization evolution (NPE) technique in a passively mode-locked laser cavity. The NPE effect induces wavelength-dependent loss in the cavity to effectively alleviate mode competition and enables the multiwavelength mode locking. The laser exhibits tunable dual-wavelength mode locking over a wide range from 1852 to 1886 nm. The system has compact structure and both the wavelength tuning and switching capabilities can be realized by controlling the polarization in the fiber ring cavity.
High frequency quasi-normal modes for black-holes with generic singularities
Das, Saurya; Shankaranarayanan, S.
2004-01-01
We compute the high frequency quasi-normal modes (QNM) for scalar perturbations of spherically symmetric single horizon black-holes in $(D+2)$-space-time dimensions with generic curvature singularities and having metrics of the form $ds^2 = \\eta x^p (dy^2-dx^2) + x^q d\\O_D^2$ near the singularity $x=0$. The real part of the QN frequencies is shown to be proportional to $\\log \\le[ 1 + 2\\cos \\le(\\p \\le[ qD -2 \\ri]/2 \\ri) \\ri]$ where the constant of proportionality is equal to the Hawking temper...
Directory of Open Access Journals (Sweden)
Guowei Cai
2014-01-01
Full Text Available As to strong nonlinearity of doubly fed induction generators (DFIG and uncertainty of its model, a novel rotor current controller with nonlinearity and robustness is proposed to enhance fault ride-though (FRT capacities of grid-connected DFIG. Firstly, the model error, external disturbances, and the uncertain factors were estimated by constructing extended state observer (ESO so as to achieve linearization model, which is compensated dynamically from nonlinear model. And then rotor current controller of DFIG is designed by using terminal sliding mode variable structure control theory (TSMC. The controller has superior dynamic performance and strong robustness. The simulation results show that the proposed control approach is effective.
Fan, Quan-Yong; Yang, Guang-Hong
2016-01-01
This paper is concerned with the problem of integral sliding-mode control for a class of nonlinear systems with input disturbances and unknown nonlinear terms through the adaptive actor-critic (AC) control method. The main objective is to design a sliding-mode control methodology based on the adaptive dynamic programming (ADP) method, so that the closed-loop system with time-varying disturbances is stable and the nearly optimal performance of the sliding-mode dynamics can be guaranteed. In the first step, a neural network (NN)-based observer and a disturbance observer are designed to approximate the unknown nonlinear terms and estimate the input disturbances, respectively. Based on the NN approximations and disturbance estimations, the discontinuous part of the sliding-mode control is constructed to eliminate the effect of the disturbances and attain the expected equivalent sliding-mode dynamics. Then, the ADP method with AC structure is presented to learn the optimal control for the sliding-mode dynamics online. Reconstructed tuning laws are developed to guarantee the stability of the sliding-mode dynamics and the convergence of the weights of critic and actor NNs. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.
Distributed Adaptive Fuzzy Control for Nonlinear Multiagent Systems Via Sliding Mode Observers.
Shen, Qikun; Shi, Peng; Shi, Yan
2016-12-01
In this paper, the problem of distributed adaptive fuzzy control is investigated for high-order uncertain nonlinear multiagent systems on directed graph with a fixed topology. It is assumed that only the outputs of each follower and its neighbors are available in the design of its distributed controllers. Equivalent output injection sliding mode observers are proposed for each follower to estimate the states of itself and its neighbors, and an observer-based distributed adaptive controller is designed for each follower to guarantee that it asymptotically synchronizes to a leader with tracking errors being semi-globally uniform ultimate bounded, in which fuzzy logic systems are utilized to approximate unknown functions. Based on algebraic graph theory and Lyapunov function approach, using Filippov-framework, the closed-loop system stability analysis is conducted. Finally, numerical simulations are provided to illustrate the effectiveness and potential of the developed design techniques.
Drift Wave versus Interchange Turbulence in Tokamak Geometry Linear versus Nonlinear Mode Structure
Scott, B D
2002-01-01
The competition between drift wave and interchange physics in general E-cross-B drift turbulence is studied with computations in three dimensional tokamak flux tube geometry. For a given set of background scales, the parameter space can be covered by the plasma beta and drift wave collisionality. At large enough plasma beta the turbulence breaks out into ideal ballooning modes and saturates only by depleting the free energy in the background pressure gradient. At high collisionality it finds a more gradual transition to resistive ballooning. At moderate beta and collisionality it retains drift wave character, qualitatively identical to simple two dimensional slab models. The underlying cause is the nonlinear vorticity advection through which the self sustained drift wave turbulence supersedes the linear instabilities, scattering them apart before they can grow, imposing its own physical character on the dynamics. This vorticity advection catalyses the gradient drive, while saturation occurs solely through tur...
Directory of Open Access Journals (Sweden)
Yi-You Hou
2014-01-01
Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
Quasi-normal modes of Schwarzschild-de Sitter black holes
Zhidenko, A
2004-01-01
The low-laying frequencies of characteristic quasi-normal modes (QNM) of Schwarzschild-de Sitter (SdS) black holes have been calculated for fields of different spin using the 6th-order WKB approximation and the approximation by the P"{o}shl-Teller potential. The well-known asymptotic formula for large $l$ is generalized here on a case of the Schwarzchild-de Sitter black hole. In the limit of the near extreme $L$ term the results given by both methods are in a very good agreement, and in this limit fields of different spin decay with the same rate. In addition, the fact that the spectrum of massless Dirac quasi-normal frequencies is the same for opposite chyrality has been numerically proved for SdS background.
Kristensen, Philip Trøst; Ge, Rong-Chun; Hughes, Stephen
2017-07-01
We refute all claims of the "Comment on `Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators' " by E. A. Muljarov and W. Langbein. Based entirely on information already contained in our original article [P. T. Kristensen, R.-C. Ge, and S. Hughes, Phys. Rev. A 92, 053810 (2015), 10.1103/PhysRevA.92.053810], we dismiss every point of criticism as being unsupported and point out how important parts of our argumentation appear to have been overlooked by the Comment authors. In addition, we provide additional calculations showing directly the connection between the normalizations by Sauvan et al. and Muljarov et al., which were not included in our original article.
Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows
Energy Technology Data Exchange (ETDEWEB)
Xu, X Q; Belli, E; Bodi, K; Candy, J; Chang, C S; Cohen, B I; Cohen, R H; Colella, P; Dimits, A M; Dorr, M R; Gao, Z; Hittinger, J A; Ko, S; Krasheninnikov, S; McKee, G R; Nevins, W M; Rognlien, T D; Snyder, P B; Suh, J; Umansky, M V
2008-09-18
We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependence of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.
Energy Technology Data Exchange (ETDEWEB)
Li, Jin [Chongqing University, Department of Physics, Chongqing (China); Lin, Kai [Universidade de Sao Paulo, Instituto de Fisica, CP 66318, Sao Paulo (Brazil); Yang, Nan [Huazhong University of Science and Technology, Department of Physics, Wuhan (China)
2015-03-01
Based on a regular exact black hole (BH) from nonlinear electrodynamics (NLED) coupled to general relativity, we investigate the stability of such BH through the Quasinormal Modes (QNMs) of electromagnetic (EM) field perturbations and its thermodynamics through Hawking radiation. In perturbation theory, we can deduce the effective potential from a nonlinear EM field. The comparison of the potential function between regular and RN BHs could predict similar QNMs. The QNM frequencies tell us the effect of the magnetic charge q, the overtone n, and the angular momentum number l on the dynamic evolution of NLED EM field. Furthermore we also discuss the cases of near-extreme conditions of such a magnetically charged regular BH. The corresponding QNM spectrum illuminates some special properties in the near-extreme cases. For the thermodynamics, we employ the Hamilton-Jacobi method to calculate the near-horizon Hawking temperature of the regular BH and reveal the relationship between the classical parameters of the black hole and its quantum effects. (orig.)
Institute of Scientific and Technical Information of China (English)
TANG NianSheng; CHEN XueDong; WANG XueRen
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backtitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
Pierce, R. B.; Johnson, Donald R.; Reames, Fred M.; Zapotocny, Tom H.; Wolf, Bart J.
1991-01-01
The normal-mode characteristics of baroclinically amplifying disturbances were numerically investigated in a series of adiabatic simulations by a hybrid isentropic-sigma model, demonstrating the effect of coupling an isentropic-coordinate free atmospheric domain with a sigma-coordinate PBL on the normal-mode characteristics. Next, the normal-mode model was modified by including a transport equation for water vapor and adiabatic heating by condensation. Simulations with and without a hydrological component showed that the overall effect of latent heat release is to markedly enhance cyclogenesis and frontogenesis.
Sadhu, Arunangshu; Sarkar, Somenath
2016-08-01
We investigate the Kerr nonlinear optical processes (NOPs) in the case of a single-mode trapezoidal index fiber based on recently formulated and appropriate Marcuse-type relations for spot size in terms of normalized frequency corresponding to such fiber having various aspect ratios. With the help of these relations, we have analyzed the maximum NOP in these fibers having prospective the merits of tight light confinement in the subwavelength diameter waveguiding region. The comparative investigation reveals that the aspect ratio having a value of 0.7 is the most promising candidate for maximum optical nonlinearity, constructional convenience, and less diffraction. The analysis should be attractive for system users as a ready reference.
Application of Normal Mode Expansion to AE Waves in Finite Plates
Gorman, M. R.; Prosser, W. H.
1997-01-01
Breckenridge et al. (1975), Hsu (1985) and Pao (1978) adapted approaches from seismology to calculate the response at the surface of an infinite half-space and an infinite plate. These approaches have found use in calibrating acoustic emission (AE) transducers. However, it is difficult to extend this theoretical approach to AE testing of practical structures. Weaver and Pao (1982) considered a normal mode solution to the Lamb equations. Hutchinson (1983) pointed out the potential relevance of Mindlin's plate theory (1951) to AE. Pao (1982) reviewed Medick s (1961) classical plate theory for a point source, but rejected it as useful for AE and no one seems to have investigated its relevance to AE any further. Herein, a normal mode solution to the classical plate bending equation was investigated for its applicability to AE. The same source-time function chosen by Weaver and Pao is considered. However, arbitrary source and receiver positions are chosen relative to the boundaries of the plate. This is another advantage of the plate theory treatment in addition to its simplicity. The source does not have to be at the center of the plate as in the axisymmetric treatment. The plate is allowed to remain finite and reflections are predicted. The importance of this theory to AE is that it can handle finite plates, realistic boundary conditions, and can be extended to composite materials.
Robles-Uriza, A. X.; Reyes Gómez, F.; Mejía-Salazar, J. R.
2016-09-01
We report the existence of multiple omnidirectional defect modes in the zero-nbar gap of photonic stacks, made of alternate layers of conventional dielectric and double-negative metamaterial, with a polaritonic defect layer. In the case of nonlinear magnetic metamaterials, the optical bistability phenomenon leads to switching from negligible to perfect transmission around these defect modes. We hope these findings have potential applications in the design and development of multichannel optical filters, power limiters, optical-diodes and optical-transistors.
Mode decomposition of nonlinear eigenvalue problems and application in flow stability
Institute of Scientific and Technical Information of China (English)
高军; 罗纪生
2014-01-01
Direct numerical simulations are carried out with different disturbance forms introduced into the inlet of a flat plate boundary layer with the Mach number 4.5. According to the biorthogonal eigenfunction system of the linearized Navier-Stokes equations and the adjoint equations, the decomposition of the direct numerical simulation results into the discrete normal mode is easily realized. The decomposition coefficients can be solved by doing the inner product between the numerical results and the eigenfunctions of the adjoint equations. For the quadratic polynomial eigenvalue problem, the inner product operator is given in a simple form, and it is extended to an N th-degree polynomial eigenvalue problem. The examples illustrate that the simplified mode decomposition is available to analyze direct numerical simulation results.
Event-triggered sliding mode control for a class of nonlinear systems
Behera, Abhisek K.; Bandyopadhyay, Bijnan
2016-09-01
Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.
Directory of Open Access Journals (Sweden)
Muammar Sadrawi
2016-01-01
Full Text Available Good quality cardiopulmonary resuscitation (CPR is the mainstay of treatment for managing patients with out-of-hospital cardiac arrest (OHCA. Assessment of the quality of the CPR delivered is now possible through the electrocardiography (ECG signal that can be collected by an automated external defibrillator (AED. This study evaluates a nonlinear approximation of the CPR given to the asystole patients. The raw ECG signal is filtered using ensemble empirical mode decomposition (EEMD, and the CPR-related intrinsic mode functions (IMF are chosen to be evaluated. In addition, sample entropy (SE, complexity index (CI, and detrended fluctuation algorithm (DFA are collated and statistical analysis is performed using ANOVA. The primary outcome measure assessed is the patient survival rate after two hours. CPR pattern of 951 asystole patients was analyzed for quality of CPR delivered. There was no significant difference observed in the CPR-related IMFs peak-to-peak interval analysis for patients who are younger or older than 60 years of age, similarly to the amplitude difference evaluation for SE and DFA. However, there is a difference noted for the CI (p<0.05. The results show that patients group younger than 60 years have higher survival rate with high complexity of the CPR-IMFs amplitude differences.
Extreme-Point Symmetric Mode Decomposition Method for Nonlinear and Non-Stationary Signal Processing
Wang, Jin-Liang
2013-01-01
To process nonlinear and non-stationary signals, an extreme-point symmetric mode decomposition (ESMD) method is developed. It can be seen as a new alternate of the well-known Hilbert-Huang transform (HHT) method which is widely used nowadays. There are two parts for it. The first part is the decomposition approach which yields a series of intrinsic mode functions (IMFs) together with an optimal adaptive global mean (AGM) curve, the second part is the direct interpolating (DI) approach which yields instantaneous amplitudes and frequencies for the IMFs together with a time-varying energy. Relative to the HHT method it has five characteristics as follows: (1) Different from constructing 2 outer envelopes, its sifting process is implemented by the aid of 1, 2 or 3 inner interpolating curves; (2) It does not decompose the signal to the last trend curve with at most one extreme point, it optimizes the residual component to be an optimal AGM curve which possesses a certain number of extreme points; (3) Its symmetry ...
Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere
Hsieh, Yi-Kai; Omura, Yoshiharu
2017-01-01
We perform test particle simulations for relativistic electrons interacting with a whistler mode chorus packet propagating at oblique angles. By confirming that the energy transport of oblique lower band chorus is nearly along the ambient magnetic field, we apply the gyroaveraging method in calculating equations of motion of electrons. We trace evolution of a delta function of relativistic electrons in a phase space of kinetic energy and equatorial pitch angle and obtain numerical Green's functions of the chorus wave-particle interactions. Examining the Green's functions in a wide range of kinetic energies, we find that Landau resonance can accelerate MeV electrons efficiently and that higher nth resonances such as n =- 1 and n = 2 also contribute to acceleration of electrons at high equatorial pitch angles (˜70°) and high energies (˜2 MeV). We investigate the rate of energy gain of the cyclotron resonance acceleration and the Landau resonance acceleration and find that the perpendicular component of wave electric field dominates both accelerations for MeV electrons. Furthermore, the proximity between the parallel components of Vp and Vg of oblique whistler mode waves and the nonlinear trapping condition make the interaction time of Landau resonance much longer than that of n = 1 cyclotron resonance, resulting in efficient acceleration of MeV electrons.
Ayten, B.; Westerhof, E.; ASDEX Upgrade team,
2014-01-01
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived
Institute of Scientific and Technical Information of China (English)
SUN Xue-ming; ZHANG Hui-jian; ZUO Meng; GU Wan-yi; XU Da-xiong
2006-01-01
Dense wavelength division multiplexing (DWDM) system is the ultimate selection as an optical communication system because of its high speeds and capacities.However,the fiber nonlinear effects and polarization mode dispersion severely limit the performance of the system when signal propagates at 40 Gbit/s in a single channel.The coupled nonlinear Schr(o)dinger equations of a single channel in DWDM,which are all considered factors of group velocity dispersion (GVD),self phase modulation (SPM),cross phase modulation (XPM),four wave mixing (FWM) and polarization mode dispersion (PMD),are derived,while their number results are obtained with extended split-step Fourier method.Finally,to analyze the impacts of the fiber nonlinear effects and PMD on the optical communication system,the simulated results of an 8x40 Gbit/s DWDM system are discussed under different conditions respectively.
Scherpen, J. M. A.; Scherpen, J. M. A.
2005-01-01
This paper considers the nonlinear left coprime factorization (NLCF) of a nonlinear system. In order to study the balanced realization of such NLCF first a dual system notion is introduced. The important energy functions for the original NLCF and their relation with the dual NLCF are studied and rel
A Non-linear Scaling Algorithm Based on chirp-z Transform for Squint Mode FMCW-SAR
Directory of Open Access Journals (Sweden)
Yu Bin-bin
2012-03-01
Full Text Available A non-linear scaling chirp-z imaging algorithm for squint mode Frequency Modulated Continuous Wave Synthetic Aperture Radar (FMCW-SAR is presented to solve the problem of the focus accuracy decline. Based on the non-linear characteristics in range direction for the echo signal in Doppler domain, a non-linear modulated signal is introduced to perform a non-linear scaling based on chirp-z transform. Then the error due to range compression and range migration correction can be reduced, therefore the range resolution of radar image is improved. By using the imaging algorithm proposed, the imaging performances for point targets, compared with that from the original chirp-z algorithm, are demonstrated to be improved in range resolution and image contrast, and to be maintained the same in azimuth resolution.
Tuia, Devis; Marcos, Diego; Camps-Valls, Gustau
2016-10-01
Remote sensing image classification exploiting multiple sensors is a very challenging problem: data from different modalities are affected by spectral distortions and mis-alignments of all kinds, and this hampers re-using models built for one image to be used successfully in other scenes. In order to adapt and transfer models across image acquisitions, one must be able to cope with datasets that are not co-registered, acquired under different illumination and atmospheric conditions, by different sensors, and with scarce ground references. Traditionally, methods based on histogram matching have been used. However, they fail when densities have very different shapes or when there is no corresponding band to be matched between the images. An alternative builds upon manifold alignment. Manifold alignment performs a multidimensional relative normalization of the data prior to product generation that can cope with data of different dimensionality (e.g. different number of bands) and possibly unpaired examples. Aligning data distributions is an appealing strategy, since it allows to provide data spaces that are more similar to each other, regardless of the subsequent use of the transformed data. In this paper, we study a methodology that aligns data from different domains in a nonlinear way through kernelization. We introduce the Kernel Manifold Alignment (KEMA) method, which provides a flexible and discriminative projection map, exploits only a few labeled samples (or semantic ties) in each domain, and reduces to solving a generalized eigenvalue problem. We successfully test KEMA in multi-temporal and multi-source very high resolution classification tasks, as well as on the task of making a model invariant to shadowing for hyperspectral imaging.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that decentralized BP neural networks are used to adaptively learn the uncertainty bounds of interconnected subsystems in the Lyapunov sense, and the outputs of the decentralized BP neural networks are then used as the parameters of the sliding mode controller to compensate for the effects of subsystems uncertainties. Using this scheme, not only strong robustness with respect to uncertainty dynamics and nonlinearities can be obtained, but also the output tracking error between the actual output of each subsystem and the corresponding desired reference output can asymptotically converge to zero. A simulation example is presented to support the validity of the proposed BP neural-networks-based sliding mode controller.
Rey, Michaël; Nikitin, Andrei V; Tyuterev, Vladimir G
2012-06-28
A rovibrational model based on the normal-mode complete nuclear Hamiltonian is applied to methane using our recent potential energy surface [A. V. Nikitin, M. Rey, and Vl. G. Tyuterev, Chem. Phys. Lett. 501, 179 (2011)]. The kinetic energy operator and the potential energy function are expanded in power series to which a new truncation-reduction technique is applied. The vibration-rotation Hamiltonian is transformed systematically to a full symmetrized form using irreducible tensor operators. Each term of the Hamiltonian expansion can be thus cast in the tensor form whatever the order of the development. This allows to take full advantage of the symmetry properties for doubly and triply degenerate vibrations and vibration-rotation states. We apply this model to variational computations of energy levels for (12)CH(4), (13)CH(4), and (12)CD(4).
Crossley, D.; Rivera, L.; Hinderer, J.; Rosat, S.
2009-04-01
For several years, it has been the goal of the Global Geodynamics Project (GGP) to convert high rate acceleration data recorded on superconducting gravimeters (SG) to a format compatible with the seismic data archived at IRIS. The problem for the GGP community has been to properly establish the metadata for characterizing the response of the instrument, particularly its phase characteristics. Although SG data exists at IRIS from the Membach GGP station in Belgium, up to now most of the data from the GGP network has been on hold until the response problem was solved. This we have now been able to do, and we hope to show that data from the Strasbourg SG station will be at IRIS and available. We will also upload all the data from the SGs from after the Sumatra earthquake and show some results on normal mode analysis that demonstrates the benefit of the good amplitude calibration feature and high precision of the SG instruments.
Regional variation of inner core anisotropy from seismic normal mode observations.
Deuss, Arwen; Irving, Jessica C E; Woodhouse, John H
2010-05-21
Earth's solid inner core is surrounded by a convecting liquid outer core, creating the geodynamo driving the planet's magnetic field. Seismic studies using compressional body waves suggest hemispherical variation in the anisotropic structure of the inner core, but are poorly constrained because of limited earthquake and receiver distribution. Here, using normal mode splitting function measurements from large earthquakes, based on extended cross-coupling theory, we observe both regional variations and eastern versus western hemispherical anisotropy in the inner core. The similarity of this pattern with Earth's magnetic field suggests freezing-in of crystal alignment during solidification or texturing by Maxwell stress as origins of the anisotropy. These observations limit the amount of inner core super rotation, but would be consistent with oscillation.
A NEW MOMENT METHOD FOR THE FAST AND ACCURATE ANALYSIS OF NORMAL MODE HELICAL ANTENNAS
Institute of Scientific and Technical Information of China (English)
Ji Yicai; Sun Baohua; Liu Qizhong
2001-01-01
In this letter, a new moment method using helical segments is presented to model Normal Mode Helical Antenna (NMHA). Using this method, the NMHA can be modeled by a few segments. The current distributions and radiation patterns of some NMHAs are calculated.A comparison is made between results obtained using this helical segment algorithm and a linear segment algorithm, and the results of the two algorithms agree fairly well. When calculating the impedance matrix [Z], all the elements of the matrix can be obtained by only calculating a few elements with the application of the symmetric and periodic characteristics of the NMHA.Therefore, the CPU time and the memory storage are significantly reduced, with the accuracy and speed enhanced.
Simple illustrations of range-dependence and 3-D effects by normal-mode sound propagation modelling
Ivansson, Sven
2016-01-01
As is well known, the sound-speed profile has significant effects on underwater acoustic sound propagation. These effects can be quantified by normal-mode models, for example. The basic case is a laterally homogeneous medium, for which the sound speed and the density depend on depth only and not on horizontal position. Effects of horizontal medium-parameter variation can be quantified by coupled-mode models, with coupling between mode expansions for laterally homogeneous parts of the medium. In the present paper, these effects are illustrated for media with a particularly simple horizontal parameter variation such that mode shapes do not vary with horizontal position. The modal wavenumbers depend on horizontal position, however. At a vertical interface between regions with laterally homogeneous medium parameters, each mode is reflected as well as transmitted. For the media considered, reflection and transmission coefficients can be computed separately for each mode without mode coupling, and this is done recu...
Comparing the Quasi-Normal and Natural Modes of an open cavity
Settimi, A; Hoenders, B J; Hauss, J W; Napoli, A; Messina, A; Perina, J; Sibilia, C; Bertolotti, M
2009-01-01
The present paper proposes, for the first time to the best of our knowledge, a systematic comparison between the Quasi Normal Modes (QNMs) and the Natural Modes (NMs) for one-dimensional (1D) two side opened cavities. We clarify, in classical electrodynamics, why, for the description of an e.m. field outgoing from a one-layer homogeneous structure (as a laser cavity), the QNM eigen-functions should be the most suitable expansion basis, whilst, for discussing the scattering properties of a multi-layer inhomogeneous structure (as a Photonic Crystal (PC)), the NM eigen-functions seem a better choice. The QNM eigen-frequencies and eigen-functions are calculated for a linear Fabry-Perot (FP) cavity. The first-order Born approximation is applied to the same cavity in order to make a comparison between the first-order Born approximated and the actual QNM eigen-functions of the cavity. We prove that the first-order Born approximation for a FP cavity introduces a symmetry breaking: in fact, each Born approximated QNM ...
Exact quasi-normal modes for the near horizon Kerr metric
Cvetic, M
2013-01-01
We study the quasi-normal modes of a massless scalar field in a general sub-extreme Kerr back- ground by exploiting the hidden SL(2, R) x SL(2, R) x SO(3) symmetry of the subtracted geometry approximation. This faithfully models the near horizon geometry but locates the black hole in a confining asymptotically conical box analogous to the anti-de-Sitter backgrounds used in string the- ory. There are just two series of modes, given in terms of hypergeometric functions and spherical harmonics, reminiscent of the left-moving and right-moving degrees in string theory: one is over- damped, the other is underdamped and exhibits rotational splitting. The remarkably simple exact formulae for the complex frequencies would in principle allow the determination of the mass and angular momentum from observations of a black hole. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole.
Single file and normal dual mode diffusion in highly confined hard sphere mixtures under flow.
Wanasundara, Surajith N; Spiteri, Raymond J; Bowles, Richard K
2012-09-14
We use Monte Carlo simulations to study the dual-mode diffusion regime of binary and tertiary mixtures of hard spheres confined in narrow cylindrical pores under the influence of an imposed flow. The flow is introduced to the dynamics by adding a small bias directed along the long axis of the pore to the random displacement of each Monte Carlo move. As a result, the motion of the particles in all the components is dominated by a drift velocity that causes the mean squared displacements to increase quadratically in the long time limit. However, an analysis of the mean squared displacements at intermediate time scales shows that components of the mixture above and below their passing thresholds still exhibit behaviors consistent with normal and single-file diffusion, respectively. The difference between the mean squared displacements of the various components is shown to go though a maximum, suggesting there may be an optimal pore diameter for the separation of mixtures exhibiting dual-mode diffusion.
Quasi-normal modes for de Sitter-Reissner-Nordstr\\"om Black Holes
Iantchenko, Alexei
2014-01-01
The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless charged Dirac fields propagating in the outer region of de Sitter-Reissner-Nordstr{\\"o}m Black Holes, which is spherically symmetric charged exact solution of the Einstein-Maxwell equations. Using the spherical symmetry of the equation and restricting to a fixed harmonic the problem is reduced to a scattering problem for the 1D massless Dirac operator on the line. The resonances for the problem are related to the resonances for a certain semi-classical Schr{\\"o}dinger operators with exponentially decreasing positive potentials. The asymptotic distribution of the resonances are close to the lattice of quasi-poles associated to the non-degenerate maxima of the potentials. Using the techniques of semi-classical Birkhoff normal form we give the complete asymptotic formulas for the resonances. In particular, we calculate the first three leading terms in the expansio...
Nonlinear dynamics of tapping mode atomic force microscopy in the bistable phase
Bahrami, Arash; Nayfeh, Ali H.
2013-03-01
Nonlinear dynamics of amplitude modulation atomic force microscopy (AFM) is studied employing a reduced-order model based on a differential quadrature method (DQM). The AFM microcantilever is assumed to be operating in the dynamic contact or tapping mode while the microcantilever tip being initially located in the bistable region. We have found that the DQM is capable of precise prediction of the static bifurcation diagram and natural frequencies of the microcantilever. We have used the DQM to discretize the partial-differential equation governing the microcantilever motion and a finite difference method (FDM) to calculate limit-cycle responses of the AFM tip. It is shown that a combination of the DQM and FDM applied, respectively, to discretize the spatial and temporal derivatives provides an efficient, accurate procedure to address the complicated dynamic behavior exhibited by the AFM probe. The procedure was, therefore, utilized to study the response of the microcantilever to a base harmonic excitation through several numerical examples. We found that the dynamics of the AFM probe in the bistable region is totally different from those in the monostable region.
Nonlinear localized modes in dipolar Bose–Einstein condensates in two-dimensional optical lattices
Energy Technology Data Exchange (ETDEWEB)
Rojas-Rojas, Santiago, E-mail: srojas@cefop.cl [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Naether, Uta [Instituto de Ciencia de Materiales de Aragón and Departamento de Física de la Materia Condensada, CSIC-Universidad de Zaragoza, 50009 Zaragoza (Spain); Delgado, Aldo [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Vicencio, Rodrigo A. [Center for Optics and Photonics and MSI-Nucleus on Advanced Optics, Universidad de Concepción, Casilla 160-C, Concepción (Chile); Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago (Chile)
2016-09-16
Highlights: • We study discrete two-dimensional breathers in dipolar Bose–Einstein Condensates. • Important differences in the properties of three fundamental modes are found. • Norm threshold for existence of 2D breathers varies with dipolar interaction. • The Effective Potential Method is implemented for stability analysis. • Uncommon mobility of 2D discrete solitons is observed. - Abstract: We analyze the existence and properties of discrete localized excitations in a Bose–Einstein condensate loaded into a periodic two-dimensional optical lattice, when a dipolar interaction between atoms is present. The dependence of the Number of Atoms (Norm) on the energy of solutions is studied, along with their stability. Two important features of the system are shown, namely, the absence of the Norm threshold required for localized solutions to exist in finite 2D systems, and the existence of regions in the parameter space where two fundamental solutions are simultaneously unstable. This feature enables mobility of localized solutions, which is an uncommon feature in 2D discrete nonlinear systems. With attractive dipolar interaction, a non-trivial behavior of the Norm dependence is obtained, which is well described by an analytical model.
Directory of Open Access Journals (Sweden)
Luis G. Garcia-Valdovinos
2015-04-01
Full Text Available Transparency has been a major objective in bilateral teleoperation systems, even in the absence of time delay induced by the communication channel, since a high degree of transparency would allow humans to drive the remote teleoperator as if he or she were directly interacting with the remote environment, with the remote teleoperator as a physical and sensorial extension of the operator. When fast convergence of position and force tracking errors are ensured by the control system, then complete transparency is obtained, which would ideally guarantee humans to be tightly kinaesthetically coupled. In this paper a model-free Cartesian second order sliding mode (SOSM PD control scheme for nonlinear master-slave systems is presented. The proposed scheme does not rely on velocity measurements and attains very fast convergence of position trajectories, with bounded tracking of force trajectories, rendering a high degree of transparency with lesser knowledge of the system. The degree of transparency can easily be improved by tuning a feedback gain in the force loop. A unique energy storage function is introduced; such that a similar Cartesian-based controller is implemented in the master and slave sides. The resulting properties of the Cartesian control structure allows the human operator to input directly Cartesian variables, which makes clearer the kinaesthetic coupling, thus the proposed controller becomes a suitable candidate for practical implementation. The performance of the proposed scheme is evaluated in a semi-experimental setup.
Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation
Kiessling, A; Heavens, A F
2011-01-01
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Eucl...
Energy Technology Data Exchange (ETDEWEB)
Bessa, Wallace M. [Universidade Federal do Rio Grande do Norte, Department of Mechanical Engineering, Campus Universitario Lagoa Nova, 59072-970 Natal, RN (Brazil)], E-mail: wmbessa@ufrnet.br; Paula, Aline S. de [Universidade Federal do Rio de Janeiro, COPPE - Department of Mechanical Engineering, P.O. Box 68.503, 21941-972 Rio de Janeiro, RJ (Brazil)], E-mail: alinesp27@gmail.com; Savi, Marcelo A. [Universidade Federal do Rio de Janeiro, COPPE - Department of Mechanical Engineering, P.O. Box 68.503, 21941-972 Rio de Janeiro, RJ (Brazil)], E-mail: savi@mecanica.ufrj.br
2009-10-30
Chaos control may be understood as the use of tiny perturbations for the stabilization of unstable periodic orbits embedded in a chaotic attractor. The idea that chaotic behavior may be controlled by small perturbations of physical parameters allows this kind of behavior to be desirable in different applications. In this work, chaos control is performed employing a variable structure controller. The approach is based on the sliding mode control strategy and enhanced by an adaptive fuzzy algorithm to cope with modeling inaccuracies. The convergence properties of the closed-loop system are analytically proven using Lyapunov's direct method and Barbalat's lemma. As an application of the control procedure, a nonlinear pendulum dynamics is investigated. Numerical results are presented in order to demonstrate the control system performance. A comparison between the stabilization of general orbits and unstable periodic orbits embedded in chaotic attractor is carried out showing that the chaos control can confer flexibility to the system by changing the response with low power consumption.
Study of Super-Twisting sliding mode control for U model based nonlinear system
Zhang, Jianhua; Li, Yang; Xueli WU; Jianan HUO; Shenyang ZHUANG
2016-01-01
The Super-Twisting control algorithm is adopted to analyze the U model based nonlinear control system in order to solve the controller design problems of non-affine nonlinear systems. The non-affine nonlinear systems are studied, the neural network approximation of the nonlinear function is performed, and the Super-Twisting control algorithm is used to control. The convergence of the Super-Twisting algorithm is proved by selecting an appropriate Lyapunov function. The Matlab simulation is car...
Institute of Scientific and Technical Information of China (English)
ZHANG; Yimin; (张义民); WANG; Shun; (王; 顺); LIU; Qiaoling; (刘巧伶); WEN; Bangchun; (闻邦椿)
2003-01-01
Based on the generalized probabilistic finite element method, this paper presents an approximate solution technique for general multi-degree-of-freedom nonlinear random vibration systems with random parameters. The fourth-moment technique, maximum entropy theory and incomplete probability information theory are employed to systematically develop a reliability analysis method for dynamic random structural systems with correlation failure modes under unavailable joint probability density functions of basic random variables. The first passage problem of multi-degree-of-freedom nonlinear random vibration systems is solved.
Modal analysis of nonlinear mechanical systems
2014-01-01
The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.
Resonance modes in optical fibres
Institute of Scientific and Technical Information of China (English)
余寿绵; 余恬
2002-01-01
The weakly nonlinear boundary value problem of wave propagation in an optical fibre (for the transverse electric mode, for example) is formulated and a modified linear solution is obtained. It is shown that a self-consistent theory of fibre optics should be weakly nonlinear. The mode of critical refraction that does not exist in the linear theory is obtained, showing that it is a mode consisting of resonance modes. It is shown that the signal carriers in a long fibre are of resonance modes, not normal modes. Some experimental data are given for comparison with the theoretical predictions, and the agreement seems satisfactory.
Finite-beta effects on the nonlinear evolution of the (m = 1; n = 1) mode in tokamaks
Energy Technology Data Exchange (ETDEWEB)
Holmes, J.A.; Carreras, B.A.; Hicks, H.R.; Lynch, V.E.; Rothe, K.E.
1982-01-01
The stability and evolution of ISX-B-like plasmas are numerically studied using a reduced set of resistive magnetohydrodynamic (MHD) equations. For a sequence of equilibria stable to ideal modes, the n = 1 mode changes from a tearing branch to a pressure-driven branch as ..beta../sup p/ is increased. When this mode is unstable at low beta, it is just the (m = 1;n = 1) tearing mode. Higher n modes also become linearly unstable with increasing ..beta../sub p/; they are essentially pressure driven and have a ballooning character. For low values of beta the instability is best described as a ..beta../sub p/ distortion of the (m = 1;n = 1) tearing mode. This mode drives many other helicities through toroidal and nonlinear couplings. As ..beta../sub p/ is increased, the growth of the m = 1 island slows down in time, going from exponential to linear before reconnection occurs. If ..beta../sub p/ is large enough, the island saturates without reconnection. A broad spectrum of other modes, driven by the (m = 1;n = 1) instability, is produced. These results agree with some observed features of MHD activity in ISX-B.
Energy Technology Data Exchange (ETDEWEB)
Baik, I.C.; Kim, K.H.; Cho, K.Y.; Youn, M.J. [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1998-04-01
A DSP-based robust nonlinear speed control of a permanent magnet synchronous motor (PMSM) which is robust to unknown parameter variations and speed measurement error is presented. The model reference adaptive system (MRAS) based adaptation mechanisms for the estimation of slowly varying parameters are derived using the Lyapunov stability theory. For the disturbances or quickly varying parameters, a quasi-linearized and decoupled model including the influence of parameter variations and speed measurement error on the nonlinear speed control of a PMSM is derived. Based on this model, a boundary layer integral sliding mode controller to improve the robustness and performance of the nonlinear speed control of a PMSM is designed and compared with the conventional controller. To show the validity of the proposed control scheme, simulations and experimental works are carried out and compared with the conventional control scheme. (author). 19 refs., 14 figs., 6 tabs.
Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing
2017-02-01
In this work, we employ a focused beam theory to modify the phase reversal at the stress-free boundary, and consequently enhance the second harmonic generation during its back-propagation toward the initial source position. We first confirmed this concept through experiment by using a spherically focused beam at the water-air interface, and measuring the reflected second harmonic and comparing with a planar wave reflected from the same stress-free or a rigid boundary. In order to test the feasibility of this idea for measuring the nonlinearity parameter of solids in a reflection mode, a focused nonlinear ultrasonic beam is modeled for focusing at and reflection from a stress-free boundary. A nonlinearity parameter expression is then defined together with diffraction and attenuation corrections.
Design of a High-Nonlinearity Single-Mode Holey Fiber with Flattened Dispersion around 800 nm
Institute of Scientific and Technical Information of China (English)
WANG Wei; SOU Lan-Tian; LIU Zhao-Lun; ZHOU Gui-Yao
2009-01-01
We numerically demonstrate a high-nonlinearity single-mode holey fiber with flattened dispersion around the Ti-Za laser band at 800 nm. The dispersion profile of the fiber has the shape of a quadratic curve, which reaches its maximun 5.96ps·km~(-1)·nm~(-1)at 800nm and its minimum -0.897 ps·km-1·nm~(-1) at both 750 and 850 nm.The nonlinear coefficient is 170 W~(-1)km~(-1) at 800nm and so higher order modes exit. A six-layer air-hole cladding ensures a loss less than 0.067 db/m in the 750 to 850nm range. Two more air-hole rings will reduce the loss to below 0.1db/km.
Mou Chen; Rong Mei; Bin Jiang
2013-01-01
We propose a robust sliding mode control (SMC) scheme for a class of uncertain multi-input and multi-output (MIMO) nonlinear systems with the unknown external disturbance, the system uncertainty, and the backlash-like hysteresis. To tackle the continuous system uncertainty, the radial basis function (RBF) neural network is employed to approximate it. And then, combine the unknown external disturbance, and the unknown neural network approximation error with the affection caused by backlash-lik...
Theory and Normal Mode Analysis of Change in Protein Vibrational Dynamics on Ligand Binding
Energy Technology Data Exchange (ETDEWEB)
Mortisugu, Kei [RIKEN, Japan; Njunda, Brigitte [Computational Molecular Biophysics, Interdisciplinary Center for Scientific Computing (IWR); Smith, Jeremy C [ORNL
2009-12-01
The change of protein vibrations on ligand binding is of functional and thermodynamic importance. Here, this process is characterized using a simple analytical 'ball-and-spring' model and all-atom normal-mode analysis (NMA) of the binding of the cancer drug, methotrexate (MTX) to its target, dihydrofolate reductase (DHFR). The analytical model predicts that the coupling between protein vibrations and ligand external motion generates entropy-rich, low-frequency vibrations in the complex. This is consistent with the atomistic NMA which reveals vibrational softening in forming the DHFR-MTX complex, a result also in qualitative agreement with neutron-scattering experiments. Energy minimization of the atomistic bound-state (B) structure while gradually decreasing the ligand interaction to zero allows the generation of a hypothetical 'intermediate' (I) state, without the ligand force field but with a structure similar to that of B. In going from I to B, it is found that the vibrational entropies of both the protein and MTX decrease while the complex structure becomes enthalpically stabilized. However, the relatively weak DHFR:MTX interaction energy results in the net entropy gain arising from coupling between the protein and MTX external motion being larger than the loss of vibrational entropy on complex formation. This, together with the I structure being more flexible than the unbound structure, results in the observed vibrational softening on ligand binding.
The Theoretical Foundation of 3D Alfvén Resonances: Normal Modes
Wright, Andrew N.; Elsden, Thomas
2016-12-01
We consider the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a 3D equilibrium. Numerical solutions to normal modes (\\propto \\exp (-iω t)) are presented, along with a theoretical framework to interpret them. The solutions we find are fundamentally different from those in 1D and 2D. In 3D there exists an infinite number of possible resonant solutions within a “Resonant Zone,” and we show how boundary conditions and locally 2D regions can favor particular solutions. A unique feature of the resonance in 3D is switching between different permissible solutions when the boundary of the Resonant Zone is encountered. The theoretical foundation that we develop relies upon recognizing that, in 3D, the orientation of the resonant surface will not align in a simple fashion with an equilibrium coordinate. We present a method for generating the Alfvén wave natural frequencies for an arbitrarily oriented Alfvén wave, which requires a careful treatment of scale factors describing the background magnetic field geometry.
Normal mode Rossby waves and their effects on chemical composition in the late summer stratosphere
Directory of Open Access Journals (Sweden)
D. Pendlebury
2007-08-01
Full Text Available During past MANTRA campaigns, ground-based measurements of several long-lived chemical species have revealed quasi-periodic fluctuations on time scales of several days. These fluctuations could confound efforts to detect long-term trends from MANTRA, and need to be understood and accounted for. Using the Canadian Middle Atmosphere Model, we investigate the role of dynamical variability in the late summer stratosphere due to normal mode Rossby waves and the impact of this variability on fluctuations in chemical species. Wavenumber~1, westward travelling waves are considered with average periods of 5, 10 and 16 days. Time-lagged correlations between the temperature and nitrous oxide, methane and ozone fields are calculated in order to assess the possible impact of these waves on the chemical species, although transport may be the dominant effect. Using Fourier-wavelet decomposition and correlating the fluctuations between the temperature and chemical fields, we determine that variations in the chemical species are well-correlated with the 5-day wave and the 10-day wave between 30 and 60 km. Interannual variability of the waves is also examined.
Nonradiating normal modes in a classical many-body model of matter-radiation interaction
Carati, A.; Galgani, L.
2003-08-01
We consider a classical model of matter-radiation interaction, in which the matter is represented by a system of infinitely many dipoles on a one-dimensional lattice, and the system is dealt with in the so-called dipole ( linearized) approximation. We prove that there exist normal-mode solutions of the complete system, so that in particular the dipoles, though performing accelerated motions, do not radiate energy. This comes about in virtue of an exact compensation which we prove to occur, for each dipole, between the “radiation reaction force” and a part of the retarded forces due to all the other dipoles. This fact corresponds to a certain identity which we name after Oseen, since it occurs that this researcher did actually propose it, already in the year 1916. We finally make a connection with a paper of Wheeler and Feynman on the foundations of electrodynamics. It turns out indeed that the Oseen identity, which we prove here in a particular model, is in fact a weak form of a general identity that such authors were assuming as an independent postulate.
Theory of the normal modes of vibrations in the lanthanide type crystals
Energy Technology Data Exchange (ETDEWEB)
Acevedo, Roberto [Instituto de Ciencias Basicas. Facultad de Ingenieria, Universidad Diego Portales, Avenida Ejercito 441, Santiago (Chile); Soto-Bubert, Andres, E-mail: roberto.acevedo@umayor.cl
2008-11-01
For the lanthanide type crystals, a vast and rich, though incomplete amount of experimental data has been accumulated, from linear and non linear optics, during the last decades. The main goal of the current research work is to report a new methodology and strategy to put forward a more representative approach to account for the normal modes of vibrations for a complex N-body system. For illustrative purposes, the chloride lanthanide type crystals Cs{sub 2}NaLnCl{sub 6} have been chosen and we develop new convergence tests as well as a criterion to deal with the details of the F-matrix (potential energy matrix). A novel and useful concept of natural potential energy distributions (NPED) is introduced and examined throughout the course of this work. The diagonal and non diagonal contributions to these NPED-values, are evaluated for a series of these crystals explicitly. Our model is based upon a total of seventy two internal coordinates and ninety eight internal Hooke type force constants. An optimization mathematical procedure is applied with reference to the series of chloride lanthanide crystals and it is shown that the strategy and model adopted is sound from both a chemical and a physical viewpoints. We can argue that the current model is able to accommodate a number of interactions and to provide us with a very useful physical insight. The limitations and advantages of the current model and the most likely sources for improvements are discussed in detail.
Nonlinear excitation of low-n harmonics in reduced MHD simulations of edge-localized modes
Krebs, Isabel; Lackner, Karl; Guenter, Sibylle
2013-01-01
Nonlinear simulations of the early ELMphase based on a typical type-I ELMy ASDEX Upgrade discharge have been carried out using the reduced MHD code JOREK. The analysis is focused on the evolution of the toroidal Fourier spectrum. It is found that during the nonlinear evolution, linearly subdominant low-n Fourier components, in particular the n = 1, grow to energies comparable with linearly dominant harmonics. A simple model is developed, based on the idea that energy is transferred among the toroidal harmonics via second order nonlinear interaction. The simple model reproduces and explains very well the early nonlinear evolution of the toroidal spectrum in the JOREK simulations. Furthermore, it is shown for the n = 1 harmonic, that its spatial structure changes significantly during the transition from linear to nonlinearly driven growth. The rigidly growing structure of the linearly barely unstable n = 1 reaches far into the plasma core. In contrast, the nonlinearly driven n = 1 has a rigidly growing structur...
Devi, Seema; Agarwal, Asha; Pandey, Kiran; Pradhan, Asima
2015-03-01
Reflectance spectroscopy contains information of scatterers and absorbers present inside biological tissues and has been successfully used to diagnose disease. Success of any diagnostic tool depends upon the potential of statistical algorithm to extract appropriate diagnostic features from the measured optical data. In our recent study, we have used the potential of the classification algorithm, Nonlinear Maximum Representation and Discrimination Features (NMRDF) to extract important diagnostic features from reflectance spectra of normal and dysplastic human cervical tissue. This NMRDF algorithm uses the higher order correlation information in the input data, which helps to represent the asymmetrically distributed data and provides the closed form solution of the nonlinear transform for maximum discrimination. We have recorded unpolarized, co and cross-polarized reflectance spectra from 350nm to 650nm, illuminating the human cervical tissue epithelium with white light source. A total of 139 samples were divided into training and validation data sets. The input parameters were optimized using training data sets to extract the appropriate nonlinear features from the input reflectance spectra. These extracted nonlinear features are used as input for nearest mean classifier to calculate the sensitivity and specificity for both training as well as validation data sets. We have observed that co-polarized components provide maximum sensitivity and specificity compared to cross-polarized components and unpolarized data. This is expected since co-polarized light provides subsurface information while cross-polarized and unpolarized data mask the vital epithelial information through high diffuse scattering.
Hu, Jun; Gao, Huijun
2014-01-01
This monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity. Such phenomena include communication delay, packet dropout, signal quantization or saturation, randomly occurring nonlinearities and randomly occurring uncertainties.The text is self-contained, beginning with an introduction to nonlinear stochastic systems, network-induced phenomena and filtering and control, moving through a collection of the latest research results which focuses on the three aspects
Directory of Open Access Journals (Sweden)
Jing Lei
2013-01-01
Full Text Available The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.
Two-fluid sub-grid-scale viscosity in nonlinear simulation of ballooning modes in a heliotron device
Miura, H.; Hamba, F.; Ito, A.
2017-07-01
A large eddy simulation (LES) approach is introduced to enable the study of the nonlinear growth of ballooning modes in a heliotron-type device, by solving fully 3D two-fluid magnetohydrodynamic (MHD) equations numerically over a wide range of parameter space, keeping computational costs as low as possible. A model to substitute the influence of scales smaller than the grid size, at sub-grid scale (SGS), and at the scales larger than it—grid scale (GS)—has been developed for LES. The LESs of two-fluid MHD equations with SGS models have successfully reproduced the growth of the ballooning modes in the GS and nonlinear saturation. The numerical results show the importance of SGS effects on the GS components, or the effects of turbulent fluctuation at small scales in low-wavenumber unstable modes, over the course of the nonlinear saturation process. The results also show the usefulness of the LES approach in studying instability in a heliotron device. It is shown through a parameter survey over many SGS model coefficients that turbulent small-scale components in experiments can contribute to keeping the plasma core pressure from totally collapsing.
Li, Y.; Gubbiotti, G.; Casoli, F.; Gonçalves, F. J. T.; Morley, S. A.; Rosamond, M. C.; Linfield, E. H.; Marrows, C. H.; McVitie, S.; Stamps, R. L.
2017-01-01
We report the results, from experimental and micromagnetic studies, of the magnetic normal modes in artificial square spin ice systems consisting of ferromagnetic-monodomain islands. Spin-wave properties are measured by Brillouin light scattering. The mode spectra contain several branches whose frequencies are sensitive to the magnitude and in-plane orientation of an applied magnetic field. We also identify soft modes that exhibit different behaviours depending on the direction of the applied magnetic field. The obtained results are well described with micromagnetic simulations of independent magnetic elements arranged along two sublattices.
Jinno, Souma; Toki, Hiroshi; Abe, Masayoshi
2017-02-01
In this study, the coupling between the common and normal modes in distributed lines and the resulting electromagnetic noise were considered. The telegraph equations of three distributed lines with the boundary conditions of a lumped circuit reveal the presence of mode-coupling noise. To reduce the coupling noise, the geometrically and electrically symmetric configuration of the three distributed lines is proposed. The simulation results show that the proposed configuration can decrease the mode-coupling noise by a factor of 1 ×10-8 in comparison with that of asymmetric configurations.
Normal modes of oscillation of the Asinelli and Garisenda towers in Bologna (Italy)
Morelli, A.; Azzara, R. M.; Cavaliere, A.; Zaccarelli, L.
2013-12-01
The Asinelli and Garisenda medieval towers represent the best-know city landmark in Bologna. Asinelli is also known to physics historians for early experiments on free fall of bodies for the first measurements of g (Giovanni Battista Riccioli, ca. 1650) and proof of Earth rotation (Giovanni Battista Guglielmini, 1791). The Two Towers (as they are commonly known) are essentially tall, square cross-section hollow masonry cuboids. Taller Asinelli, built between 1109 and 1119, is 97 m high, with an overhang of 2.2 m, while more seriously leaning Garisenda has an overhang of 3.2 m with a heigth of 48 m. During the summer of 2012 -- in the aftermath of two M≈6 earthquakes occurred in the proximity of the city -- the permanent engineering monitoring system of the towers has been temporarily supplemented by 6 seismometric stations installed at different levels inside the masonry buildings, to study their dynamical response to induced vibrations. We have thus been able to observe and measure the oscillation of the two towers excited by ambient noise, mostly due to city traffic. The two towers show similar behaviour, more clear in taller Asinelli. The first three flexural normal modes of oscillation, and the first torsional mode, can easily be detected. Their frequencies are split because of the asymmetry due to leaning of the tower. This asymmetry produces slightly different frequencies of oscillation in two orthogonal directions, quite consistent with preliminary dynamical modeling. Horizontal particle-motion polarization plots clearly show the cyclic energy transfer between these two degrees of freedom of the system. Oscillations of taller Asinelli influence its close sister, such that the Asinelli spectral signature can also be easily recognized in the motion recorded at the base of Garisenda, overimposed over Garisenda own free oscillations. Horizontal component polarization analysis done simultaneously at the two ground-level stations often point to a nearby common
Institute of Scientific and Technical Information of China (English)
Ahcene Boubakir; Fares Boudjema; Salim Labiod
2009-01-01
The aim of this paper is to develop a neuro-fuzzy-sliding mode controller (NFSMC) with a nonlinear sliding surface for a coupled tank system.The main purpose is to eliminate the chattering phenomenon and to overcome the problem of the equivalent control computation.A first-order nonlinear sliding surface is presented,on which the developed sliding mode controller (SMC) is based.Mathematical proof for the stability and convergence of the system is presented.In order to reduce the chattering in SMC,a fixed boundary layer around the switch surface is used.Within the boundary layer,where the fuzzy logic control is applied,the chattering phenomenon,which is inherent in a sliding mode control,is avoided by smoothing the switch signal.Outside the boundary,the sliding mode control is applied to drive the system states into the boundary layer.Moreover,to compute the equivalent controller,a feed-forward neural network (NN) is used.The weights of the net are updated such that the corrective control term of the NFSMC goes to zero.Then,this NN also alleviates the chattering phenomenon because a big gain in the corrective control term produces a more serious chattering than a small gain.Experimental studies carried out on a coupled tank system indicate that the proposed approach is good for control applications.
Sato, M; Imai, S; Fujita, N; Shi, W; Takao, Y; Sada, Y; Hubbard, B E; Ilic, B; Sievers, A J
2013-01-01
An intrinsic localized mode (ILM) represents a localized vibrational excitation in a nonlinear lattice. Such a mode will stay in resonance as the driver frequency is changed adiabatically until a bifurcation point is reached, at which point the ILM switches and disappears. The dynamics behind switching in such a many body system is examined here through experimental measurements and numerical simulations. Linear response spectra of a driven micromechanical array containing an ILM were measured in the frequency region between two fundamentally different kinds of bifurcation points that separate the large amplitude ILM state from the two low amplitude vibrational states. Just as a natural frequency can be associated with a driven harmonic oscillator, a similar natural frequency has been found for a driven ILM via the beat frequency between it and a weak, tunable probe. This finding has been confirmed using numerical simulations. The behavior of this nonlinear natural frequency plays important but different roles as the two bifurcation points are approached. At the upper transition its frequency coalesces with the driver and the resulting bifurcation is very similar to the saddle-node bifurcation of a single driven Duffing oscillator, which is treated in an Appendix. The lower transition occurs when the four-wave mixing partner of the natural frequency of the ILM intersects the topmost extended band mode of the same symmetry. The properties of linear local modes associated with the driven ILM are also identified experimentally for the first time and numerically but play no role in these transitions.
Sato, M.; Imai, S.; Fujita, N.; Shi, W.; Takao, Y.; Sada, Y.; Hubbard, B. E.; Ilic, B.; Sievers, A. J.
2013-01-01
An intrinsic localized mode (ILM) represents a localized vibrational excitation in a nonlinear lattice. Such a mode will stay in resonance as the driver frequency is changed adiabatically until a bifurcation point is reached, at which point the ILM switches and disappears. The dynamics behind switching in such a many body system is examined here through experimental measurements and numerical simulations. Linear response spectra of a driven micromechanical array containing an ILM were measured in the frequency region between two fundamentally different kinds of bifurcation points that separate the large amplitude ILM state from the two low amplitude vibrational states. Just as a natural frequency can be associated with a driven harmonic oscillator, a similar natural frequency has been found for a driven ILM via the beat frequency between it and a weak, tunable probe. This finding has been confirmed using numerical simulations. The behavior of this nonlinear natural frequency plays important but different roles as the two bifurcation points are approached. At the upper transition its frequency coalesces with the driver and the resulting bifurcation is very similar to the saddle-node bifurcation of a single driven Duffing oscillator, which is treated in an Appendix. The lower transition occurs when the four-wave mixing partner of the natural frequency of the ILM intersects the topmost extended band mode of the same symmetry. The properties of linear local modes associated with the driven ILM are also identified experimentally for the first time and numerically but play no role in these transitions.
Energy Technology Data Exchange (ETDEWEB)
Baher, S. [Department of Physics, Lorestan University, Khoramabad (Iran, Islamic Republic of) and Research Institute of Applied Sciences (ACECR), Shahid Beheshti University (Iran, Islamic Republic of)]. E-mail: bahersalar@yahoo.com; Baharvand, A. [Department of Physics, Lorestan University, Khoramabad (Iran, Islamic Republic of); Sepahvand, R. [Department of Physics, Lorestan University, Khoramabad (Iran, Islamic Republic of); Badraghi, J. [Research Institute of Applied Sciences (ACECR), Shahid Beheshti University (Iran, Islamic Republic of)
2007-04-30
The propagation of nonlinear s-polarized polariton waves (TE modes) in an infinitely extended superlattice is considered. The periodic system is composed of two different components where the layers are arranged in an alternating fashion so that each layer of material 1 is bounded by two layers of material 2 and vice versa. In general, each of the individual layers may be characterized by a Kerr-type nonlinear dielectric function with a frequency-dependent characteristic of either the plasmons in a metal/semiconductor or the optical phonons in an ionic crystal. To investigate the propagation of polariton modes in such a system, a theoretical model is formulated leading to Jacobi elliptic functions for the electric field amplitude across the layers. Subsequently, the application of boundary conditions at the interfaces gives rise to dispersion relations. Numerical examples are given for plasmon-polariton and phonon-polariton modes and a comparison is made with phonon-polariton modes propagating in a three layered system.
Hayward, S; Kitao, A; Berendsen, HJC
1997-01-01
Model-free methods are introduced to determine quantities pertaining to protein domain motions from normal mode analyses and molecular dynamics simulations, For the normal mode analysis, the methods are based on the assumption that in low frequency modes, domain motions can be well approximated by m
Seismic Noise Generation by Ocean Waves: Views from Normal-mode Theory
Tanimoto, T.
2012-12-01
The continuous seismic records (noise) and the cross-correlation techniques are making a huge impact on study for the crust and upper mantle. Such studies rely on microseisms for frequencies about 0.05-0.3 Hz that are excited by ocean waves but detailed processes for the excitation are still vague. Our views of noise excitation have been influenced by the results in Longuet-Higgins (1950) who showed how colliding ocean waves generate the dominant secondary microseisms. There are two main points to his results; the first is the generation of pressure at deep ocean bottom, even though ocean waves have energy only in the upper 100-200 meters. This result on deep penetrating pressure was originally derived for an incompressible fluid. The second is the existence of specific ocean depths that preferentially excite secondary microseisms (0.15 Hz). This result was derived for a medium with a compressible fluid layer over an elastic half-space. The purpose of this study is to examine these two points from the views of the normal-mode theory. The first point was shown in Tanimoto (2007, GJI). Excitation by the advection term in the Navier-Stokes equation was shown to lead to the equivalent result with Longuet-Higgins (1950). Mathematically, dominant contributions are from colliding ocean waves and the resulting force exactly matches the Longuet-Higgins pressure formula in the low-frequency range (below 0.05 Hz). It is somewhat surprising that a result in an incompressible fluid emerged in the analysis of elastic medium with compressible ocean. However, in the low frequency range, the eigenfunctions of Rayleigh waves become (almost) constant in the ocean, meaning that the entire fluid layer moves coherently up and down just like an incompressible medium. Then the emergence of the Longuet-Higgins pressure formula is not surprising. However, as Longuet-Higgins (1950) noted, such a situation does not apply to noise at 0.15 Hz as it is above such a frequency range. In a
Normal mode analysis of macromolecular systems with the mobile block Hessian method
Energy Technology Data Exchange (ETDEWEB)
Ghysels, An; Van Speybroeck, Veronique; Van Neck, Dimitri; Waroquier, Michel [Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde (Belgium); Brooks, Bernard R. [Laboratory for Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, 5636 Fisher' s Ln, Rockville, MD 20851 (United States)
2015-01-22
Until recently, normal mode analysis (NMA) was limited to small proteins, not only because the required energy minimization is a computationally exhausting task, but also because NMA requires the expensive diagonalization of a 3N{sub a}×3N{sub a} matrix with N{sub a} the number of atoms. A series of simplified models has been proposed, in particular the Rotation-Translation Blocks (RTB) method by Tama et al. for the simulation of proteins. It makes use of the concept that a peptide chain or protein can be seen as a subsequent set of rigid components, i.e. the peptide units. A peptide chain is thus divided into rigid blocks with six degrees of freedom each. Recently we developed the Mobile Block Hessian (MBH) method, which in a sense has similar features as the RTB method. The main difference is that MBH was developed to deal with partially optimized systems. The position/orientation of each block is optimized while the internal geometry is kept fixed at a plausible - but not necessarily optimized - geometry. This reduces the computational cost of the energy minimization. Applying the standard NMA on a partially optimized structure however results in spurious imaginary frequencies and unwanted coordinate dependence. The MBH avoids these unphysical effects by taking into account energy gradient corrections. Moreover the number of variables is reduced, which facilitates the diagonalization of the Hessian. In the original implementation of MBH, atoms could only be part of one rigid block. The MBH is now extended to the case where atoms can be part of two or more blocks. Two basic linkages can be realized: (1) blocks connected by one link atom, or (2) by two link atoms, where the latter is referred to as the hinge type connection. In this work we present the MBH concept and illustrate its performance with the crambin protein as an example.
Full-Order Sliding Mode Control for High-Order Nonlinear System Based on Extended State Observer
Institute of Scientific and Technical Information of China (English)
CHEN Qiang; TAO Liang; NAN Yurong
2016-01-01
In this paper,a full-order sliding mode control based on extended state observer (FSMC+ESO) is proposed for high-order nonlinear system with unknown system states and uncertainties.The extended state observer (ESO) is employed to estimate both the unknown system states and uncertainties so that the restriction that the system states should be completely measurable is relaxed,and a full-order sliding mode controller is designed based on the ESO estimation to overcome the chattering problem existing in ordinary reduced-order sliding mode control.Simulation results show that the proposed method facilitates the practical application with respect to good tracking performance and chattering elimination.
Yashkir, O. V.; Yashkir, Yu N.
1987-06-01
A theoretical investigation is made of nonlinear excitation of planar waveguide modes at frequencies ω when external plane optical waves of frequency ω1 are incident on the waveguide surface. The general formulas for the efficiency of the excitation of modes by a monochromatic wave are obtained and analyzed for the case of self-interaction of the ω = ω1 + ω1 - ω1 type and by a biharmonic wave in the case of generation of the difference frequency ω = ω1 - ω1'. The efficiency of parametric conversion of waveguide modes ω accompanied by an increase of the frequency to the range ω' is considered for the case when the sum frequency ω + ω1 = ω1' is generated. The numerical method developed by the authors is used to analyze the characteristic features of these processes in some specific cases.
Chen, W; Yu, L M; Ji, X Q; Dong, J Q; Yang, Q W; Liu, Yi; Yan, L W; Zhou, Y; Li, W; Song, X M; Chen, S Y; Cheng, J; Shi, Z B; Duan, X R
2012-01-01
In this letter, it is reported that the ?rst experimental results are associated with the GAM induced by energetic electrons (eEGAM) in HL-2A Ohmic plasma. The energetic-electrons are generated by parallel electric ?elds during magnetic reconnection associated with tearing mode (TM). The eEGAM localizes in the core plasma, i.e. in the vicinity of q=2 surface, and is very di?erent from one excited by the drift-wave turbulence in the edge plasma. The analysis indicated that the eEGAM is provided with the magnetic components, whose intensities depend on the poloidal angles, and its mode numbers are jm/nj=2/0. Further, there exist intense nonlinear interactions among eEGAM, BAEs and strong tearing modes (TMs). These new ?ndings shed light on the underlying physics mechanism for the excitation of the low frequency (LF) Alfv?enic and acoustic uctuations.
Rossit, C. A.; Laura, P. A. A.
2001-12-01
An exact solution for the title problem is obtained by means of the classical eigenfunction approach. The natural frequencies are computed for a wide range of the intervening mechanical and geometric parameters. Normal modes of transverse vibration are plotted for some cases of practical interest. The problem is technically important in several areas of applied science and technology.
Bertaccini, Edward J; Trudell, James R; Lindahl, Erik
2010-08-18
We have previously used molecular modeling and normal-mode analyses combined with experimental data to visualize a plausible model of a transmembrane ligand-gated ion channel. We also postulated how the gating motion of the channel may be affected by the presence of various ligands, especially anesthetics. As is typical for normal-mode analyses, those studies were performed in vacuo to reduce the computational complexity of the problem. While such calculations constitute an efficient way to model the large scale structural flexibility of transmembrane proteins, they can be criticized for neglecting the effects of an explicit phospholipid bilayer or hydrated environment. Here, we show the successful calculation of normal-mode motions for our model of a glycine α-1 receptor, now suspended in a fully hydrated lipid bilayer. Despite the almost uniform atomic density, the introduction of water and lipid does not grossly distort the overall gating motion. Normal-mode analysis revealed that even a fully immersed glycine α-1 receptor continues to demonstrate an iris-like channel gating motion as a low-frequency, high-amplitude natural harmonic vibration consistent with channel gating. Furthermore, the introduction of periodic boundary conditions allows the examination of simultaneous harmonic vibrations of lipid in synchrony with the protein gating motions that are compatible with reasonable lipid bilayer perturbations. While these perturbations tend to influence the overall protein motion, this work provides continued support for the iris-like motion model that characterizes gating within the family of ligand-gated ion channels.
Institute of Scientific and Technical Information of China (English)
Bing Wang; Xiuqing Wu
2008-01-01
@@ Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method.
Nonlinear Modelling of Orthopyroxene and Amphibole Mineral Modes in Orbicules from Fisher Lake CA
Durant, D. G.; Fowler, A. D.
2004-05-01
Geochemical self-organization or spontaneous patterning, caused by positive feedback between reaction and transport, which creates amplification of any fluctuations in the system, can occur when a system is pushed into a far-from-equilibrium (FFE) state. The patterning is thus a construct of the system that allows the dissipation of those energies that pushed it into the FFE state and not a template forced onto the system by boundary conditions. The Fisher Lake CA orbicules contain plagioclase and orthopyroxene that show characteristics of FFE cooling; for instance, reverse-zoned radiating crystals organized in a highly complex pattern. The decimetre-scale orbicules are surrounded by a homogeneous mosaic of crystals characteristic of near-to-equilibrium (NTE) plutonic cooling environments. Thus the orbicular comb texture is interpreted as the response of a FFE magma toward achieving equilibrium. The innermost shell of an orbicule, containing the largest, most spectacular reverse-zoned branching orthopyroxene crystals, represents the largest step towards NTE. Rapid precipitation of minerals quickly decreased the free energy of the system such that an overshooting occurred, resulting in a chemical oscillation about the equilibrium value, which gradually decreased as the system approached NTE. Evidence of this mechanism is seen in the shell mineral modes of orthopyroxene and amphibole. Initially the oscillations are large and antithetical, i.e. as the amount of one mineral increases the other decreases and vice versa. The amplitudes of the oscillations gradually decrease flattening out to a more constant value or stable state; thus looking much like a damped pendulum. An empirical nonlinear model based on the modified Volterra-Lotka equations models these curves. The modelling demonstrates that pattern formation can occur without a periodic external forcing of the intensive variables of the magmatic system as the magma cools and solidifies. Smooth changes in these
Sung, C.; White, A. E.; Mikkelsen, D. R.; Greenwald, M.; Holland, C.; Howard, N. T.; Churchill, R.; Theiler, C.
2016-04-01
Long wavelength turbulent electron temperature fluctuations (kyρs 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (kyρs ≲ 1.7) performed at r/a ˜ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the "Transport Shortfall" [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].
Energy Technology Data Exchange (ETDEWEB)
Sung, C., E-mail: csung@physics.ucla.edu [University of California, Los Angeles, Los Angeles, California 90095 (United States); White, A. E.; Greenwald, M.; Howard, N. T. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); Mikkelsen, D. R.; Churchill, R. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Holland, C. [University of California, San Diego, La Jolla, California 92093 (United States); Theiler, C. [Ecole Polytechnique Fédérale de Lausanne, SPC, Lausanne 1015 (Switzerland)
2016-04-15
Long wavelength turbulent electron temperature fluctuations (k{sub y}ρ{sub s} < 0.3) are measured in the outer core region (r/a > 0.8) of Ohmic L-mode plasmas at Alcator C-Mod [E. S. Marmar et al., Nucl. Fusion 49, 104014 (2009)] with a correlation electron cyclotron emission diagnostic. The relative amplitude and frequency spectrum of the fluctuations are compared quantitatively with nonlinear gyrokinetic simulations using the GYRO code [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] in two different confinement regimes: linear Ohmic confinement (LOC) regime and saturated Ohmic confinement (SOC) regime. When comparing experiment with nonlinear simulations, it is found that local, electrostatic ion-scale simulations (k{sub y}ρ{sub s} ≲ 1.7) performed at r/a ∼ 0.85 reproduce the experimental ion heat flux levels, electron temperature fluctuation levels, and frequency spectra within experimental error bars. In contrast, the electron heat flux is robustly under-predicted and cannot be recovered by using scans of the simulation inputs within error bars or by using global simulations. If both the ion heat flux and the measured temperature fluctuations are attributed predominantly to long-wavelength turbulence, then under-prediction of electron heat flux strongly suggests that electron scale turbulence is important for transport in C-Mod Ohmic L-mode discharges. In addition, no evidence is found from linear or nonlinear simulations for a clear transition from trapped electron mode to ion temperature gradient turbulence across the LOC/SOC transition, and also there is no evidence in these Ohmic L-mode plasmas of the “Transport Shortfall” [C. Holland et al., Phys. Plasmas 16, 052301 (2009)].
Siwicki, Bartłomiej; Kasztelanic, Rafał; Klimczak, Mariusz; Cimek, Jarosław; Pysz, Dariusz; Stępień, Ryszard; Buczyński, Ryszard
2016-06-01
The bandwidth of coherent supercontinuum generated in optical fibres is strongly determined by the all-normal dispersion characteristic of the fibre. We investigate all-normal dispersion limitations in all-solid oxide-based soft glass photonic crystal fibres with various relative inclusion sizes and lattice constants. The influence of material dispersion on fibre dispersion characteristics for a selected pair of glasses is also examined. A relation between the material dispersion of the glasses and the fibre dispersion has been described. We determined the parameters which limit the maximum range of flattened all-normal dispersion profile achievable for the considered pair of heavy-metal-oxide soft glasses.
Mahmoudi, S.; Trivaudey, F.; Bouhaddi, N.
2015-07-01
The aim of this study is the prediction of the dynamic response of damaged laminated composite structures in the context of component mode synthesis. Hence, a method of damage localization of complex structures is proposed. The dynamic behavior of transversely isotropic layers is expressed through elasticity coupled with damage based on an existing macro model for cracked structures. The damage is located only in some regions of the whole structure, which is decomposed on substructures. The incremental linear dynamic governing equations are obtained by using the classical linear Kirchhoff-Love theory of plates. Then, considering the damage-induced nonlinearity, the obtained nonlinear dynamic equations are solved in time domain. However, a detailed finite element modelling of such structure on the scale of localized damage would generate very high computational costs. To reduce this cost, Component Mode Synthesis method (CMS) is used for modelling a nonlinear fine-scale substructure damaged, connected to linear dynamic models of the remaining substructures, which can be condensed and not updated at each iteration. Numerical results show that the mechanical properties of the structure highly change when damage is taken into account. Under an impact load, damage increases and reaches its highest value with the maximum of the applied load and then remains unchanged. Besides, the eigenfrequencies of the damaged structure decrease comparing with those of an undamaged one. This methodology can be used for monitoring strategies and lifetime estimations of hybrid complex structures due to the damage state is known in space and time.
Directory of Open Access Journals (Sweden)
Wameedh Riyadh Abdul-Adheem
2016-12-01
Full Text Available This paper presents a new strategy for the active disturbance rejection control (ADRC of a general uncertain system with unknown bounded disturbance based on a nonlinear sliding mode extended state observer (SMESO. Firstly, a nonlinear extended state observer is synthesized using sliding mode technique for a general uncertain system assuming asymptotic stability. Then the convergence characteristics of the estimation error are analyzed by Lyapunov strategy. It revealed that the proposed SMESO is asymptotically stable and accurately estimates the states of the system in addition to estimating the total disturbance. Then, an ADRC is implemented by using a nonlinear state error feedback (NLSEF controller; that is suggested by J. Han and the proposed SMESO to control and actively reject the total disturbance of a permanent magnet DC (PMDC motor. These disturbances caused by the unknown exogenous disturbances and the matched uncertainties of the controlled model. The proposed SMESO is compared with the linear extended state observer (LESO. Through digital simulations using MATLAB / SIMULINK, the chattering phenomenon has been reduced dramatically on the control input channel compared to LESO. Finally, the closed-loop system exhibits a high immunity to torque disturbance and quite robustness to matched uncertainties in the system.
Johansson; Aubry
2000-05-01
We investigate the long-time evolution of weakly perturbed single-site breathers (localized stationary states) in the discrete nonlinear Schrodinger equation. The perturbations we consider correspond to time-periodic solutions of the linearized equations around the breather, and can be either (i) spatially localized or (ii) spatially extended. For case (i), which corresponds to the excitation of an internal mode of the breather, we find that the nonlinear interaction between the breather and its internal mode always leads to a slow growth of the breather amplitude and frequency. In case (ii), corresponding to interaction between the breather and a standing-wave phonon, the breather will grow provided that the wave vector of the phonon is such that the generation of radiating higher harmonics at the breather is possible. In other cases, breather decay is observed. This condition yields a limit value for the breather frequency above which no further growth is possible. We also discuss another mechanism for breather growth and destruction which becomes important when the amplitude of the perturbation is non-negligible, and which originates from the oscillatory instabilities of the nonlinear standing-wave phonons.
Energy Technology Data Exchange (ETDEWEB)
Zhao, Peng [School of Physics, University of Chinese Academy of Sciences, Beijing 100049 (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences, Beijing 100049 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Wu, Xiaoning [State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Institute of Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190 (China); Sun, Zhao-Yong [School of Physics, University of Chinese Academy of Sciences, Beijing 100049 (China)
2015-11-24
It is well-known that there is a geometric correspondence between high-frequency quasi-normal modes (QNMs) and null geodesics (spherical photon orbits). In this paper, we generalize such correspondence to charged scalar field in Kerr-Newman space-time. In our case, the particle and black hole are all charged, so one should consider non-geodesic orbits. Using the WKB approximation, we find that the real part of quasi-normal frequency corresponds to the orbits frequency, the imaginary part of the frequency corresponds to the Lyapunov exponent of these orbits and the eigenvalue of angular equation corresponds to carter constant. From the properties of the imaginary part of quasi-normal frequency of charged massless scalar field, we can still find that the QNMs of charged massless scalar field possess the zero damping modes in extreme Kerr-Newman spacetime under certain condition which has been fixed in this paper.
Study of Super-Twisting sliding mode control for U model based nonlinear system
Directory of Open Access Journals (Sweden)
Jianhua ZHANG
2016-08-01
Full Text Available The Super-Twisting control algorithm is adopted to analyze the U model based nonlinear control system in order to solve the controller design problems of non-affine nonlinear systems. The non-affine nonlinear systems are studied, the neural network approximation of the nonlinear function is performed, and the Super-Twisting control algorithm is used to control. The convergence of the Super-Twisting algorithm is proved by selecting an appropriate Lyapunov function. The Matlab simulation is carried out to verify the feasibility and effectiveness of the described method. The result shows that the output of the controlled system can be tracked in a very short time by using the designed Super-Twisting controller, and the robustness of the controlled system is significantly improved as well.
Calculation, normalization and perturbation of quasinormal modes in coupled cavity-waveguide systems
DEFF Research Database (Denmark)
Kristensen, Philip Trøst; de Lasson, Jakob Rosenkrantz; Gregersen, Niels
2014-01-01
We show how one can use a non-local boundary condition, which is compatible with standard frequency domain methods, for numerical calculation of quasinormal modes in optical cavities coupled to waveguides. In addition, we extend the definition of the quasinormal mode norm by use of the theory of ...
The (Quasi)Normal Natural Mode description of the scattering process by dispersive photonic crystals
Hoenders, Bernhard J.; Bertolotti, Mario; DeLaRue, RM; Viktorovitch, P; Lopez, C; Midrio, M
2006-01-01
A scattering theory for finite photonic crystals in terms of the natural modes of the scatterer is developed. This theory generalizes the classical Hilbert-Schmidt type of bilinear expansions of the propagator to a bilinear expansion into natural modes. It is shown that the Sturm-Liouville type of
Nazemosadat, Elham; Mafi, Arash
2013-12-16
The main differences in nonlinear switching behavior between multicore versus multimode waveguide couplers are highlighted. By gradually decreasing the separation between the two cores of a dual-core waveguide and interpolating from a multicore to a multimode scenario, the role of the linear coupling, self-phase modulation, cross-phase modulation, and four-wave mixing terms are explored, and the key reasons are identified behind higher switching power requirements and lower switching quality in multimode nonlinear couplers.
Ayten, B
2013-01-01
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived previously by Harvey et al, Phys. Rev. Lett. 62 (1989) 426. We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker-Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a typical NTM stabilization experiment on ASDEX Upgrade. A particular feature of these experiments is that the rays of the EC wave beam propagate tangential to the flux surfaces in the power deposition region. The calculations show significant non-linear effects on the ECCD efficiency, when the ECCD power is increased from its experimental value of 1 MW to a larger value of 4 MW. The nonlinear effects are largest in case of...
Yang, Qingchun; Wang, Hongxin; Chetehouna, Khaled; Gascoin, Nicolas
2017-01-01
The supersonic combustion ramjet (scramjet) engine remains the most promising airbreathing engine cycle for hypersonic flight, particularly the high-performance dual-mode scramjet in the range of flight Mach number from 4 to 7, because it can operates under different combustion modes. Isolator is a very key component of the dual-mode scramjet engine. In this paper, nonlinear characteristics of combustion mode transition is theoretically analyzed. The discontinuous sudden changes of static pressure and Mach number are obtained as the mode transition occurs, which emphasizing the importance of predication and control of combustion modes. In this paper, a predication model of different combustion modes is developed based on these these nonlinear features in the isolator flow field. it can provide a valuable reference for control system design of the scramjet-powered aerospace vehicle.
Thurgood, J. O.; McLaughlin, J. A.
2012-09-01
Context. Coronal magnetic null points have been implicated as possible locations for localised heating events in 2D models. We investigate this possibility about fully 3D null points. Aims: We investigate the nature of the fast magnetoacoustic wave about a fully 3D magnetic null point, with a specific interest in its propagation, and we look for evidence of MHD mode coupling and/or conversion to the Alfvén mode. Methods: A special fieldline and flux-based coordinate system was constructed to permit the introduction of a pure fast magnetoacoustic wave in the vicinity of proper and improper 3D null points. We considered the ideal, β = 0, MHD equations, which are solved using the LARE3D numerical code. The constituent modes of the resulting wave were isolated and identified using the special coordinate system. Numerical results were supported by analytical work derived from perturbation theory and a linear implementation of the WKB method. Results: An initially pure fast wave is found to be permanently decoupled from the Alfvén mode both linearly and nonlinearly for both proper and improper 3D null points. The pure fast mode also generates and sustains a nonlinear disturbance aligned along the equilibrium magnetic field. The resulting pure fast magnetoacoustic pulse has transient behaviour, which is found to be governed by the (equilibrium) Alfvén-speed profile, and a refraction effect focuses all the wave energy towards the null point. Conclusions: Thus, the main results from previous 2D work do indeed carry over to the fully 3D magnetic null points and so we conclude that 3D null points are locations for preferential heating in the corona by 3D fast magnetoacoustic waves.
Pavelko, V.; Lapsa, K.; Pavlovskis, P.
2016-07-01
The aim of this study is estimation of the effect of large deflections of a double-cantilever beam (DCB) on the accuracy of determination of the mode I interlaminar fracture toughness GIc of layered composites by using the nonlinear theory of bending of beams. The differential equation of the deflection curve of arm of the DCB specimen in the natural form was used to analyze the strain energy of the specimen and its strain energy release rate GI upon propagation of delamination under the action of cleavage forces at the ends of cantilevers. An algorithm for calculating the strain energy and its release rate in the DCB specimens is realized in the form of a MATLAB code. An experimental study was carried out on DCB specimens of a highly flexible carbon/epoxy laminate. The validity of the nonlinear model developed is demonstrated. The standard methods used to determine GIc are refined for the case of highly flexible specimens.
Sun, Y; Liang, Y; Liu, Y Q; Gu, S; Yang, X; Guo, W; Shi, T; Jia, M; Wang, L; Lyu, B; Zhou, C; Liu, A; Zang, Q; Liu, H; Chu, N; Wang, H H; Zhang, T; Qian, J; Xu, L; He, K; Chen, D; Shen, B; Gong, X; Ji, X; Wang, S; Qi, M; Song, Y; Yuan, Q; Sheng, Z; Gao, G; Fu, P; Wan, B
2016-09-01
Evidence of a nonlinear transition from mitigation to suppression of the edge localized mode (ELM) by using resonant magnetic perturbations (RMPs) in the EAST tokamak is presented. This is the first demonstration of ELM suppression with RMPs in slowly rotating plasmas with dominant radio-frequency wave heating. Changes of edge magnetic topology after the transition are indicated by a gradual phase shift in the plasma response field from a linear magneto hydro dynamics modeling result to a vacuum one and a sudden increase of three-dimensional particle flux to the divertor. The transition threshold depends on the spectrum of RMPs and plasma rotation as well as perturbation amplitude. This means that edge topological changes resulting from nonlinear plasma response plays a key role in the suppression of ELM with RMPs.
Sincore, Alex; Bodnar, Nathan; Bradford, Joshua; Abdulfattah, Ali; Shah, Lawrence; Richardson, Martin C.
2017-03-01
This work studies the accumulated nonlinearities when amplifying a narrow linewidth 2053 nm seed in a single mode Tm:fiber amplifier. A control of repetition rate and pulse duration (>30 ns). The pulses are subsequently amplified and the repetition rate is further reduced using a second acousto-optic modulator. It is well known that spectral degradation occurs in such fibers for peak powers over 100's of watts due to self-phase modulation, four-wave mixing, and stimulated Raman scattering. In addition to enabling a thorough test bed to study such spectral broadening, this system will also enable the investigation of stimulated Brillouin scattering thresholds in the same system. This detailed study of the nonlinearities encountered in 2 μm fiber amplifiers is important in a range of applications from telecommunications to the amplification of ultrashort laser pulses.
Non-linear interaction between high energy ions and MHD-modes
Energy Technology Data Exchange (ETDEWEB)
Bergkvist, Tommy
2001-12-01
When heating a fusion plasma with ICRE or NBI a non-Maxwellian distribution function with high energy ions is created. Ions which are in resonance with a MHD mode will interact with the electric field from the mode and in some circumstances energy will flow from the particles to the mode or opposite. A quasi-linear model for the interaction between high energy ions and a MHD mode has been developed. To solve the time evolution of the MHD mode a module has been implemented into the Monte Carlo code FIDO, which is used for calculating a 3-dimensional distribution function. The model has been tested for an internal kink mode during fishbone oscillations.
Normalized gradient fields for nonlinear motion correction of DCE-MRI time series.
Hodneland, Erlend; Lundervold, Arvid; Rørvik, Jarle; Munthe-Kaas, Antonella Z
2014-04-01
Dynamic MR image recordings (DCE-MRI) of moving organs using bolus injections create two different types of dynamics in the images: (i) spatial motion artifacts due to patient movements, breathing and physiological pulsations that we want to counteract and (ii) signal intensity changes during contrast agent wash-in and wash-out that we want to preserve. Proper image registration is needed to counteract the motion artifacts and for a reliable assessment of physiological parameters. In this work we present a partial differential equation-based method for deformable multimodal image registration using normalized gradients and the Fourier transform to solve the Euler-Lagrange equations in a multilevel hierarchy. This approach is particularly well suited to handle the motion challenges in DCE-MRI time series, being validated on ten DCE-MRI datasets from the moving kidney. We found that both normalized gradients and mutual information work as high-performing cost functionals for motion correction of this type of data. Furthermore, we demonstrated that normalized gradients have improved performance compared to mutual information as assessed by several performance measures. We conclude that normalized gradients can be a viable alternative to mutual information regarding registration accuracy, and with promising clinical applications to DCE-MRI recordings from moving organs.
Stable, accurate and efficient computation of normal modes for horizontal stratified models
Wu, Bo; Chen, Xiaofei
2016-08-01
We propose an adaptive root-determining strategy that is very useful when dealing with trapped modes or Stoneley modes whose energies become very insignificant on the free surface in the presence of low-velocity layers or fluid layers in the model. Loss of modes in these cases or inaccuracy in the calculation of these modes may then be easily avoided. Built upon the generalized reflection/transmission coefficients, the concept of `family of secular functions' that we herein call `adaptive mode observers' is thus naturally introduced to implement this strategy, the underlying idea of which has been distinctly noted for the first time and may be generalized to other applications such as free oscillations or applied to other methods in use when these cases are encountered. Additionally, we have made further improvements upon the generalized reflection/transmission coefficient method; mode observers associated with only the free surface and low-velocity layers (and the fluid/solid interface if the model contains fluid layers) are adequate to guarantee no loss and high precision at the same time of any physically existent modes without excessive calculations. Finally, the conventional definition of the fundamental mode is reconsidered, which is entailed in the cases under study. Some computational aspects are remarked on. With the additional help afforded by our superior root-searching scheme and the possibility of speeding calculation using a less number of layers aided by the concept of `turning point', our algorithm is remarkably efficient as well as stable and accurate and can be used as a powerful tool for widely related applications.
Nonlinear effects in the propagation of optically generated magnetostatic volume mode spin waves
van Tilburg, L. J. A.; Buijnsters, F. J.; Fasolino, A.; Rasing, T.; Katsnelson, M. I.
2017-08-01
Recent experimental work has demonstrated optical control of spin wave emission by tuning the shape of the optical pulse [Satoh et al., Nat. Photon. 6, 662 (2012), 10.1038/nphoton.2012.218]. We reproduce these results and extend the scope of the control by investigating nonlinear effects for large amplitude excitations. We observe an accumulation of spin wave power at the center of the initial excitation combined with short-wavelength spin waves. These kinds of nonlinear effects have not been observed in earlier work on nonlinearities of spin waves. Our observations pave the way for the manipulation of magnetic structures at a smaller scale than the beam focus, for instance in devices with all-optical control of magnetism.
Numerical {Delta}` studies of the nonlinear finite-{beta} tearing mode
Energy Technology Data Exchange (ETDEWEB)
Pletzer, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1996-09-01
Tearing modes have recently attracted attention following theoretical successes in predicting the presence of magnetic island with moderate poloidal m = 3,4 and toroidal n = 2,3 mode numbers during TFTR (Tokamak Fusion Test Reactor) supershots. Classical linear resistive mode theory predicts instability when the asymptotic matching index {Delta}` defined as the jump of logarithmic derivative of the radial magnetic perturbation across the rational surface is positive. Recently, it was suggested that tearing modes could also persist when {Delta}`<0 provided bootstrap current effects are taken into account. In all the above theories, the crucial parameter which determines the stability from both the geometry and equilibrium profiles is {Delta}`. It is shown in the present study that the {Delta}` of the (m=2, n=1) mode computed with the PEST-3 code is virtually always positive. Saturation can nevertheless be achieved provided the symmetry breaking term of a current gradient is included in the resistive layer. (author) 3 figs., 11 refs.
Yin, L; Daughton, W; Albright, B J; Bezzerides, B; DuBois, D F; Kindel, J M; Vu, H X
2006-02-01
The parametric coupling involving backward stimulated scattering of a laser and electron beam acoustic modes (BAM) is described as observed in particle-in-cell (PIC) simulations. The BAM modes evolve from Langmuir waves (LW) as the electron velocity distribution is nonlinearly modified to be non-Maxwellian by backward stimulated Raman scattering (BSRS). With a marginal damping rate, BAM can be easily excited and allow an extended chirping in frequency to occur as later SRS pulses encounter modified distributions. Coincident with the emergence of this non-Maxwellian distribution is a rapid increase in BSRS reflectivities with laser intensities. Both the reflectivity scaling with laser intensity and the observed spectral features from PIC simulations are consistent with recent Trident experiments.
Rational harmonic mode-locked laser using a bismuth-oxide-based highly nonlinear erbium-doped fiber
Fukuchi, Yutaka; Hirata, Kouji; Muraguchi, Masahiro; Maeda, Joji
2017-01-01
We report a rational harmonic mode-locked fiber laser employing a bismuth-oxide-based highly nonlinear erbium-doped fiber (Bi-HNL-EDF) with a length of 1.5 m. The Bi-HNL-EDF is used as a broadband gain medium and as a noise suppressor based on self-phase modulation. The amplitude of the rational harmonic mode-locked pulses can be regulated by properly tuning the modulation parameters of the intracavity modulator. The cavity length as short as 6 m enables generation of stable and clean short pulses with a repetition frequency up to 40 GHz over the wavelength range covering both the conventional and the longer bands.
Luo, X. W.; Xu, P.; Sun, C. W.; Jin, H.; Hou, R. J.; Leng, H. Y.; Zhu, S. N.
2017-06-01
Concurrent spontaneous parametric down-conversion (SPDC) processes have proved to be an appealing approach for engineering the path-entangled photonic state with designable and tunable spatial modes. In this work, we propose a general scheme to construct high-dimensional path entanglement and demonstrate the basic properties of concurrent SPDC processes from domain-engineered quadratic nonlinear photonic crystals, including the spatial modes and the photon flux, as well as the anisotropy of spatial correlation under noncollinear quasi-phase-matching geometry. The overall understanding about the performance of concurrent SPDC processes will give valuable references to the construction of compact path entanglement and the development of new types of photonic quantum technologies.
Moon, Chanho; Kaneko, Toshiro; Itoh, Kimitaka; Ida, Katsumi; Kobayashi, Tatsuya; Inagaki, Shigeru; Itoh, Sanae-I.; Hatakeyama, Rikizo
2016-11-01
Turbulence in fluids and plasmas is ubiquitous in Nature and in the laboratory. Contrary to the importance of the ‘scale-free’ nature of cascade in neutral fluid turbulence, the turbulence in plasma is characterised by dynamics of distinct length scales. The cross-scale interactions can be highly non-symmetric so as to generate the plasma turbulence structures. Here we report that the system of hyper-fine electron-temperature-gradient (ETG) fluctuations and microscopic drift-wave (DW) fluctuations is strongly influenced by the sign of the gradient of the radial electric field through multiscale nonlinear interactions. The selective suppression effects by radial electric field inhomogeneity on DW mode induce a new route to modify ETG mode. This suppression mechanism shows disparity with respect to the sign of the radial electric field inhomogeneity, which can be driven by turbulence, so that it could be a new source for symmetry breaking in the turbulence structure formation in plasmas.
Bachelard, Nicolas; Sebbah, Patrick; Vanneste, Christian
2014-01-01
We use time-domain numerical simulations of a two-dimensional (2D) scattering system to study the interaction of a collection of emitters resonantly coupled to an Anderson-localized mode. For a small electric field intensity, we observe the strong coupling between the emitters and the mode, which is characterized by linear Rabi oscillations. Remarkably, a larger intensity induces non-linear interaction between the emitters and the mode, referred to as the dynamical Stark effect, resulting in non-linear Rabi oscillations. The transition between both regimes is observed and an analytical model is proposed which accurately describes our numerical observations.
Pashaei, Shabnam; Badamchizadeh, Mohammadali
2016-07-01
This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers.
Yan, Ming; Li, Wenxue; Yang, Kangwen; Zhou, Hui; Shen, Xuling; Zhou, Qian; Ru, Qitian; Bai, Dongbi; Zeng, Heping
2012-05-01
We report on a simple scheme to precisely control carrier-envelope phase of a nonlinear-polarization-rotation mode-locked self-started Yb-fiber laser system with an average output power of ∼7 W and a pulse width of 130 fs. The offset frequency was locked to the repetition rate of ∼64.5 MHz with a relative linewidth of ∼1.4 MHz by using a self-referenced feed-forward scheme based on an acousto-optic frequency shifter. The phase noise and timing jitter were calculated to be 370 mrad and 120 as, respectively.
A unified normal mode approach to dynamic tides and its application to rotating Sun-like stars
Ivanov, P B; Chernov, S V
2013-01-01
We determine the response of a uniformly rotating star to tidal perturbations due to a companion. General periodic orbits and parabolic flybys are considered. We evaluate energy and angular momentum exchange rates as a sum of contributions from normal modes allowing for dissipative processes. We consider the case when the response is dominated by the contribution of an identifiable regular spectrum of low frequency modes, such as gravity modes and evaluate it in the limit of very weak dissipation. Our formalism may be applied both to Sun-like stars with radiative cores and convective envelopes and to more massive stars with convective cores and radiative envelopes. We provide general expressions for transfer of energy and angular momentum valid for an orbit with any eccentricity. Detailed calculations are made for Sun-like stars in the slow rotation regime where centrifugal distortion is neglected in the equilibrium and the traditional approximation is made for the normal modes. We use both a WKBJ procedure a...
Parametric nonlinear lumped element model for circular CMUTs in collapsed mode.
Aydoğdu, Elif; Ozgurluk, Alper; Atalar, Abdullah; Köymen, Hayrettin
2014-01-01
We present a parametric equivalent circuit model for a circular CMUT in collapsed mode. First, we calculate the collapsed membrane deflection, utilizing the exact electrical force distribution in the analytical formulation of membrane deflection. Then we develop a lumped element model of collapsed membrane operation. The radiation impedance for collapsed mode is also included in the model. The model is merged with the uncollapsed mode model to obtain a simulation tool that handles all CMUT behavior, in transmit or receive. Large- and small-signal operation of a single CMUT can be fully simulated for any excitation regime. The results are in good agreement with FEM simulations.
Wang, Xiong; Zhou, Pu; Wang, Xiaolin; Xiao, Hu; Liu, Zejin
2014-03-10
We demonstrate the nanosecond-level pulses in Tm-doped fiber laser generated by passively harmonic mode-locking. Nonlinear polarization rotation performed by two polarization controllers (PCs) is employed to induce the self-starting harmonic mode-locking. The fundamental repetition rate of the laser is 448.8 kHz, decided by the length of the cavity. Bundles of pulses with up to 17 uniform subpulses are generated due to the split of pulse when the pump power increases and the PCs are adjusted. Continuous harmonic mode-locked pulse trains are obtained with 1st to 6th and even more than 15th order when the positions of the PCs are properly fixed and the pump power is scaled up. The widths of all the uniform individual pulses are mostly 3-5 ns, and pulse with width of 304 ns at fundamental repetition rate can also be generated by adjusting the PCs. Hysteresis phenomenon of the passively harmonic mode-locked pulses' repetition frequency versus pump power is observed. The rather wide 3dB spectral bandwidth of the pulse train (25 nm) indicates that they may resemble noise-like pulses.
Pourmahmood Aghababa, Mohammad
2013-10-01
This paper investigates the problem of robust control of nonlinear fractional-order dynamical systems in the presence of uncertainties. First, a novel switching surface is proposed and its finite-time stability to the origin is proved. Subsequently, using the sliding mode theory, a robust fractional control law is proposed to ensure the existence of the sliding motion in finite time. We use a fractional Lyapunov stability theory to prove the stability of the system in a given finite time. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the fractional derivative of the control signal. The proposed chattering-free sliding mode technique is then applied for stabilisation of a broad class of three-dimensional fractional-order chaotic systems via a single variable driving control input. Simulation results reveal that the proposed fractional sliding mode controller works well for chaos control of fractional-order hyperchaotic Chen, chaotic Lorenz and chaotic Arneodo systems with no-chatter control inputs.
Directory of Open Access Journals (Sweden)
Glantz-Gashai Y
2017-06-01
Full Text Available Yitav Glantz-Gashai,* Tomer Meirson,* Eli Reuveni, Abraham O Samson Faculty of Medicine in the Galilee, Bar Ilan University, Safed, Israel *These authors contributed equally to this work Abstract: Myeloid cell leukemia-1 (Mcl-1 is often overexpressed in human cancer and is an important target for developing antineoplastic drugs. In this study, a data set containing 2.3 million lead-like molecules and a data set of all the US Food and Drug Administration (FDA-approved drugs are virtually screened for potential Mcl-1 ligands using Protein Data Bank (PDB ID 2MHS. The potential Mcl-1 ligands are evaluated and computationally docked on to three conformation ensembles generated by normal mode analysis (NMA, molecular dynamics (MD, and nuclear magnetic resonance (NMR, respectively. The evaluated potential Mcl-1 ligands are then compared with their clinical use. Remarkably, half of the top 30 potential drugs are used clinically to treat cancer, thus partially validating our virtual screen. The partial validation also favors the idea that the other half of the top 30 potential drugs could be used in the treatment of cancer. The normal mode-, MD-, and NMR-based conformation greatly expand the conformational sampling used herein for in silico identification of potential Mcl-1 inhibitors. Keywords: virtual screening, Mcl-1, molecular dynamics, NMR, normal modes
Park, Jun-Koo; Jernigan, Robert; Wu, Zhijun
2013-01-01
We investigate several approaches to coarse grained normal mode analysis on protein residual-level structural fluctuations by choosing different ways of representing the residues and the forces among them. Single-atom representations using the backbone atoms C(α), C, N, and C(β) are considered. Combinations of some of these atoms are also tested. The force constants between the representative atoms are extracted from the Hessian matrix of the energy function and served as the force constants between the corresponding residues. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The results are compared with all-atom normal mode analysis and the residue-level Gaussian Network Model. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, while their B-factor correlations are also higher. Their B-factor correlations are comparable with those estimated by the Gaussian Network Model and in many cases better. The extracted force constants are surveyed for different pairs of residues with different numbers of separation residues in sequence. The statistical averages are used to build a refined Gaussian Network Model, which is able to predict residue-level structural fluctuations significantly better than the conventional Gaussian Network Model in many test cases.
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.
Yuan, Lei; Wu, Han-Song
2010-12-01
A terminal sliding mode fuzzy control based on multiple sliding surfaces was proposed for ship course tracking steering, which takes account of rudder characteristics and parameter uncertainty. In order to solve the problem, the controller was designed by employing the universal approximation property of fuzzy logic system, the advantage of Nussbaum function, and using multiple sliding mode control algorithm based on the recursive technique. In the last step of designing, a nonsingular terminal sliding mode was utilized to drive the last state of the system to converge in a finite period of time, and high-order sliding mode control law was designed to eliminate the chattering and make the system robust. The simulation results showed that the controller designed here could track a desired course fast and accurately. It also exhibited strong robustness peculiarly to system, and had better adaptive ability than traditional PID control algorithms.
DEFF Research Database (Denmark)
Nielsen, J B; Sjöstrand, U H; Henneberg, S W
1991-01-01
-controlled intermittent positive-pressure ventilation; and SV-20P denotes pressure-controlled intermittent positive-pressure ventilation. With all modes of ventilation a PEEP of 7.5 cm H2O was used. In the abbreviations used, the number denotes the ventilatory frequency in breaths per minute (bpm). HFV indicates that all...
Drive Train Normal Modes Analysis for the ERDA/NASA 100-Kilowatt Wind Turbine Generator
Sullivan, T. L.; Miller, D. R.; Spera, D. A.
1977-01-01
Natural frequencies, as a function of power were determined using a finite element model. Operating conditions investigated were operation with a resistive electrical load and operation synchronized to an electrical utility grid. The influence of certain drive train components on frequencies and mode shapes is shown. An approximate method for obtaining drive train natural frequencies is presented.
On the structure and normal modes of hydrogenated Ti-fullerene compounds
Energy Technology Data Exchange (ETDEWEB)
Tlahuice-Flores, Alfredo, E-mail: tlahuicef@yahoo.com [Universidad Nacional Autonoma de Mexico, Instituto de Fisica (Mexico); Mejia-Rosales, Sergio, E-mail: sergio.mejiars@uanl.edu.mx [Universidad Autonoma de Nuevo Leon, CICFIM-Facultad de Ciencias Fisico Matematicas, and Centro de Innovacion, Investigacion y Desarrollo en Ingenieria y Tecnologia (Mexico); Galvan, Donald H., E-mail: donald@cnyn.unam.mx [Centro de Nanociencias y Nanotecnologia-Universidad Nacional Autonoma de Mexico (Mexico)
2012-08-15
When titanium covers a C{sub 60} core, the metal atoms may suppress the fullerene's capacity of storing hydrogen, depending on the number of Ti atoms covering the C{sub 60} framework, the Ti-C binding energy, and diffusion barriers. In this article, we study the structural and vibrational properties of the C{sub 60}TiH{sub n} (n = 2, 4, 6, and 8) and C{sub 60}Ti{sub 6}H{sub 48} compounds. The IR spectra of C{sub 60}TiH{sub n} compounds have a maximum attributable to the Ti-H stretching mode, which shifts to lower values in the structures with n = 4, 8, while their Raman spectra show two peaks corresponding to the stretching modes of H{sub 2} molecules at apical and azimuthal positions. On the other hand, the IR spectrum of C{sub 60}Ti{sub 6}H{sub 48} shows an intense peak due to the Ti-H in-phase stretching mode, while its Raman spectrum has a maximum attributed to the pentagonal pinch of the C{sub 60} core. Finally, we have found that the presence of one apical H{sub 2} molecule enhances the pentagonal pinch mode, becoming the maximum in the Raman spectrum.Graphical Abstract.
Normal Modes of a Lagrangian System Constrained in a Potential Well.
1983-12-01
minimax principle, Palais-Smale condition Work Unit Number I (Applied Analysis) *Dipartimento di Matematica , Universita di Bari, Bari, Italy...field of analytical mechanics itself. The development of the nonlinear functional analysis has renewed interest in these problems( 7’ iis paper we...exists Y N e C2(a,Q) such that (I) YNin solution of (1.2) ( ii ) Y~ has 21riod- N N (III) 3 N 2 N) C E*N2 where 2(y) _ . a(Y(t))It(t)j2 + U(Y(t)) is the
Time-domain study of acoustic pulse propagation in an ocean waveguide using a new normal mode model
Sidorovskaia, Natalia Anatol'evna
1997-11-01
This study is focused on issues of numerical modeling of sound propagation in diverse ocean waveguides. A new normal mode acoustical model (Shallow Water Acoustic Mode Propagation-SWAMP) has been developed. The algorithm for obtaining the vertical modal solution is based on a warping matrix transformation of the solution of an isovelocity (reference) waveguide to one of arbitrary velocity profile. An efficient mode coupling scheme with an adaptive step-size in range has been implemented for range-dependent environments. The new algorithm allows fairly arbitrary ocean layering and readily works at high frequency. An important advantage of the new procedure is that vertical modal eigenfunctions can easily be transformed to a spherical representation suitable for coupling in object scattering problems. Benchmarking results of the new code against established acoustic models based on parabolic equation and existing normal mode approaches show good agreement for range-independent and up-slope and down-slope bathymetries and a very competitive calculation speed. Broad-band pulse propagation in deep and shallow water with double (surface and bottom) ducts has been modeled using the new normal mode model for a variety of ocean waveguide parameters and different frequency bands. The surface duct generates a series of the surface-duct-trapped- modes, which form amplitude-modulated precursors in the far field pulse response. It has been found that the arrival times of the precursors could not be explained by the conventional concept of group velocity so that a more general principle based on the rate of energy transfer has been used. The Airy function solution was found to explain the amplitude modulation of the precursors. It has been learned from the numerical simulation that for a range-independent environment the time separation between precursors is fixed and any variations from this have been a result of range-dependence and mode coupling in the model. The time
Statistics of the single mode light in the transparent medium with cubic nonlinearity
Gorbachev, V N
1999-01-01
The quantum statistics of the light in the transparent medium with cubic nonlinearity is considered. Two types of transparent media are treated, namely, the cold transparent medium with a ground working level and the inversion-free medium with the lasing levels of the same population. The spectra of light fluctuation are found on the basis of both Scully-Lamb and Haken theories. The conditions for the use of effective Hamiltonian are determined. Basing on the exact solution of the Fokker-Planck equation for the Glauber-Sudarshan P-function the inversion-free medium with cubic nonlinearity is shown to be the source of spontaneous radiation with non-Gaussian statistics.
Nonlinear localized flat-band modes with spin-orbit coupling
Gligorić, G.; Maluckov, A.; Hadžievski, Lj.; Flach, Sergej; Malomed, Boris A.
2016-10-01
We report the coexistence and properties of stable compact localized states (CLSs) and discrete solitons (DSs) for nonlinear spinor waves on a flat-band network with spin-orbit coupling (SOC). The system can be implemented by means of a binary Bose-Einstein condensate loaded in the corresponding optical lattice. In the linear limit, the SOC opens a minigap between flat and dispersive bands in the system's band-gap structure, and preserves the existence of CLSs at the flat-band frequency, simultaneously lowering their symmetry. Adding on-site cubic nonlinearity, the CLSs persist and remain available in an exact analytical form, with frequencies that are smoothly tuned into the minigap. Inside of the minigap, the CLS and DS families are stable in narrow areas adjacent to the FB. Deep inside the semi-infinite gap, both the CLSs and DSs are stable too.
Explicit finite-difference time domain for nonlinear analysis of waveguide modes
Barakat, N. M.; Shabat, M. M.; El-Azab, S.; Jaeger, Dieter
2003-07-01
The Finite Difference Time Domain Technique is at present the most widely used tool employed in the study of light propagation in various photonic waveguide structure. In this paper we derived an explicit finite-difference time-domain (FDTD) method for solving the wave equation in a four optical waveguiding rectangular structure. We derive the stability condition to achieve the stability in nonlinear media region, we also check that the wave equation used is consistence and convergent with the approximate finite difference equation. Our method is tested against some previous problems and we find a high degree of accuracy, moreover it is easy for programming. Numerical results are illustrated for a rectangular waveguide with four layers, where one of these layers is a nonlinear medium.
Energy Technology Data Exchange (ETDEWEB)
Assadi, S.
1994-01-01
Linear and nonlinear magnetohydrodynamic (MHD) stability of current-driven modes are studied in the MST reversed field pinch. Measured low frequency (f < 35 kHz) magnetic fluctuations are consistent with the global resistive tearing instabilities predicted by 3-D MHD simulations. At frequencies above 35 kHz, the magnetic fluctuations were detected to be localized and externally resonant. Discrete dynamo events, ``sawtooth oscillations,`` have been observed in the experimental RFP plasmas. This phenomenon causes the plasma to become unstable to m = 1 tearing modes. The modes that may be important in different phases of these oscillations are identified. These results then assist in nonlinear studies and also help to interpret the spectral broadening of the measured data during a discrete dynamo event. Three-wave nonlinear coupling of spectral Fourier modes is measured in the MST by applying bispectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 poloidal and 32 toroidal modes. Comparison to bispectra predicted by resistive MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomitant with a broadened k-spectrum. During the sawtooth formation the plasma is undergoing a pure diffusive process. The dynamo only occurs during the sawtooth crash. High frequency activity prior to a sawtooth crash is caused by nonlinear frequency (small-scale) mode coupling. Growth rate and coupling coefficients of toroidal mode spectra are calculated by statistical modeling. Temporal evolution of edge toroidal mode spectra has been predicted by transfer function analysis. The driving sources of electrostatic fields are different than for the magnetic fields. The characteristics of tearing modes can be altered by external field errors and addition of impurities to the plasma.
Measurement and modeling of the nonlinearity of photovoltaic and Geiger-mode photodiodes
Kauten, Thomas; Kaufmann, Thomas; Weihs, Gregor
2013-01-01
While in most cases the absolute accuracy, resolution, and noise floor are the only relevant specifications for the dynamic range of a photodetector, there are experiments for which the linearity plays a more important role than the former three properties. In these experiments nonlinearity can lead to systematic errors. In our work we present a modern implementation of the well-known superposition method and apply it to two different types of photodetectors.
Institute of Scientific and Technical Information of China (English)
Bing Wang; Xiuqing Wu
2007-01-01
A single-mode laser system with colored cross-correlated additive and multiplicative noise terms is considered. By the means of projection operator method, we study the effects of the cross-correlation time τ and the cross-correlation intensity λ between noises on the normalized intensity correlation function C(s). It is found that if λ＞ 0 (λ＜ 0), the normalized intensity correlation function C(s) increases (decreases) with increasing the cross-correlation time τ, and at large value of τ, the variation of the normalized intensity correlation function C(s) becomes small. With the increase of the net gain a0, C(s) exhibits a maximum when λ is larger. However, a minimum and a maximum appear on C(s) curves with the increase of a0 when λ becomes smaller and smaller.
Charland, J.; Rey, V.; Touboul, J.
2012-04-01
Part of evanescent modes in the normally incident gravity surface wave's energy layout around a submerged obstacle Jenna Charland *1, Vincent Rey *2, Julien Touboul *2 *1 Mediterraneen Institute of Oceanography. Institut des Sciences de l'Ingénieur Toulon-Var. Avenue Georges Pompidou, BP 56, 83162 La Valette du Var Cedex, France. Centre National de la Recherche Scientifique, Délégation Normandie. Projet soutenu financièrement par la Délégation Générale de l'Armement. *2 Mediterraneen Institute of Oceanography. Institut des Sciences de l'Ingénieur Toulon-Var. Avenue Georges Pompidou, BP 56, 83162 La Valette du Var Cedex, France. During the last decades various studies have been performed to understand the wave propagation over varying bathymetries. Few answers related to this non linear problem were given by the Patarapanich's studies which described the reflection coefficient of a submerged plate as a function of the wavelength. Later Le-Thi-Minh [2] demonstrated the necessity of taking into account the evanescent modes to better describe the propagation of waves over a varying bathymetry. However, all these studies stare at pseudo-stationary state that allows neither the comprehension of the transient behaviour of propagative modes nor the role of the evanescent modes in this unstationnary process. Our study deals with the wave establishment over a submerged plate or step and focuses on the evanescent modes establishment. Rey [3] described the propagation of a normally incident surface gravity wave over a varying topography on the behaviour of the fluid using a linearized potential theory solved by a numerical model using an integral method. This model has a large field of application and has been adapted to our case. This code still solves a stationary problem but allows us to calculate the contribution of the evanescent modes in the energy layout around a submerged plate or a submerged step. The results will show the importance of the trapped energy
Indian Academy of Sciences (India)
P K Datta; Chandrajit Basu; S Mukhopadhyay; S K Das; G K Samanta; Antonio Agnesi
2004-11-01
A non-linear mirror consisting of a lithium triborate crystal and a dichroic output coupler are used to mode-lock (passively) an Nd : YVO4 laser, pumped by a diode laser array. The laser can operate both in cw mode-locked and simultaneously Q-switched and mode-locked (QML) regime. The peak power of the laser while operating in QML regime is much higher but pulses suffers from poor amplitude stability. The incorporation of an acousto-optic modulator as an active Q-switch enhances the stability of the QML pulse envelope. The second-order non-linearity of powdered crystalline urea is conclusively measured with respect to KDP while the laser is operating in passively Q-switched and passively mode-locked regime as well as in actively Q-switched and passively mode-locked regime.
Nonlinear Bethe-Heitler Pair Creation in an Intense Two-Mode Laser Field
Augustin, Sven
2013-01-01
We investigate electron-positron pair creation in the interaction of a nuclear Coulomb field and a highly intense two-mode laser field. For bichromatic laser fields, we examine the differences arising for commensurable and incommensurable frequencies in a continuous variation of the laser frequency ratio and the quantum interference effects, which may occur in the commensurable case. We show that the interference manifests in the angular distributions and the total pair-production rates of the created particles. Additionally, by varying the amplitudes of the two modes we study pair creation in a monochromatic laser wave of arbitrarily elliptical polarization.
A Simple Reduction Process for the Normal Vibrational Modes Occurring in Linear Molecules
McInerny, William
2005-01-01
The students in molecular spectroscopy courses are often required to determine the permitted normal vibrations for linear molecules that belong to particular groups. The reducible group representations generated by the use of Cartesian coordinates can be reduced by the use of a simple algebraic process applied to the group representations. The…
Davijani, Nafiseh Zare; Jahanfarnia, Gholamreza; Abharian, Amir Esmaeili
2017-01-01
One of the most important issues with respect to nuclear reactors is power control. In this study, we designed a fractional-order sliding mode controller based on a nonlinear fractional-order model of the reactor system in order to track the reference power trajectory and overcome uncertainties and external disturbances. Since not all of the variables in an operating reactor are measurable or specified in the control law, we propose a reduced-order fractional neutron point kinetic (ROFNPK) model based on measurable variables. In the design, we assume the differences between the approximated model and the real system is limited. We use the obtained model in the controller design process and use the Lyapunov method to perform a stability analysis of the closed-loop system. We simulate the proposed reduced-order fractional-order sliding mode controller (ROFOSMC) using Matlab/Simulink, and its performance is compared with that of a reduced order integer-order sliding mode controller (ROIOSMC). Our simulation results indicate an acceptable performance of the proposed approach in tracking the reference power trajectory with respect to ROIOSMC because of faster response of control effort signal and the smaller tracking error. Moreover, the results illustrate the capability of the controller in rejection of the disturbance and the noise signals and the robustness of controller against uncertainty.
Aleixo, A. N. F.; Balantekin, A. B.
2015-12-01
We resolve the normal ordering problem for symmetric ( D ˆ + D ˆ - ) n and asymmetric ( Dˆ + r D ˆ - ) n strings of the nonlinear deformed ladder operators D ˆ ± for supersymmetric and shape-invariant potential systems, where r and n are positive integers. We provide exact and explicit expressions for their normal forms N { ( D ˆ + D ˆ - ) n } and N { ( Dˆ + r D ˆ - ) n } , where in N { . . . } all D ˆ - are at the right side. We find that the solutions involve sequence of expansion coefficients which, for r, n > 1, corresponds to the f-deformed generalization of the classical Stirling and Bell numbers of the second kind. We apply the general formalism for the translational shape-invariant potential systems as well as for the particular case of the harmonic oscillator potential system. We show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials.
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.
Institute of Scientific and Technical Information of China (English)
CHEN Yu-Li; LIU Bin; YIN Ya-Jun; HUANG Yong-Gang; HWUANG Keh-Chih
2008-01-01
The tensile deformations and fractures of super carbon nanotubes (SCNTs) with armchair-armchair topology are investigated by using the atomic-scale finite element method. SCNTs generated from carbon nanotubes (CNTs) with different characteristic aspect ratios are found to have different nonlinear behaviours under uniaxiai tensions. Specifically, an SCNT with higher aspect ratio has three distinct stages: rotation, stretch and rupture, while an SCNT with lower aspect ratio has only two stages. This information may compensate for previous work and enrich our knowledge about Y-branched CNTs and SCNTs.
Quasi-normal mode expansion for linearized waves in gravitational systems
Ching, E S C; Suen, W M; Young, K; Ching, E S C; Leung, P T; Suen, W M; Young, K
1994-01-01
The quasinormal modes (QNM's) of gravitational systems modeled by the Klein-Gordon equation with effective potentials are studied in analogy to the QNM's of optical cavities. Conditions are given for the QNM's to form a complete set, i.e., for the Green's function to be expressible as a sum over QNM's, answering a conjecture by Price and Husain [Phys. Rev. Lett. {\\bf 68}, 1973 (1992)]. In the cases where the QNM sum is divergent, procedures for regularization are given. The crucial condition for completeness is the existence of spatial discontinuities in the system, e.g., the discontinuity at the stellar surface in the model of Price and Husain.
NORM2L: An Interactive Computer Program for Acoustic Normal Mode Calculations for the Pekeris Model.
1980-12-01
de Pekeris de i’oc~an. Le nxdibe de Pekeris est tin modale simple A deux couches dans lequel les deux couches reprdsentent l’eau de mer et leo fond de...and receiver are separated by horizontal distances less than several water depths. A standard reference for underwater acoustics is Tolstoy and Clay [5...Pedard, "Mode enhancement", Informal Communication, November 1978 5. I. Tolstoy and C.S. Clay, Ocean Acoustics, McGraw Hill, 1966 6. C.S. Clay and H
Ebrahimi, Farideh; Setarehdan, Seyed-Kamaledin; Ayala-Moyeda, Jose; Nazeran, Homer
2013-10-01
The conventional method for sleep staging is to analyze polysomnograms (PSGs) recorded in a sleep lab. The electroencephalogram (EEG) is one of the most important signals in PSGs but recording and analysis of this signal presents a number of technical challenges, especially at home. Instead, electrocardiograms (ECGs) are much easier to record and may offer an attractive alternative for home sleep monitoring. The heart rate variability (HRV) signal proves suitable for automatic sleep staging. Thirty PSGs from the Sleep Heart Health Study (SHHS) database were used. Three feature sets were extracted from 5- and 0.5-min HRV segments: time-domain features, nonlinear-dynamics features and time-frequency features. The latter was achieved by using empirical mode decomposition (EMD) and discrete wavelet transform (DWT) methods. Normalized energies in important frequency bands of HRV signals were computed using time-frequency methods. ANOVA and t-test were used for statistical evaluations. Automatic sleep staging was based on HRV signal features. The ANOVA followed by a post hoc Bonferroni was used for individual feature assessment. Most features were beneficial for sleep staging. A t-test was used to compare the means of extracted features in 5- and 0.5-min HRV segments. The results showed that the extracted features means were statistically similar for a small number of features. A separability measure showed that time-frequency features, especially EMD features, had larger separation than others. There was not a sizable difference in separability of linear features between 5- and 0.5-min HRV segments but separability of nonlinear features, especially EMD features, decreased in 0.5-min HRV segments. HRV signal features were classified by linear discriminant (LD) and quadratic discriminant (QD) methods. Classification results based on features from 5-min segments surpassed those obtained from 0.5-min segments. The best result was obtained from features using 5-min HRV
Kumar, Tarun; ManMohan,
2011-01-01
We propose a technique aimed at cooling a harmonically oscillating mirror mechanically coupled to another vibrating mirror to its quantum mechanical ground state. Our method involves optmechanical coupling between two optical cavities. We show that the cooling can be controlled by the mechanical coupling strength between the two movable mirrors, the phase difference between the mechanical modes of the two oscillating mirrors and the photon number in each cavity. We also show that both mechanical and optical cooling can be achieved by transferring energy from one cavity to the other. We also analyze the occurrence of normal-mode splitting (NMS). We find that a hybridization of the two oscillating mirrors with the fluctuations of the two driving optical fields occurs and leads to a splitting of the mechanical and optical fluctuation spectra.
Hornsby, William A; Buchholz, Rico; Grosshauser, Stefan; Weikl, Arne; Zarzoso, David; Casson, Francis J; Poli, Emanuele; Peeters, Artur G
2015-01-01
The non-linear evolution of a magnetic island is studied using the Vlasov gyro-kinetic code GKW. The interaction of electromagnetic turbulence with a self-consistently growing magnetic island, generated by a tearing unstable $\\Delta' > 0$ current profile, is considered. The turbulence is able to seed the magnetic island and bypass the linear growth phase by generating structures that are approximately an ion gyro-radius in width. The non-linear evolution of the island width and its rotation frequency, after this seeding phase, is found to be modified and is dependent on the value of the plasma beta and equilibrium pressure gradients. At low values of beta the island evolves largely independent of the turbulence, while at higher values the interaction has a dramatic effect on island growth, causing the island to grow exponentially at the growth rate of its linear phase, even though the island is larger than linear theory validity. The turbulence forces the island to rotate in the ion-diamagnetic direction as o...
Kikuchi, H; Wako, H; Yura, K; Go, M; Mimuro, M
2000-09-01
Phycobiliproteins are basic building blocks of phycobilisomes, a supra-molecular assembly for the light-capturing function of photosynthesis in cyanobacteria and red algae. One functional form of phycobiliproteins is a trimeric form consisting of three identical units having C(3) symmetry, with each unit composed of two kinds of subunits, the alpha-subunit and beta-subunit. These subunits have similar chain folds and can be divided into either globin-like or X-Y helices domains. We studied the significance of this two-domain structure for their assembled structures and biological function (light-absorption) using a normal mode analysis to investigate dynamic aspects of their three-dimensional structures. We used C-phycocyanin (C-PC) as an example, and focused on the interactions between the two domains. The normal mode analysis was carried out for the following two cases: 1) the whole subunit, including the two domains; and 2) the globin-like domain alone. By comparing the dynamic properties, such as correlative movements between residues and the fluctuations of individual residues, we found that the X-Y helices domain plays an important role not only in the C(3) symmetry assemblies of the subunits in phycobiliproteins, but also in stabilizing the light absorption property by suppressing the fluctuation of the specific Asp residues near the chromophore. Interestingly, the conformation of the X-Y helices domain corresponds to that of a module in pyruvate phosphate dikinase (PPDK). The module in PPDK is involved in the interactions of two domains, just as the X-Y helices domain is involved in the interactions of two subunits. Finally, we discuss the mechanical construction of the C-PC subunits based on the normal mode analysis.
Mori, Shigeo; Katayama, Naomi
2005-02-01
We investigated visual-vestibular interactions in normal humans, where a constant speed of optokinetic stimulation was combined with whole body oscillation of lateral linear acceleration (10 m stroke). The acceleration mode was not sinusoidal, but rectangular (step). The pure optokinetic reflex (reference OKR) and the OKR under combined stimulation (combined OKR) were induced by a random-dot pattern projected onto a hemispherical dome-screen affixed to a chair on a linear accelerator. The translational vestibulo-ocular reflex (tVOR) was determined separately in the dark during acceleration-step oscillation. Since the tVOR was masked by the OKR under combined stimulation, the interaction was assessed as changes in combined-OKR velocity at two segments of opposing acceleration; in other words, tVOR directions identical to (agonistic) and opposite to (antagonistic) the OKR direction. When a moderate optokinetic stimulus-speed of 40 deg/s was combined with a moderate acceleration of 0.3 G (3.0 m/s2) as in Experiment 1 (N=10), the combined-OKR velocity always increased during the agonistic condition, and the motion of the visual pattern was perceived as slow and clear in this segment. On the other hand, during the antagonistic condition, the combined-OKR velocity either remained unchanged or increased moderately, and the motion of the visual pattern was sensed as fast and unclear. Notably, in most subjects, the velocity difference in combined-OKR between the agonistic and antagonistic conditions was around the value of the tVOR velocity. In five of the ten subjects who completed an additional test session with the acceleration level increased from 0.3 to 0.5 G (4.9 m/s2), similar findings were maintained individually, suggesting independent behavior of tVOR. Therefore, we hypothesized that the interaction could be direction-selective; in other words, both tVOR and OKR are additive during the agonistic condition, but tVOR is suppressed during the antagonistic condition
Finite-time control for nonlinear spacecraft attitude based on terminal sliding mode technique.
Song, Zhankui; Li, Hongxing; Sun, Kaibiao
2014-01-01
In this paper, a fast terminal sliding mode control (FTSMC) scheme with double closed loops is proposed for the spacecraft attitude control. The FTSMC laws are included both in an inner control loop and an outer control loop. Firstly, a fast terminal sliding surface (FTSS) is constructed, which can drive the inner loop tracking-error and the outer loop tracking-error on the FTSS to converge to zero in finite time. Secondly, FTSMC strategy is designed by using Lyaponov's method for ensuring the occurrence of the sliding motion in finite time, which can hold the character of fast transient response and improve the tracking accuracy. It is proved that FTSMC can guarantee the convergence of tracking-error in both approaching and sliding mode surface. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.
Contribution of hidden modes to nonlinear epidemic dynamics in urban human proximity networks
Fujiwara, Naoya; Iwayama, Koji; Aihara, Kazuyuki
2015-01-01
Recently developed techniques to acquire high-quality human mobility data allow large-scale simulations of the spread of infectious diseases with high spatial and temporal resolution.Analysis of such data has revealed the oversimplification of existing theoretical frameworks to infer the final epidemic size or influential nodes from the network topology. Here we propose a spectral decomposition-based framework for the quantitative analysis of epidemic processes on realistic networks of human proximity derived from urban mobility data. Common wisdom suggests that modes with larger eigenvalues contribute more to the epidemic dynamics. However, we show that hidden dominant structures, namely modes with smaller eigenvalues but a greater contribution to the epidemic dynamics, exist in the proximity network. This framework provides a basic understanding of the relationship between urban human motion and epidemic dynamics, and will contribute to strategic mitigation policy decisions.
Han, Yaozhen; Liu, Xiangjie
2016-05-01
This paper presents a continuous higher-order sliding mode (HOSM) control scheme with time-varying gain for a class of uncertain nonlinear systems. The proposed controller is derived from the concept of geometric homogeneity and super-twisting algorithm, and includes two parts, the first part of which achieves smooth finite time stabilization of pure integrator chains. The second part conquers the twice differentiable uncertainty and realizes system robustness by employing super-twisting algorithm. Particularly, time-varying switching control gain is constructed to reduce the switching control action magnitude to the minimum possible value while keeping the property of finite time convergence. Examples concerning the perturbed triple integrator chains and excitation control for single-machine infinite bus power system are simulated respectively to demonstrate the effectiveness and applicability of the proposed approach.
Khegai, A. M.; Afanas'ev, F. V.; Riumkin, K. E.; Firstov, S. V.; Khopin, V. F.; Myasnikov, D. V.; Mel'kumov, M. A.; Dianov, E. M.
2016-12-01
The influence of the concentration of bismuth active centres (BACs) in phosphosilicate fibres on their optical parameters, including gain coefficient and non-saturable losses, has been studied. A range of BAC concentrations optimal for designing ultrashort-pulse (USP) lasers was chosen based on the obtained results. The optimised fibre was used to fabricate an all-fibre 1.3-\\unicode{956}{\\text{m}} USP laser mode-locked by a nonlinear loop mirror, which emits 11.3-{\\text{ps}} pulses with an energy of 1.65 {\\text{nJ}} and a repetition rate of 3.6 {\\text{MHz}}. A bismuth fibre amplifier made it possible to increase the pulse energy to 8.3 {\\text{nJ}}. After compression in a diffraction grating compressor, the pulse duration decreased to 530 {\\text{fs}}.
Schäfer, Christoph; Fries, Christian; Theobald, Christian; L'huillier, Johannes A
2013-01-15
Continuous-wave mode-locking of a laser exploiting the nonlinear polarization rotation (NPR) technique via Type I second harmonic generation is demonstrated for the first time. The NPR is generated by a lithium triborate crystal and transformed into nonlinear cavity losses of a 888 nm pumped Nd:YVO4 laser. Self-starting, reliable mode-locking has been achieved at a high average output power of 20.6 W and a pulse duration of 7.3 ps. Furthermore, transform limited pulses down to 2.7 ps have been demonstrated at 9.9 W.
Multiple Dissipative Solitons in a Long-Cavity Normal-Dispersion Mode-Locked Yb-Doped Fiber Laser
Institute of Scientific and Technical Information of China (English)
ZHAO Guang-Zhen; XIAO Xiao-Sheng; MEI Jia-Wei; YANG Chang-Xi
2012-01-01
Transitional operations of multiple dissipative solitons in a long-cavity normal-dispersion Yb-doped fiber laser are experimentally investigated.Multiple dissipative solitons,including a stable soliton pair and a soliton triplet are observed by increasing the pump power or adjusting the polarization controllers.Two main boundaries of the stable asymmetric soliton and oscillating soliton are found between steady mode-locking.Moreover,multiple dissipative solitons with greater quantities of solitons are observed with pump power increasing.The experimental results agree well with a previous numerical study of multiple dissipative solitons.
Bessaa, Assia; Djebli, Mourad
2017-02-01
We present a numerical analysis of several phase transitions which take place in the eigenmode spectrum of a two-dimensional (2D) logarithmic cluster subjected to an anisotropic power law confinement. Varying the anisotropy in a non-parabolic soft confinement drives the system to undergo structural phase transitions of first order, while for a hard wall confinement this variation affects strongly the eigenmode spectrum and breaks the symmetry of the system due to the removal of degeneracy and the coupling between some normal modes.
Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control
Energy Technology Data Exchange (ETDEWEB)
Behzad, Mehdi [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Postal Code 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: m_behzad@sharif.edu; Salarieh, Hassan [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Postal Code 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: salarieh@mech.sharif.edu; Alasty, Aria [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Postal Code 11365-9567, Azadi Avenue, Tehran (Iran, Islamic Republic of)], E-mail: aalasti@sharif.edu
2008-06-15
This paper presents an algorithm for synchronizing two different chaotic systems, using a combination of the extended Kalman filter and the sliding mode controller. It is assumed that the drive chaotic system has a random excitation with a stochastically chaotic behavior. Two different cases are considered in this study. At first it is assumed that all state variables of the drive system are available, i.e. complete state measurement, and a sliding mode controller is designed for synchronization. For the second case, it is assumed that the output of the drive system does not contain the whole state variables of the drive system, and it is also affected by some random noise. By combination of extended Kalman filter and the sliding mode control, a synchronizing control law is proposed. As a case study, the presented algorithm is applied to the Lur'e-Genesio chaotic systems as the drive-response dynamic systems. Simulation results show the good performance of the algorithm in synchronizing the chaotic systems in presence of noisy environment.
A Finite Element Method for Computation of Structural Intensity by the Normal Mode Approach
Gavrić, L.; Pavić, G.
1993-06-01
A method for numerical computation of structural intensity in thin-walled structures is presented. The method is based on structural finite elements (beam, plate and shell type) enabling computation of real eigenvalues and eigenvectors of the undamped structure which then serve in evaluation of complex response. The distributed structural damping is taken into account by using the modal damping concept, while any localized damping is treated as an external loading, determined by use of impedance matching conditions and eigenproperties of the structure. Emphasis is given to aspects of accuracy of the results and efficiency of the numerical procedures used. High requirements on accuracy of the structural response (displacements and stresses) needed in intensity applications are satisfied by employing the "swept static solution", which effectively takes into account the influence of higher modes otherwise inaccessible to numerical computation. A comparison is made between the results obtained by using analytical methods and the proposed numerical procedure to demonstrate the validity of the method presented.
Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner
2017-07-01
A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.
Makovetskii, D N
2011-01-01
This is a part of an overview of my early studies on nonlinear spin-phonon dynamics in solid state optical-wavelength phonon lasers (phasers) started in 1984. The main goal of this work is a short description and a qualitative analysis of experimental data on low-frequency nonlinear resonances revealed in a nonautonomous ruby phaser. Under phaser pumping modulation near these resonances, an unusual kind of self-organized motions in the ruby spin-phonon system was observed by me in 1984 for the first time. The original technique of optical-wavelength microwave-frequency acoustic stimulated emission (SE) detection and microwave-frequency power spectra (MFPS) analysis was used in these experiments (description of the technique see: D.N.Makovetskii, Cand. Sci. Diss., Kharkov, 1983). The real time evolution of MFPS was studied using this technique at scales up to several hours. The phenomenon of the self-organized periodic alternation of SE phonon modes was experimentally revealed at hyperlow frequencies from abou...
DEFF Research Database (Denmark)
Hansen, Michael Sass; Olafsdóttir, Hildur; Darvann, Tron Andre;
2007-01-01
of wild-type (normal) mice and Crouzon mice were investigated. We present for what we believe is the first time, a statistical deformation model based on independent component analysis (ICA). A set of deformation parameters for each mouse was calculated using a B-spline-based nonrigid registration. From...
Influences of Modulated Noise on Normalized Intensity Fluctuation in a Single-Mode Laser
Institute of Scientific and Technical Information of China (English)
WANG Jun; CAO Li; WU Da-Jin
2004-01-01
@@ The influences of the two forms of modulated noises, i.e. the bias signal-modulated noise and the direct signalmodulated noise, on the normalized intensity fluctuation (NIF) are investigated, and the results of the two forms of modulation are compared in detail. We find that a minimum for the case of the bias signal modulation appears in the curve of the dependence of the NIF upon the quantum and pump noise intensities when the correlation coefficient between the quantum noise and the pump noise is negative. However, the NIF for the case of the direct signal modulation is independent of the correlation coefficient between the two noises. Moreover, at the same parameter region, the NIF for the bias signal modulation is only one-eighth as much as that for the direct signal modulation.
Institute of Scientific and Technical Information of China (English)
MA Qingyu; GONG Xiufen; ZHANG Dong; MA Yong
2006-01-01
In this paper, a phase-coded pulse technique is proposed to improve the signal-to-noise ratio (SNR) in the 3rd harmonic imaging in transmission mode, where three pulses with initial phases of 0°, 120° and 240° are transmitted and their corresponding received signals are linearly summed. By means of simulations and measurements, we show that the 3rd harmonic is enhanced by 9.5 dB, whereas the fundamental or the 2nd harmonic components are suppressed; the axial and lateral beam profiles of the processed 3rd harmonics are superior to those of the fundamental or 2nd harmonic components. In addition, this technique is applied to obtain the 3rd harmonic images for two normal and pathological biological tissues in transmission mode. This technique yields a dramatically cleaner and sharper contrast than the images obtained by the traditional fundamental imaging and the 2nd harmonic imaging, which helps distinguish the normal and pathological states of tissues.
Directory of Open Access Journals (Sweden)
Guo Haigang
2012-01-01
Full Text Available Combining adaptive fuzzy sliding mode control with fuzzy or variable universe fuzzy switching technique, this study develops two novel direct adaptive schemes for a class of MIMO nonlinear systems with uncertainties and external disturbances. The proposed control schemes consist of fuzzy equivalent control terms, fuzzy switching control terms (in scheme one or variable universe fuzzy switching control terms (in scheme two, and compensation control terms. The compensation control terms are used to relax the assumption on fuzzy approximation error. Based on Lyapunov stability theory, the parameters update laws are adaptively tuned online and the global asymptotic stability of the closed-loop system can be guaranteed. The major contribution of this study is to develop a novel framework for designing direct adaptive fuzzy sliding mode control scheme facing model uncertainties and external disturbances. The derived schemes can effectively solve the chattering problem and the equivalent control calculation in that environment. Simulation results performed on a two-link robotic manipulator demonstrate the feasibility of the proposed control schemes.
Directory of Open Access Journals (Sweden)
Zhenxin He
2014-01-01
Full Text Available A continuous nonsingular fast terminal sliding mode (NFTSM control scheme with the extended state observer (ESO and the tracking differentiator (TD is proposed for second-order uncertain SISO nonlinear systems. The system’s disturbances and states can be estimated by introducing the ESO, then the disturbances are compensated effectively, and the ideal transient process of the system can be arranged based on TD to provide the target tracking signal and its high-order derivatives. The proposed controller obtains finite-time convergence property and keeps good robustness of sliding mode control (SMC for disturbances. Moreover, compared with conventional SMC, the proposed control law is continuous and no chattering phenomenon exists. The property of system stability is guaranteed by Lyapunov stability theory. The simulation results show that the proposed method can be employed to shorten the system reaching time, improve the system tracking precision, and suppress the system chattering and the input noise. The proposed control method is finally applied for the rotating control problem of theodolite servo system.