Sample records for nonlinear normal modes

  1. Evaluation of Geometrically Nonlinear Reduced Order Models with Nonlinear Normal Modes

    DOE PAGES

    Kuether, Robert J.; Deaner, Brandon J.; Hollkamp, Joseph J.; ...

    2015-09-15

    Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. But, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. Our paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinearmore » normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Moreover, various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped–clamped beam model, and a more complicated finite element model of an exhaust panel cover.« less

  2. Nonlinear normal modes in electrodynamic systems: A nonperturbative approach

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kudrin, A. V., E-mail: kud@rf.unn.ru; Kudrina, O. A.; Petrov, E. Yu.

    2016-06-15

    We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known tomore » hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.« less

  3. Nonlinear normal modes modal interactions and isolated resonance curves

    DOE PAGES

    Kuether, Robert J.; Renson, L.; Detroux, T.; ...

    2015-05-21

    The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balance technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. Furthermore, the practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweepmore » excitations of increasing amplitudes.« less

  4. Relationships between nonlinear normal modes and response to random inputs

    NASA Astrophysics Data System (ADS)

    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.

  5. Stability of strongly nonlinear normal modes

    NASA Astrophysics Data System (ADS)

    Recktenwald, Geoffrey; Rand, Richard

    2007-10-01

    It is shown that a transformation of time can allow the periodic solution of a strongly nonlinear oscillator to be written as a simple cosine function. This enables the stability of strongly nonlinear normal modes in multidegree of freedom systems to be investigated by standard procedures such as harmonic balance.

  6. Relationships between nonlinear normal modes and response to random inputs

    DOE PAGES

    Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

    2016-07-25

    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). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing.more » 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.« less

  7. Computational aspects of the nonlinear normal mode initialization of the GLAS 4th order GCM

    NASA Technical Reports Server (NTRS)

    Navon, I. M.; Bloom, S. C.; Takacs, L.

    1984-01-01

    Using the normal modes of the GLAS 4th Order Model, a Machenhauer nonlinear normal mode initialization (NLNMI) was carried out for the external vertical mode using the GLAS 4th Order shallow water equations model for an equivalent depth corresponding to that associated with the external vertical mode. A simple procedure was devised which was directed at identifying computational modes by following the rate of increase of BAL sub M, the partial (with respect to the zonal wavenumber m) sum of squares of the time change of the normal mode coefficients (for fixed vertical mode index) varying over the latitude index L of symmetric or antisymmetric gravity waves. A working algorithm is presented which speeds up the convergence of the iterative Machenhauer NLNMI. A 24 h integration using the NLNMI state was carried out using both Matsuno and leap-frog time-integration schemes; these runs were then compared to a 24 h integration starting from a non-initialized state. The maximal impact of the nonlinear normal mode initialization was found to occur 6-10 hours after the initial time.

  8. Computational modes and the Machenauer N.L.N.M.I. of the GLAS 4th order model. [NonLinear Normal Mode Initialization in numerical weather forecasting

    NASA Technical Reports Server (NTRS)

    Navon, I. M.; Bloom, S.; Takacs, L. L.

    1985-01-01

    An attempt was made to use the GLAS global 4th order shallow water equations to perform a Machenhauer nonlinear normal mode initialization (NLNMI) for the external vertical mode. A new algorithm was defined for identifying and filtering out computational modes which affect the convergence of the Machenhauer iterative procedure. The computational modes and zonal waves were linearly initialized and gravitational modes were nonlinearly initialized. The Machenhauer NLNMI was insensitive to the absence of high zonal wave numbers. The effects of the Machenhauer scheme were evaluated by performing 24 hr integrations with nondissipative and dissipative explicit time integration models. The NLNMI was found to be inferior to the Rasch (1984) pseudo-secant technique for obtaining convergence when the time scales of nonlinear forcing were much smaller than the time scales expected from the natural frequency of the mode.

  9. Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

    PubMed

    Basko, D M

    2014-02-01

    We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

  10. Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

    NASA Astrophysics Data System (ADS)

    Denis, V.; Jossic, M.; Giraud-Audine, C.; Chomette, B.; Renault, A.; Thomas, O.

    2018-06-01

    In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

  11. Ideal and resistive plasma resistive wall modes and control: linear and nonlinear

    NASA Astrophysics Data System (ADS)

    Finn, J. M.; Chacon, L.

    2004-11-01

    Our recent work* on control of linear and nonlinear resistive wall modes (RWM) showed that if there is an ideal plasma mode and a resistive plasma mode, and if the beta limit for the latter is lower (as is typical), then nonlinear resistive wall modes behave basically as nonlinear tearing-like modes locked to the wall. We investigate here the effect of plasma rotation sufficient to stabilize the resistive-plasma RWM but not the ideal plasma RWM. We also review results** showing the effect of normal and poloidal magnetic field sensing, and describe a simple model which is amenable to analytic solution, and which makes previously obtained simulation results transparent. *J. Finn and L. Chacon, 'Control of linear and nonlinear resistive wall modes', Phys. Plas 11, 1866 (2004). **J. Finn, 'Control of resistive wall modes in a cylindrical tokamak with radial and poloidal magnetic field sensors', to appear in Phys. Plasmas, 2004.

  12. Large-amplitude nonlinear normal modes of the discrete sine lattices.

    PubMed

    Smirnov, Valeri V; Manevitch, Leonid I

    2017-02-01

    We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically coupled pendulums without any restrictions on their amplitudes (excluding a vicinity of π). Although this model has numerous applications in different fields of physics, it was studied earlier in the infinite limit only. The discrete chain with a finite length can be considered as a well analytical analog of the coarse-grain models of flexible polymers in the molecular dynamics simulations. The developed approach allows to find the dispersion relations for arbitrary amplitudes of the nonlinear normal modes. We emphasize that the long-wavelength approximation, which is described by well-known sine-Gordon equation, leads to an inadequate zone structure for the amplitudes of about π/2 even if the chain is long enough. An extremely complex zone structure at the large amplitudes corresponds to multiple resonances between nonlinear normal modes even with strongly different wave numbers. Due to the complexity of the dispersion relations the modes with shorter wavelengths may have smaller frequencies. The stability of the nonlinear normal modes under condition of the resonant interaction are discussed. It is shown that this interaction of the modes in the vicinity of the long wavelength edge of the spectrum leads to the localization of the oscillations. The thresholds of instability and localization are determined explicitly. The numerical simulation of the dynamics of a finite-length chain is in a good agreement with obtained analytical predictions.

  13. Scaling and interaction of self-similar modes in models of high Reynolds number wall turbulence.

    PubMed

    Sharma, A S; Moarref, R; McKeon, B J

    2017-03-13

    Previous work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the self-similarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence, modelling and simulation are outlined.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

  14. Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

    PubMed

    Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

    2012-03-01

    We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

  15. Vibrational dynamics of vocal folds using nonlinear normal modes.

    PubMed

    Pinheiro, Alan P; Kerschen, Gaëtan

    2013-08-01

    Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

  16. Mean flow generation mechanism by inertial waves and normal modes

    NASA Astrophysics Data System (ADS)

    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, respectively. The former is used to find the analytical solution of the normal modes (Borcia 2012). Plugging two independent solutions into the latter we investigate the generation mechanism of INMMF. We found R1^1=overbar{partial_z(u_r1 u_z^1)}, R2^1=overbar{partial_r(u_r1 u_r^1)} as source terms responsible for the generation of INMMF. The helical structure of the inertial waves causes the nonlinear terms R1 and R2 to be nonzero, contributing to the generation of INMMF. We used u_ra and u_za obtained from the analytical solution (Borcia 2012) and computed the source terms R1a and R2a and found a structural correspondence with the corresponding field computed from the DNS solution for the three normal modes investigated. The sum of R11 and R21 exhibits a good structural correspondence with INMMF. Interestingly, INMMF magnitude depends on the inertial wave beams and normal modes. For instance we found that INMMF is generated more efficiently for the libration frequency ω=1.58, although the resonant frequency is predicted by the analytical solution to be at ω=1.576 (normal mode (2,1)). Separating the inertial wave beams from the flow field obtained by DNS, using the analytical normal mode solution, we explored the phase lag between inertial wave beams and normal mode. We inferred that the normal mode amplitude is high only if the phase lag between the inertial wave beam and the normal mode is predominantly positive. In this case a high amplitude INMMF amplitude can be found. This supports the hypothesis that the normal modes are generated by the inertial wave beam in analogy to resonant forcing in classical mechanics. Interestingly, the 'optimum' phase lag found is much smaller than π/2. {Acknowledgement:} This work is a part of the project "Mischung und Grundstromanregung durch propagierende Trgheitswellen: Theorie, Experiment und Simulation" supported by the German Science Foundation (DFG). We would like to thank M. Klein, U. Harlander, I. Borcia and E. Schaller for helpful discussions and invaluable contributions. {References:} Borcia, I. D. & Harlander, U. 2012 Inertial waves in a rotating annulus with inclined inner cylinder: comparing the spectrum of wave attractor frequency bands and the eigenspectrum in the limit of zero inclination. Theor. Comput. Fluid Dyn. 27, 397-413.

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

    NASA Astrophysics Data System (ADS)

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

    2018-05-01

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

  18. Identification of nonlinear normal modes of engineering structures under broadband forcing

    NASA Astrophysics Data System (ADS)

    Noël, Jean-Philippe; Renson, L.; Grappasonni, C.; Kerschen, G.

    2016-06-01

    The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end.

  19. Nonlinear Reduced-Order Simulation Using An Experimentally Guided Modal Basis

    NASA Technical Reports Server (NTRS)

    Rizzi, Stephen A.; Przekop, Adam

    2012-01-01

    A procedure is developed for using nonlinear experimental response data to guide the modal basis selection in a nonlinear reduced-order simulation. The procedure entails using nonlinear acceleration response data to first identify proper orthogonal modes. Special consideration is given to cases in which some of the desired response data is unavailable. Bases consisting of linear normal modes are then selected to best represent the experimentally determined transverse proper orthogonal modes and either experimentally determined inplane proper orthogonal modes or the special case of numerically computed in-plane companions. The bases are subsequently used in nonlinear modal reduction and dynamic response simulations. The experimental data used in this work is simulated to allow some practical considerations, such as the availability of in-plane response data and non-idealized test conditions, to be explored. Comparisons of the nonlinear reduced-order simulations are made with the surrogate experimental data to demonstrate the effectiveness of the approach.

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

    NASA Astrophysics Data System (ADS)

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

    2012-08-01

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

  1. Three key regimes of single pulse generation per round trip of all-normal-dispersion fiber lasers mode-locked with nonlinear polarization rotation.

    PubMed

    Smirnov, Sergey; Kobtsev, Sergey; Kukarin, Sergey; Ivanenko, Aleksey

    2012-11-19

    We show experimentally and numerically new transient lasing regime between stable single-pulse generation and noise-like generation. We characterize qualitatively all three regimes of single pulse generation per round-trip of all-normal-dispersion fiber lasers mode-locked due to effect of nonlinear polarization evolution. We study spectral and temporal features of pulses produced in all three regimes as well as compressibility of such pulses. Simple criteria are proposed to identify lasing regime in experiment.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhang, Z.; Nanjing University of Posts and Communications, Nanjing 210003; Popa, D., E-mail: dp387@cam.ac.uk

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

  3. Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation

    NASA Astrophysics Data System (ADS)

    Peter, Simon; Leine, Remco I.

    2017-11-01

    Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.

  4. Angular motion equations for a satellite with hinged flexible solar panel

    NASA Astrophysics Data System (ADS)

    Ovchinnikov, M. Yu.; Tkachev, S. S.; Roldugin, D. S.; Nuralieva, A. B.; Mashtakov, Y. V.

    2016-11-01

    Non-linear mathematical model for the satellite with hinged flexible solar panel is presented. Normal modes of flexible elements are used for motion description. Motion equations are derived using virtual work principle. A comparison of normal modes calculation between finite element method and developed model is presented.

  5. The dance of molecules: new dynamical perspectives on highly excited molecular vibrations.

    PubMed

    Kellman, Michael E; Tyng, Vivian

    2007-04-01

    At low energies, molecular vibrational motion is described by the normal modes model. This model breaks down at higher energy, with strong coupling between normal modes and onset of chaotic dynamics. New anharmonic modes are born in bifurcations, or branchings of the normal modes. Knowledge of these new modes is obtained through the window of frequency-domain spectroscopy, using techniques of nonlinear classical dynamics. It may soon be possible to "watch" molecular rearrangement reactions spectroscopically. Connections are being made with reaction rate theories, condensed phase systems, and motions of electrons in quantum dots.

  6. Secular instabilities of Keplerian stellar discs

    NASA Astrophysics Data System (ADS)

    Kaur, Karamveer; Kazandjian, Mher V.; Sridhar, S.; Touma, Jihad R.

    2018-05-01

    We present idealized models of a razor-thin, axisymmetric, Keplerian stellar disc around a massive black hole, and study non-axisymmetric secular instabilities in the absence of either counter-rotation or loss cones. These discs are prograde mono-energetic waterbags, whose phase-space distribution functions are constant for orbits within a range of eccentricities (e) and zero outside this range. The linear normal modes of waterbags are composed of sinusoidal disturbances of the edges of distribution function in phase space. Waterbags that include circular orbits (polarcaps) have one stable linear normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the m = 1 mode has positive pattern speed. Waterbags excluding circular orbits (bands) have two linear normal modes for each m, which can be stable or unstable. We derive analytical expressions for the instability condition, pattern speeds, growth rates, and normal mode structure. Narrow bands are unstable to modes with a wide range in m. Numerical simulations confirm linear theory and follow the non-linear evolution of instabilities. Long-time integration suggests that instabilities of different m grow, interact non-linearly, and relax collisionlessly to a coarse-grained equilibrium with a wide range of eccentricities.

  7. Macroscopic response in active nonlinear photonic crystals.

    PubMed

    Alagappan, Gandhi; John, Sajeev; Li, Er Ping

    2013-09-15

    We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.

  8. Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

    NASA Technical Reports Server (NTRS)

    Subrahmanyam, K. B.; Kaza, K. R. V.

    1985-01-01

    The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

  9. Analysis of the nonlinearity of Asian summer monsoon intraseasonal variability using spherical PDFs

    NASA Astrophysics Data System (ADS)

    Jajcay, Nikola; Hannachi, Abdel

    2013-04-01

    The Asian summer monsoon (ASM) is a high-dimensional and highly complex phenomenon affecting more than one fifth of the world population. The intraseasonal component of the ASM undergoes periods of active and break phases associated respectively with enhanced and reduced rainfall over the Indian subcontinent and surroundings. In this paper the nonlinear nature of the intraseasonal monsoon variability is investigated using the leading EOFs of ERA-40 sea level pressure reanalyses field over the ASM region. The probability density function is then computed in spherical coordinates using a Epaneshnikov kernel method. Three significant modes are identified. They represent respectively (i) East - West mode with above normal sea level pressure over East China sea and below normal pressure over Himalayas, (ii) mode with above normal sea level pressure over East China sea (without compensating centre of opposite sign as in (i)) and (iii) mode with below normal sea level pressure over East China sea (same as (ii) but with opposite sign). Relationship to large scale flow are also investigated and discussed.

  10. Mode localization in a class of multidegree-of-freedom nonlinear systems with cyclic symmetry

    NASA Astrophysics Data System (ADS)

    Vakakis, Alexander F.; Cetinkaya, Cetin

    1993-02-01

    The free oscillations of n-degree-of-freedom (DOF) nonlinear systems with cyclic symmetry and weak coupling between substructures are examined. An asymptotic methodology is used to detect localized nonsimilar normal modes, i.e., free periodic motions spatially confined to only a limited number of substructures of the cyclic system. It is shown that nonlinear mode localization occurs in the perfectly symmetric, weakly coupled structure, in contrast to linear mode localization, which exists only in the presence of substructure 'mistuning'. In addition to the localized modes, nonlocalized modes are also found in the weakly coupled system. The stability of the identified modes is investigated by means of an approximate two-timing averaging mothodology, and the general theory is applied to the case of a cyclic system with three-DOF. The theoretical results are then verified by direct numerical integrations of the equations of motion.

  11. Oscillatory Dynamics of One-Dimensional Homogeneous Granular Chains

    NASA Astrophysics Data System (ADS)

    Starosvetsky, Yuli; Jayaprakash, K. R.; Hasan, Md. Arif; Vakakis, Alexander F.

    The acoustics of the homogeneous granular chains has been studied extensively both numerically and experimentally in the references cited in the previous chapters. This chapter focuses on the oscillatory behavior of finite dimensional homogeneous granular chains. It is well known that normal vibration modes are the building blocks of the vibrations of linear systems due to the applicability of the principle of superposition. One the other hand, nonlinear theory is deprived of such a general superposition principle (although special cases of nonlinear superpositions do exist), but nonlinear normal modes ‒ NNMs still play an important role in the forced and resonance dynamics of these systems. In their basic definition [1], NNMs were defined as time-periodic nonlinear oscillations of discrete or continuous dynamical systems where all coordinates (degrees-of-freedom) oscillate in-unison with the same frequency; further extensions of this definition have been considered to account for NNMs of systems with internal resonances [2]...

  12. The use of normal forms for analysing nonlinear mechanical vibrations

    PubMed Central

    Neild, Simon A.; Champneys, Alan R.; Wagg, David J.; Hill, Thomas L.; Cammarano, Andrea

    2015-01-01

    A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations. PMID:26303917

  13. Experimental observation of different soliton types in a net-normal group-dispersion fiber laser.

    PubMed

    Feng, Zhongyao; Rong, Qiangzhou; Qiao, Xueguang; Shao, Zhihua; Su, Dan

    2014-09-20

    Different soliton types are observed in a net-normal group-dispersion fiber laser based on nonlinear polarization rotation for passive mode locking. The proposed laser can deliver a dispersion-managed soliton, typical dissipation solitons, and a quasi-harmonic mode-locked pulse, a soliton bundle, and especially a dark pulse by only appropriately adjusting the linear cavity phase delay bias using one polarization controller at the fixed pump power. These nonlinear waves show different features, including the spectral shapes and time traces. The experimental observations show that the five soliton types could exist in the same laser cavity, which implies that integrable systems, dissipative systems, and dark pulse regimes can transfer and be switched in a passively mode-locked laser. Our studies not only verify the numeral simulation of the different soliton-types formation in a net-normal group-dispersion operation but also provide insight into Ginzburg-Landau equation systems.

  14. Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes

    DTIC Science & Technology

    2016-04-20

    10 5.1 Results for Four Models with Different Nonlinearities ..................................................11 5.2 Effects of...Force Research Laboratory or the U.S. Government. 1.0 SUMMARY In this report, the effects of incorporating nonlinearities in sequential relative orbit...exactly. Huxel and Bishop [1] discussed the effects of using both inertial range measurements from tracking stations and relative range measurements

  15. Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

    NASA Technical Reports Server (NTRS)

    Pai, P. F.; Lee, S.-Y.

    2003-01-01

    This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

  16. FIBER AND INTEGRATED OPTICS: Propagation of radiation in a light-induced active waveguide

    NASA Astrophysics Data System (ADS)

    Afanas'ev, Anatolii A.; Samson, B. A.; Drits, V. V.; Yukhimenko, S. I.; Yakite, R. V.

    1990-10-01

    An investigation is reported of the properties of the normal modes of an active light-induced waveguide. It is shown that, in contrast to a dielectric waveguide, the presence of the active component may increase considerably the number of the normal modes and the angles of their scattering. In the case of an active light-induced waveguide in the form of a thin filament the normal modes exist and are amplified only in the case when the nonlinear correction to the refractive index is positive.

  17. Towards an Understanding of Atmospheric Balance

    NASA Technical Reports Server (NTRS)

    Errico, Ronald M.

    2015-01-01

    During a 35 year period I published 30+ pear-reviewed papers and technical reports concerning, in part or whole, the topic of atmospheric balance. Most used normal modes, either implicitly or explicitly, as the appropriate diagnostic tool. This included examination of nonlinear balance in several different global and regional models using a variety of novel metrics as well as development of nonlinear normal mode initialization schemes for particular global and regional models. Recent studies also included the use of adjoint models and OSSEs to answer some questions regarding balance. lwill summarize what I learned through those many works, but also present what l see as remaining issues to be considered or investigated.

  18. A NASTRAN primer for the analysis of rotating flexible blades

    NASA Technical Reports Server (NTRS)

    Lawrence, Charles; Aiello, Robert A.; Ernst, Michael A.; Mcgee, Oliver G.

    1987-01-01

    This primer provides documentation for using MSC NASTRAN in analyzing rotating flexible blades. The analysis of these blades includes geometrically nonlinear (large displacement) analysis under centrifugal loading, and frequency and mode shape (normal modes) determination. The geometrically nonlinear analysis using NASTRAN Solution sequence 64 is discussed along with the determination of frequencies and mode shapes using Solution Sequence 63. A sample problem with the complete NASTRAN input data is included. Items unique to rotating blade analyses, such as setting angle and centrifugal softening effects are emphasized.

  19. Nonlinear Spectral Singularity and Laser Output Intensity for the TE and TM Modes

    NASA Astrophysics Data System (ADS)

    Ghaemidizicheh, Hamed; Mostafazadeh, Ali

    The nonlinear spectral singularity arising from a Kerr nonlinearity is explored in. This reference studies the effect of nonlinearity in Lasing condition and shows that Kerr nonlinearity with spectral singularity for a normally incident wave provides an explanation of lasing at gain coefficient g. Lasing occurs when it exceeds threshold gain g0. For oblique waves, Ref. looks at the behavior of threshold gain coefficient g0 which is given by the condition that there is a linear spectral singularity. We investigated imposing the condition of the existence of nonlinear spectral singularity in the TE / TM modes of a mirrorless slab of gain materials and studied the θ-dependence of intensity. Supported by TUBITAK Project No: 114F357 and by the Turkish Academy of Science (TUBA).

  20. Normal modes of a small gamelan gong.

    PubMed

    Perrin, Robert; Elford, Daniel P; Chalmers, Luke; Swallowe, Gerry M; Moore, Thomas R; Hamdan, Sinin; Halkon, Benjamin J

    2014-10-01

    Studies have been made of the normal modes of a 20.7 cm diameter steel gamelan gong. A finite-element model has been constructed and its predictions for normal modes compared with experimental results obtained using electronic speckle pattern interferometry. Agreement was reasonable in view of the lack of precision in the manufacture of the instrument. The results agree with expectations for an axially symmetric system subject to small symmetry breaking. The extent to which the results obey Chladni's law is discussed. Comparison with vibrational and acoustical spectra enabled the identification of the small number of modes responsible for the sound output when played normally. Evidence of non-linear behavior was found, mainly in the form of subharmonics of true modes. Experiments using scanning laser Doppler vibrometry gave satisfactory agreement with the other methods.

  1. Metastable states and energy flow pathway in square graphene resonators

    NASA Astrophysics Data System (ADS)

    Wang, Yisen; Zhu, Zhigang; Zhang, Yong; Huang, Liang

    2018-01-01

    Nonlinear interaction between flexural modes is critical to heat conductivity and mechanical vibration of two-dimensional materials such as graphene. Much effort has been devoted to understand the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during thermalization process. The key is the development of a universal scheme that numerically characterizes the strength of nonlinear interactions between normal modes. In particular, for our square graphene system, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes. As a result, the equations for the normal modes in the same class as the initially excited one can be approximated by driven harmonic oscillators, therefore, they get energy almost instantaneously. Because of the hierarchical organization of the mode coupling, the energy distribution among the modes will arrive at a stable profile, where most of the energy is localized on a few modes, leading to the formation of "natural package" and metastable states. The dynamics for modes in other symmetry classes follows a Mathieu type of equation, thus, interclass energy flow, when the initial excitation energy is small, starts typically when there is a mode that lies in the unstable region in the parameter space of Mathieu equation. Due to strong coupling of the modes inside the class, the whole class will get energy and be lifted up by the unstable mode. This characterizes the energy flow pathway of the system. These results bring fundamental understandings to the Fermi-Pasta-Ulam problem in two-dimensional systems with complex potentials, and reveal clearly the physical picture of dynamical interactions between the flexural modes, which will be crucial to the understanding of their abnormal contribution to heat conduction and nonlinear mechanical vibrations.

  2. New type of synchronization of oscillators with hard excitation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kovaleva, M. A., E-mail: margo.kovaleva@gmail.com; Manevich, L. I., E-mail: manevichleonid3@gmail.com; Pilipchuk, V. N.

    2013-08-15

    It is shown that stable limiting cycles corresponding to nonlinear beats with complete energy exchange between oscillators can exist in a system of two weakly coupled active oscillators (generators). The oscillatory regime of this type, which implements a new type of synchronization in an active system, is an alternative to the well-studied synchronization in a regime close to a nonlinear normal mode. In this case, the ranges of dissipative parameters corresponding to different types of synchronization do not intersect. The analytic description of attractors revealed in analysis is based on the concept of limiting phase trajectories, which was developed earliermore » by one of the authors for conservative systems. A transition (in the parametric space) from the complete energy exchange between oscillators to predominant localization of energy in one of the oscillators can be naturally described using this concept. The localized normal mode is an attractor in the range of parameters in which neither the limiting phase trajectory nor any of the collective normal modes is an attractor.« less

  3. Veering and nonlinear interactions of a clamped beam in bending and torsion

    NASA Astrophysics Data System (ADS)

    Ehrhardt, David A.; Hill, Thomas L.; Neild, Simon A.; Cooper, Jonathan E.

    2018-03-01

    Understanding the linear and nonlinear dynamic behaviour of beams is critical for the design of many engineering structures such as spacecraft antennae, aircraft wings, and turbine blades. When the eigenvalues of such structures are closely-spaced, nonlinearity may lead to interactions between the underlying linear normal modes (LNMs). This work considers a clamped-clamped beam which exhibits nonlinear behaviour due to axial tension from large amplitudes of deformation. An additional cross-beam, mounted transversely and with a movable mass at each tip, allows tuning of the primary torsion LNM such that it is close to the primary bending LNM. Perturbing the location of one mass relative to that of the other leads to veering between the eigenvalues of the bending and torsion LNMs. For a number of selected geometries in the region of veering, a nonlinear reduced order model (NLROM) is created and the nonlinear normal modes (NNMs) are used to describe the underlying nonlinear behaviour of the structure. The relationship between the 'closeness' of the eigenvalues and the nonlinear dynamic behaviour is demonstrated in the NNM backbone curves, and veering-like behaviour is observed. Finally, the forced and damped dynamics of the structure are predicted using several analytical and numerical tools and are compared to experimental measurements. As well as showing a good agreement between the predicted and measured responses, phenomena such as a 1:1 internal resonance and quasi-periodic behaviour are identified.

  4. Nonlinear interactions and their scaling in the logarithmic region of turbulent channels

    NASA Astrophysics Data System (ADS)

    Moarref, Rashad; Sharma, Ati S.; Tropp, Joel A.; McKeon, Beverley J.

    2014-11-01

    The nonlinear interactions in wall turbulence redistribute the turbulent kinetic energy across different scales and different wall-normal locations. To better understand these interactions in the logarithmic region of turbulent channels, we decompose the velocity into a weighted sum of resolvent modes (McKeon & Sharma, J. Fluid Mech., 2010). The resolvent modes represent the linear amplification mechanisms in the Navier-Stokes equations (NSE) and the weights represent the scaling influence of the nonlinearity. An explicit equation for the unknown weights is obtained by projecting the NSE onto the known resolvent modes (McKeon et al., Phys. Fluids, 2013). The weights of triad modes -the modes that directly interact via the quadratic nonlinearity in the NSE- are coupled via interaction coefficients that depend solely on the resolvent modes. We use the hierarchies of self-similar modes in the logarithmic region (Moarref et al., J. Fluid Mech., 2013) to extend the notion of triad modes to triad hierarchies. It is shown that the interaction coefficients for the triad modes that belong to a triad hierarchy follow an exponential function. These scalings can be used to better understand the interaction of flow structures in the logarithmic region and develop analytical results therein. The support of Air Force Office of Scientific Research under Grants FA 9550-09-1-0701 (P.M. Rengasamy Ponnappan) and FA 9550-12-1-0469 (P.M. Doug Smith) is gratefully acknowledged.

  5. Analytical and Experimental Random Vibration of Nonlinear Aeroelastic Structures.

    DTIC Science & Technology

    1987-01-28

    firstorder differential equations. In view of the system complexi- ty an attempt s made to close the infinite hierarchy by using a Gaussian scheme. This sc...year of this project-. When the first normal mode is externally excited by a band-limited random excitation, the system mean square response is found...governed mainly by the internal detuning parameter and the system damping ratios. The results are completely different when the second normal mode is

  6. Nonlinear Wave Propagation

    DTIC Science & Technology

    2009-02-09

    grey) soliton , to a nearly linear wavetrain at the front moving with its group velocity ; like KdV the NLS DSW has two speeds. The 1-D NLS theory was...studies of wave phenomena in nonlinear optics include ultrashort pulse dynamics in mode- locked lasers, dynamics and perturbations of dark solitons ...nonlinear Kerr response and has a large normal group - velocity dispersion (GVD). This requires a set of prisms and/or mirrors specially designed to have

  7. Energy exchange and transition to localization in the asymmetric Fermi-Pasta-Ulam oscillatory chain

    NASA Astrophysics Data System (ADS)

    Smirnov, Valeri V.; Shepelev, Denis S.; Manevitch, Leonid I.

    2013-01-01

    A finite (periodic) FPU chain is chosen as a convenient model for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant interaction between high-frequency nonlinear normal modes. This interaction determines both the complete energy exchange between different parts of the chain and the transition to energy localization in an excited group of particles. In the paper, we demonstrate that this mechanism can exist in realistic (asymmetric) models of atomic or molecular oscillatory chains. Also, we study the resonant interaction of conjugated nonlinear normal modes and prove a possibility of linearization of the equations of motion. The theoretical constructions developed in this paper are based on the concepts of "effective particles" and Limiting Phase Trajectories. In particular, an analytical description of energy exchange between the "effective particles" in the terms of non-smooth functions is presented. The analytical results are confirmed with numerical simulations.

  8. Normal modes of a superconducting transmission-line resonator with embedded lumped element circuit components

    NASA Astrophysics Data System (ADS)

    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.

  9. Modal Substructuring of Geometrically Nonlinear Finite-Element Models

    DOE PAGES

    Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

    2015-12-21

    The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

  10. Modal Substructuring of Geometrically Nonlinear Finite-Element Models

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

    The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

  11. First report of resonant interactions between whistler mode waves in the Earth's magnetosphere

    NASA Astrophysics Data System (ADS)

    Gao, Xinliang; Lu, Quanming; Wang, Shui

    2017-06-01

    Nonlinear physics related to whistler mode waves in the Earth's magnetosphere are now becoming a hot topic. In this letter, based on Time History of Events and Macroscale Interactions during Substorms waveform data, we report several interesting whistler mode wave events, where the upper band whistler mode waves are believed to be generated through the nonlinear wave-wave coupling between two lower band waves. This is the first report on resonant interactions between whistler mode waves in the Earth's magnetosphere. In these events, the two lower band whistler mode waves are observed to have oppositely propagating directions, while the generated upper band wave has the same propagating direction as the lower band wave with the relatively higher frequency. Moreover, the wave normal angle of the excited upper band wave is usually larger than those of two lower band whistler mode waves. Our results reveal the large diversity of the evolution of whistler mode waves in the Earth's magnetosphere.

  12. Polyad breaking phenomenon associated with a local-to-normal mode transition and suitability to estimate force constants

    NASA Astrophysics Data System (ADS)

    Bermúdez-Montaña, M.; Lemus, R.; Castaños, O.

    2017-12-01

    In a system of two interacting harmonic oscillators a local-to-normal mode transition is manifested as a polyad breaking phenomenon. This phenomenon is associated with the suitability to estimate zeroth-order force constants in the framework of a local mode description. This transition is also exhibited in two interacting Morse oscillators. To study this case, an appropriate parameterisation going from a molecule with local mode behaviour (H2O) to a molecule presenting a normal mode behaviour (CO2) is introduced. Concepts from quantum mechanics like fidelity, entropy and probability density, as well from nonlinear classical mechanics like Poincaré sections are used to detect the transition region. It is found that fidelity and entropy are sensitive complementary properties to detect the local-to-normal transition. Poincaré sections allow the local-to-normal transition to be detected through the appearance of chaos as a consequence of the polyad breaking phenomenon. In addition, two kinds of avoided energy crossings are identified in accordance with the different regions of the spectrum.

  13. The effects of differential flow between rational surfaces on toroidal resistive MHD modes

    NASA Astrophysics Data System (ADS)

    Brennan, Dylan; Halfmoon, Michael; Rhodes, Dov; Cole, Andrew; Okabayashi, Michio; Paz-Soldan, Carlos; Finn, John

    2016-10-01

    Differential flow between resonant surfaces can strongly affect the coupling and penetration of resonant components of resistive modes, and yet this mechanism is not yet fully understood. This study focuses on the evolution of tearing instabilities and the penetration of imposed resonant magnetic perturbations (RMPs) in tokamak configurations relevant to DIII-D and ITER, including equilibrium flow shear. It has been observed on DIII-D that the onset of tearing instabilities leading to disruption is often coincident with a loss of differential rotation between a higher m/n tearing surface (normally the 4/3 or 3/2) and a lower m/n tearing surface (normally the 2/1). Imposing RMPs can strongly affect this coupling and the torques between the modes. We apply the nonlinear 3-D resistive magnetohydrodynamic (MHD) code NIMROD to study the mechanisms by which these couplings occur. Reduced MHD analyses are applied to study the effects of differential flow between resonant surfaces in the simulations. Interaction between resonant modes can cause significant energy transfer between them, effectively stabilizing one mode while the other grows. The flow mitigates this transfer, but also affects the individual modes. The combination of these effects determines the nonlinear outcome. Supported by US DOE Grants DE-SC0014005 and DE-SC0014119.

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

    NASA Astrophysics Data System (ADS)

    Hsieh, Y.; Omura, Y.

    2017-12-01

    Nonlinear trapping of electrons through Landau resonance is a characteristic dynamics in oblique whistler-mode wave particle interactions. The resonance velocity of the Landau resonance at quasi-parallel propagation becomes very close to the parallel group velocity of whistler-mode wave at frequency around 0.5 Ωe, causing a long distance of resonant interaction and strong acceleration of resonant electrons [1]. We demonstrate these effective accelerations for electrons with high equatorial pitch angle ( > 60°) by test particle simulations with parameters for the Earth's inner magnetosphere at L=5. In the simulations, we focus on slightly oblique whistler mode waves with wave normal angle < 20°. Analyzing the wave electric field E and the resonant current J, which is composed of electrons undergoing the Landau resonance, we find that the J·E is mainly positive, which denotes the damping of the wave. Furthermore, we confirm that this positive J•E is dominated by transverse component Jperp·Eperp rather than by longitudinal component Jpara·Eperp. The simulation results reveal that the Landau resonance contributes to the nonlinear damping at 0.5 Ωe for whistler mode waves. Reference [1] Hsieh, Y.-K., and Y. Omura (2017), Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere, J. Geophys. Res. Space Physics, 122, doi:10.1002/2016JA023255.

  15. Fluctuations and discrete particle noise in gyrokinetic simulation of drift waves

    NASA Astrophysics Data System (ADS)

    Jenkins, Thomas G.; Lee, W. W.

    2007-03-01

    The relevance of the gyrokinetic fluctuation-dissipation theorem (FDT) to thermal equilibrium and nonequilibrium states of the gyrokinetic plasma is explored, with particular focus being given to the contribution of weakly damped normal modes to the fluctuation spectrum. It is found that the fluctuation energy carried in the normal modes exhibits the proper scaling with particle count (as predicted by the FDT in thermal equilibrium) even in the presence of drift waves, which grow linearly and attain a nonlinearly saturated steady state. This favorable scaling is preserved, and the saturation amplitude of the drift wave unaffected, for parameter regimes in which the normal modes become strongly damped and introduce a broad spectrum of discreteness-induced background noise in frequency space.

  16. Demonstration of the Jaynes-Cummings ladder with Rydberg-dressed atoms

    DOE PAGES

    Lee, Jongmin; Martin, Michael J.; Jau, Yuan-Yu; ...

    2017-04-06

    Here, we observe the nonlinearity of the Jaynes-Cummings (JC) ladder in the Autler-Townes spectroscopy of the hyperfine ground states for a Rydberg-dressed two-atom system. The role of the two-level system in the JC model is played by the presence or absence of a collective Rydberg excitation, and the bosonic mode manifests as the number n of single-atom spin flips, symmetrically distributed between the atoms. We also measure the normal-mode splitting and √ n nonlinearity as a function of detuning and Rabi frequency, thereby experimentally establishing the isomorphism with the JC model.

  17. Development and Breakdown of Goertler Vortices in High Speed Boundary Layers

    NASA Technical Reports Server (NTRS)

    Li, Fei; Choudhari, Meelan; Chang, Chau-Lyan; Wu, Minwei; Greene, Ptrick T.

    2010-01-01

    The nonlinear development of G rtler instability over a concave surface gives rise to a highly distorted stationary flow in the boundary layer that has strong velocity gradients in both spanwise and wall-normal directions. This distorted flow is susceptible to strong, high frequency secondary instability that leads to the onset of transition. For high Mach number flows, the boundary layer is also subject to the second mode instability. The nonlinear development of G rtler vortices and the ensuing growth and breakdown of secondary instability, the G rtler vortex interactions with second mode instabilities as well as oblique second mode interactions are examined in the context of both internal and external hypersonic configurations using nonlinear parabolized stability equations, 2-D eigenvalue analysis and direct numerical simulation. For G rtler vortex development inside the Purdue Mach 6 Ludwieg tube wind tunnel, multiple families of unstable secondary eigenmodes are identified and their linear and nonlinear evolution is examined. The computation of secondary instability is continued past the onset of transition to elucidate the physical mechanisms underlying the laminar breakdown process. Nonlinear breakdown scenarios associated with transition over a Mach 6 compression cone configuration are also explored.

  18. Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

    Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

  19. Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

    DOE PAGES

    Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

    2017-03-29

    Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

  20. Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2)

    NASA Technical Reports Server (NTRS)

    Clark, Robert; Cottter, Paul; Michalopoulos, Constantine

    2013-01-01

    This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known.

  1. Dynamic Identification for Control of Large Space Structures

    NASA Technical Reports Server (NTRS)

    Ibrahim, S. R.

    1985-01-01

    This is a compilation of reports by the one author on one subject. It consists of the following five journal articles: (1) A Parametric Study of the Ibrahim Time Domain Modal Identification Algorithm; (2) Large Modal Survey Testing Using the Ibrahim Time Domain Identification Technique; (3) Computation of Normal Modes from Identified Complex Modes; (4) Dynamic Modeling of Structural from Measured Complex Modes; and (5) Time Domain Quasi-Linear Identification of Nonlinear Dynamic Systems.

  2. Nonlinear acoustic experiments for landmine detection: the significance of the top-plate normal modes

    NASA Astrophysics Data System (ADS)

    Korman, Murray S.; Alberts, W. C. K., II; Sabatier, James M.

    2004-09-01

    In nonlinear acoustic detection experiments involving a buried inert VS 2.2 anti-tank landmine, airborne sound at two closely spaced primary frequencies f1 and f2 couple into the ground and interact nonlinearly with the soil-top pressure plate interface. Scattering generates soil vibration at the surface at the combination frequencies | m f1 +- n f2 | , where m and n are integers. The normal component of the particle velocity at the soil surface has been measured with a laser Doppler velocimeter (LDV) and with a geophone by Sabatier et. al. [SPIE Proceedings Vol. 4742, (695-700), 2002; Vol. 5089, (476-486), 2003] at the gravel lane test site. Spatial profiles of the particle velocity measured for both primary components and for various combination frequencies indicate that the modal structure of the mine is playing an important role. Here, an experimental modal analysis is performed on a VS 1.6 inert anti-tank mine that is resting on sand but is not buried. Five top-plate mode shapes are described. The mine is then buried in dry finely sifted natural loess soil and excited at f1 = 120 Hz and f2 = 130 Hz. Spatial profiles at the primary components and the nonlinearly generated f1 - (f2 - f1) component are characterized by a single peak. For the 2f1+f2 and 2f2 + f1 components, the doubly peaked profiles can be attributed to the familiar mode shape of a timpani drum (that is shifted lower in frequency due to soil mass loading). Other nonlinear profiles appear to be due to a mixture of modes. This material is based upon work supported by the U. S. Army RDECOM CERDEC Night Vision and Electronic Sensors Directorate under Contract DAAB15-02-C-0024.

  3. Dark solitons in mode-locked lasers.

    PubMed

    Ablowitz, Mark J; Horikis, Theodoros P; Nixon, Sean D; Frantzeskakis, Dimitri J

    2011-03-15

    Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model that incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve (mode-lock) into dark solitons under appropriate requirements also met in experimental observations. The resulting pulses are essentially dark solitons of the unperturbed nonlinear Schrödinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.

  4. Acoustic multipath arrivals in the horizontal plane due to approaching nonlinear internal waves.

    PubMed

    Badiey, Mohsen; Katsnelson, Boris G; Lin, Ying-Tsong; Lynch, James F

    2011-04-01

    Simultaneous measurements of acoustic wave transmissions and a nonlinear internal wave packet approaching an along-shelf acoustic path during the Shallow Water 2006 experiment are reported. The incoming internal wave packet acts as a moving frontal layer reflecting (or refracting) sound in the horizontal plane. Received acoustic signals are filtered into acoustic normal mode arrivals. It is shown that a horizontal multipath interference is produced. This has previously been called a horizontal Lloyd's mirror. The interference between the direct path and the refracted path depends on the mode number and frequency of the acoustic signal. A mechanism for the multipath interference is shown. Preliminary modeling results of this dynamic interaction using vertical modes and horizontal parabolic equation models are in good agreement with the observed data.

  5. Nonlinear adaptive networks: A little theory, a few applications

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jones, R.D.; Qian, S.; Barnes, C.W.

    1990-01-01

    We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We than present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series tidal prediction in Venice Lagoon, sonar transient detection, control of nonlinear processes, balancing a double inverted pendulum and design advice for free electron lasers. 26 refs., 23 figs.

  6. Polariton biexciton transitions in a ZnSe-based microcavity

    NASA Astrophysics Data System (ADS)

    Neukirch, U.; Bolton, S. R.; Fromer, N. A.; Sham, L. J.; Chemla, D. S.

    2000-06-01

    The optical third-order nonlinearity of a ZnSe-based microcavity is investigated by the pump-and-probe method. In the specially designed non-monolithic sample the biexciton binding energy exceeds all damping constants and the normal-mode splitting between exciton and cavity photon. For counter-circular polarized beams the nonlinear response exhibits strong oscillatory structures in the spectral vicinity of the polariton-biexciton transition. Comparison to model calculations shows that in this case the coherent nonlinearity is completely dominated by biexciton-exciton interactions beyond the Hartree-Fock approximation.

  7. Experimental study of isolas in nonlinear systems featuring modal interactions

    PubMed Central

    Noël, Jean-Philippe; Virgin, Lawrence N.; Kerschen, Gaëtan

    2018-01-01

    The objective of the present paper is to provide experimental evidence of isolated resonances in the frequency response of nonlinear mechanical systems. More specifically, this work explores the presence of isolas, which are periodic solutions detached from the main frequency response, in the case of a nonlinear set-up consisting of two masses sliding on a horizontal guide. A careful experimental investigation of isolas is carried out using responses to swept-sine and stepped-sine excitations. The experimental findings are validated with advanced numerical simulations combining nonlinear modal analysis and bifurcation monitoring. In particular, the interactions between two nonlinear normal modes are shown to be responsible for the creation of the isolas. PMID:29584758

  8. Evaluation of MARC for the analysis of rotating composite blades

    NASA Technical Reports Server (NTRS)

    Bartos, Karen F.; Ernst, Michael A.

    1993-01-01

    The suitability of the MARC code for the analysis of rotating composite blades was evaluated using a four-task process. A nonlinear displacement analysis and subsequent eigenvalue analysis were performed on a rotating spring mass system to ensure that displacement-dependent centrifugal forces were accounted for in the eigenvalue analysis. Normal modes analyses were conducted on isotropic plates with various degrees of twist to evaluate MARC's ability to handle blade twist. Normal modes analyses were conducted on flat composite plates to validate the newly developed coupled COBSTRAN-MARC methodology. Finally, normal modes analyses were conducted on four composite propfan blades that were designed, analyzed, and fabricated at NASA Lewis Research Center. Results were compared with experimental data. The research documented herein presents MARC as a viable tool for the analysis of rotating composite blades.

  9. Evaluation of MARC for the analysis of rotating composite blades

    NASA Astrophysics Data System (ADS)

    Bartos, Karen F.; Ernst, Michael A.

    1993-03-01

    The suitability of the MARC code for the analysis of rotating composite blades was evaluated using a four-task process. A nonlinear displacement analysis and subsequent eigenvalue analysis were performed on a rotating spring mass system to ensure that displacement-dependent centrifugal forces were accounted for in the eigenvalue analysis. Normal modes analyses were conducted on isotropic plates with various degrees of twist to evaluate MARC's ability to handle blade twist. Normal modes analyses were conducted on flat composite plates to validate the newly developed coupled COBSTRAN-MARC methodology. Finally, normal modes analyses were conducted on four composite propfan blades that were designed, analyzed, and fabricated at NASA Lewis Research Center. Results were compared with experimental data. The research documented herein presents MARC as a viable tool for the analysis of rotating composite blades.

  10. Nonlinear Laser Lithography implementation for both ``normal'' and ``anomalous'' laser induced periodic structuring

    NASA Astrophysics Data System (ADS)

    Pavlov, Ihor; Tokel, Onur; Yavuz, Ozgun; Makey, Ghaith; Ilday, Omer; Omer Ilday Team

    Laser Induced Periodic Surface Structuring (LIPSS) is one of the most prominent directions in laser-material interaction due to both practical and theoretical importance, especially after the discovery of Nonlinear Laser Lithography (NLL), which opens new area for industrial application of LIPSS as an effective tool for controllable, highly ordered large area nanostructuring. LIPSS appear on the surface under laser beam in the form of periodical lines. The LIPSS, that appear perpendicular to laser polarization are called ``normal'', in contrast to ``anomalous'' LIPSS appearing parallel to the polarization. Although, NLL technique was already demonstrated for ``normal'' and ``anomalous'' LIPSS separately, up to now, there is no clear understanding of switching mechanism between these two modes. In presented paper we have shown that the mechanism relies on interplay between two feedbacks: long range, low intensity dipole-like scattering of light along the surface, and short range, high intensity plasmon-polariton wave. For the first time, we are able to create both types of LIPSS on the same surface by controlling these two feedbacks, obtaining highly-ordered large-area structured patterns in both modes.

  11. Nonlinear equations of motion for Landau resonance interactions with a whistler mode wave

    NASA Technical Reports Server (NTRS)

    Inan, U. S.; Tkalcevic, S.

    1982-01-01

    A simple set of equations is presented for the description of the cyclotron averaged motion of Landau resonant particles in a whistler mode wave propagating at an angle to the static magnetic field. A comparison is conducted of the wave magnetic field and electric field effects for the parameters of the magnetosphere, and the parameter ranges for which the wave magnetic field effects would be negligible are determined. It is shown that the effect of the wave magnetic field can be neglected for low pitch angles, high normal wave angles, and/or high normalized wave frequencies.

  12. Dynamics of a movable micromirror in a nonlinear optical cavity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kumar, Tarun; ManMohan; Bhattacherjee, Aranya B.

    We consider the dynamics of a movable mirror (cantilever) of a nonlinear optical cavity. We show that a chi{sup (3)} medium with a strong Kerr nonlinearity placed inside a cavity inhibits the normal mode splitting (NMS) due to the photon blockade mechanism. This study demonstrates that the displacement spectrum of the micromirror could be used as a tool to detect the photon blockade effect. Moreover the ability to control the photon number fluctuation by tuning the Kerr nonlinearity emerges as a new handle to coherently control the dynamics of the micromirror, which further could be useful in the realization ofmore » tuneable quantum-mechanical devices. We also found that the temperature of the micromechanical mirror increases with increasing Kerr nonlinearity.« less

  13. On the nonlinear development of the most unstable Goertler vortex mode

    NASA Technical Reports Server (NTRS)

    Denier, James P.; Hall, Philip

    1991-01-01

    The nonlinear development of the most unstable Gortler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Gortler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Gortler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Gortler equations valid for O(1) Gortler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

  14. Prediction and control of chaotic processes using nonlinear adaptive networks

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jones, R.D.; Barnes, C.W.; Flake, G.W.

    1990-01-01

    We present the theory of nonlinear adaptive networks and discuss a few applications. In particular, we review the theory of feedforward backpropagation networks. We then present the theory of the Connectionist Normalized Linear Spline network in both its feedforward and iterated modes. Also, we briefly discuss the theory of stochastic cellular automata. We then discuss applications to chaotic time series, tidal prediction in Venice lagoon, finite differencing, sonar transient detection, control of nonlinear processes, control of a negative ion source, balancing a double inverted pendulum and design advice for free electron lasers and laser fusion targets.

  15. Pulsed ytterbium-doped fibre laser with a combined modulator based on single-wall carbon nanotubes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Khudyakov, D V; Borodkin, A A; Vartapetov, S K

    2015-09-30

    This paper describes an all-normal-dispersion pulsed ytterbium-doped fibre ring laser mode-locked by a nonlinear combined modulator based on single-wall carbon nanotubes. We have demonstrated 1.7-ps pulse generation at 1.04 μm with a repetition rate of 35.6 MHz. At the laser output, the pulses were compressed to 180 fs. We have examined an intracavity nonlinear modulator which utilises nonlinear polarisation ellipse rotation in conjunction with a saturable absorber in the form of a polymer-matrix composite film containing single-wall carbon nanotubes. (lasers)

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

    NASA Astrophysics Data System (ADS)

    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.

  17. Dynamical criterion for a marginally unstable, quasi-linear behavior in a two-layer model

    NASA Technical Reports Server (NTRS)

    Ebisuzaki, W.

    1988-01-01

    A two-layer quasi-geostrophic flow forced by meridional variations in heating can be in regimes ranging from radiative equilibrium to forced geostrophic turbulence. Between these extremes is a regime where the time-mean (zonal) flow is marginally unstable. Using scaling arguments, it is concluded that such a marginally unstable state should occur when a certain parameter, measuring the strength of wave-wave interactions relative to the beta effect and advection by the thermal wind, is small. Numerical simulations support this proposal. A transition from the marginally unstable regime to a more nonlinear regime is then examined through numerical simulations with different radiative forcings. It is found that transition is not caused by secondary instability of waves in the marginally unstable regime. Instead, the time-mean flow can support a number of marginally unstable normal modes. These normal modes interact with each other, and if they are of sufficient amplitude, the flow enters a more nonlinear regime.

  18. Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

    NASA Technical Reports Server (NTRS)

    Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

    2003-01-01

    An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

  19. Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay

    NASA Astrophysics Data System (ADS)

    Ehrhardt, David A.; Allen, Matthew S.

    2016-08-01

    Nonlinear Normal Modes (NNMs) offer tremendous insight into the dynamic behavior of a nonlinear system, extending many concepts that are familiar in linear modal analysis. Hence there is interest in developing methods to experimentally and numerically determine a system's NNMs for model updating or simply to characterize its dynamic response. Previous experimental work has shown that a mono-harmonic excitation can be used to isolate a system's dynamic response in the neighborhood of a NNM along the main backbones of a system. This work shows that a multi-harmonic excitation is needed to isolate a NNM when well separated linear modes of a structure couple to produce an internal resonance. It is shown that one can tune the multiple harmonics of the input excitation using a plot of the input force versus the response velocity until the area enclosed by the force-velocity curve is minimized. Once an appropriated NNM is measured, one can increase the force level and retune the frequency to obtain a NNM at a higher amplitude or remove the excitation and measure the structure's decay down a NNM backbone. This work explores both methods using simulations and measurements of a nominally-flat clamped-clamped beam excited at a single point with a magnetic force. Numerical simulations are used to validate the method in a well defined environment and to provide comparison with the experimentally measured NNMs. The experimental results seem to produce a good estimate of two NNMs along their backbone and part of an internal resonance branch. Full-field measurements are then used to further explore the couplings between the underlying linear modes along the identified NNMs.

  20. Time-dependent local-to-normal mode transition in triatomic molecules

    NASA Astrophysics Data System (ADS)

    Cruz, Hans; Bermúdez-Montaña, Marisol; Lemus, Renato

    2018-01-01

    Time-evolution of the vibrational states of two interacting harmonic oscillators in the local mode scheme is presented. A local-to-normal mode transition (LNT) is identified and studied from temporal perspective through time-dependent frequencies of the oscillators. The LNT is established as a polyad-breaking phenomenon from the local standpoint for the stretching degrees of freedom in a triatomic molecule. This study is carried out in the algebraic representation of bosonic operators. The dynamics of the states are determined via the solutions of the corresponding nonlinear Ermakov equation and a local time-dependent polyad is obtained as a tool to identify the LNT. Applications of this formalism to H2O, CO2, O3 and NO2 molecules in the adiabatic, sudden and linear regime are considered.

  1. Wiener sliding-mode control for artificial pancreas: a new nonlinear approach to glucose regulation.

    PubMed

    Abu-Rmileh, Amjad; Garcia-Gabin, Winston

    2012-08-01

    Type 1 diabetic patients need insulin therapy to keep their blood glucose close to normal. In this paper an attempt is made to show how nonlinear control-oriented model may be used to improve the performance of closed-loop control of blood glucose in diabetic patients. The nonlinear Wiener model is used as a novel modeling approach to be applied to the glucose control problem. The identified Wiener model is used in the design of a robust nonlinear sliding mode control strategy. Two configurations of the nonlinear controller are tested and compared to a controller designed with a linear model. The controllers are designed in a Smith predictor structure to reduce the effect of system time delay. To improve the meal compensation features, the controllers are provided with a simple feedforward controller to inject an insulin bolus at meal time. Different simulation scenarios have been used to evaluate the proposed controllers. The obtained results show that the new approach outperforms the linear control scheme, and regulates the glucose level within safe limits in the presence of measurement and modeling errors, meal uncertainty and patient variations. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

  2. Third order nonlinear phenomena in silica solid and hollow whispering gallery mode resonators

    NASA Astrophysics Data System (ADS)

    Farnesi, D.; Barucci, A.; Berneschi, S.; Cosi, F.; Righini, G. C.; Nunzi Conti, G.; Soria, Silvia

    2016-03-01

    We report efficient generation of nonlinear phenomena related to third order optical non-linear susceptibility χ(3) interactions in resonant silica microspheres and microbubbles in the regime of normal dispersion. The interactions here reported are: Stimulated Raman Scattering (SRS), and four wave mixing processes comprising Stimulated Anti-stokes Raman Scattering (SARS) and comb generation. Unusually strong anti-Stokes components and extraordinarily symmetric spectra have been observed. Resonant SARS and SRS corresponding to different Raman bands were also observed. The lack of correlation between stimulated anti-stokes and stokes scattering spectra indicates that the signal has to be resonant with the cavity.

  3. Phenomenology in minimal theory of massive gravity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Felice, Antonio De; Mukohyama, Shinji; Kavli Institute for the Physics and Mathematics of the Universe

    2016-04-15

    We investigate the minimal theory of massive gravity (MTMG) recently introduced. After reviewing the original construction based on its Hamiltonian in the vielbein formalism, we reformulate it in terms of its Lagrangian in both the vielbein and the metric formalisms. It then becomes obvious that, unlike previous attempts in the literature of Lorentz-violating massive gravity, not only the potential but also the kinetic structure of the action is modified from the de Rham-Gabadadze-Tolley (dRGT) massive gravity theory. We confirm that the number of physical degrees of freedom in MTMG is two at fully nonlinear level. This proves the absence ofmore » various possible pathologies such as superluminality, acausality and strong coupling. Afterwards, we discuss the phenomenology of MTMG in the presence of a dust fluid. We find that on a flat homogeneous and isotropic background we have two branches. One of them (self-accelerating branch) naturally leads to acceleration without the genuine cosmological constant or dark energy. For this branch both the scalar and the vector modes behave exactly as in general relativity (GR). The phenomenology of this branch differs from GR in the tensor modes sector, as the tensor modes acquire a non-zero mass. Hence, MTMG serves as a stable nonlinear completion of the self-accelerating cosmological solution found originally in dRGT theory. The other branch (normal branch) has a dynamics which depends on the time-dependent fiducial metric. For the normal branch, the scalar mode sector, even though as in GR only one scalar mode is present (due to the dust fluid), differs from the one in GR, and, in general, structure formation will follow a different phenomenology. The tensor modes will be massive, whereas the vector modes, for both branches, will have the same phenomenology as in GR.« less

  4. Probabilistic estimation of splitting coefficients of normal modes of the Earth, and their uncertainties, using an autoregressive technique

    NASA Astrophysics Data System (ADS)

    Pachhai, S.; Masters, G.; Laske, G.

    2017-12-01

    Earth's normal-mode spectra are crucial to studying the long wavelength structure of the Earth. Such observations have been used extensively to estimate "splitting coefficients" which, in turn, can be used to determine the three-dimensional velocity and density structure. Most past studies apply a non-linear iterative inversion to estimate the splitting coefficients which requires that the earthquake source is known. However, it is challenging to know the source details, particularly for big events as used in normal-mode analyses. Additionally, the final solution of the non-linear inversion can depend on the choice of damping parameter and starting model. To circumvent the need to know the source, a two-step linear inversion has been developed and successfully applied to many mantle and core sensitive modes. The first step takes combinations of the data from a single event to produce spectra known as "receiver strips". The autoregressive nature of the receiver strips can then be used to estimate the structure coefficients without the need to know the source. Based on this approach, we recently employed a neighborhood algorithm to measure the splitting coefficients for an isolated inner-core sensitive mode (13S2). This approach explores the parameter space efficiently without any need of regularization and finds the structure coefficients which best fit the observed strips. Here, we implement a Bayesian approach to data collected for earthquakes from early 2000 and more recent. This approach combines the data (through likelihood) and prior information to provide rigorous parameter values and their uncertainties for both isolated and coupled modes. The likelihood function is derived from the inferred errors of the receiver strips which allows us to retrieve proper uncertainties. Finally, we apply model selection criteria that balance the trade-offs between fit (likelihood) and model complexity to investigate the degree and type of structure (elastic and anelastic) required to explain the data.

  5. Rheology of Foam Near the Order-Disorder Transition

    NASA Technical Reports Server (NTRS)

    Holt, R. Glynn; McDaniel, J. Gregory

    2001-01-01

    The first part of our research results are summarized in the recent journal publication: J. Gregory McDaniel and R. Glynn Holt, 'Measurement of aqueous foam rheology by acoustic levitation', Phys. Rev. E 61, 2204 (2000). This aspect of the work was a combination of experiment and analysis. We built a levitation system capable of acoustically levitating small samples of aqueous foam of arbitrary gas and liquid volume fractions. We then modulated the acoustic field to induce normal mode oscillations of the foam samples. The observables from the experiment were frequency and mode number. For dry (roughly > 70% gas by volume) foams and small deformations, we developed an effective medium, normal-modes analysis which took the frequency and mode number from experiment, and gave us the shear elastic modulus of the foam as a function of Poisson's ratio. The second part of our results may be found in a soon-to-be submitted manuscript 'Dynamics of aqueous foam drops', I.Sh. Akhatov, J.G. McDaniel and R.G. Holt, describing our modeling in the wet foam limit by considering the acoustic problem. This aspect of the research is purely theoretical. Beginning from a mass-conserving mixture law, the fully nonlinear equations of motion for a wet (roughly < 10% gas by volume) foam drop of initially spherical shape were derived. The frequencies for normal mode oscillations were derived in the linear inviscid limit. The nonlinear equations were numerically solved to elicit the motion of a foam drop under acoustic excitation. The role of the time-varying void fraction in breathing-mode oscillations is of particular interest. As of the end of the current (NAG#3-2121) grant, this work was not yet concluded. We continue to work on this aspect in order to extend the analysis to cover the transition regime of gas volume fractions, as well as to compare to experiments in the wet regime.

  6. Nonlinear Tides in Close Binary Systems

    NASA Astrophysics Data System (ADS)

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

    2012-06-01

    We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' >~ 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static "equilibrium" tidal distortion is, however, stable to parametric resonance except for solar binaries with P <~ 2-5 days. (2) For companion masses larger than a few Jupiter masses, the dynamical tide causes short length scale waves to grow so rapidly that they must be treated as traveling waves, rather than standing waves. (3) We show that the global three-wave treatment of parametric instability typically used in the astrophysics literature does not yield the fastest-growing daughter modes or instability threshold in many cases. We find a form of parametric instability in which a single parent wave excites a very large number of daughter waves (N ≈ 103[P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P <~ a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing; this coupling appears particularly efficient at draining energy out of the dynamical tide and may be more important than either wave breaking or parametric resonance at determining the nonlinear dissipation of the dynamical tide.

  7. Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation

    NASA Astrophysics Data System (ADS)

    Macdonald, J. H. G.

    2016-02-01

    Cables are often prone to potentially damaging large amplitude vibrations. The dynamic excitation may be from external loading or motion of the cable ends, the latter including direct excitation, normally from components of end motion transverse to the cable, and parametric excitation induced by axial components of end motion causing dynamic tension variations. Geometric nonlinearity can be important, causing stiffening behaviour and nonlinear modal coupling. Previous analyses of the vibrations, often neglecting sag, have generally dealt with direct and parametric excitation separately or have reverted to numerical solutions of the responses. Here a nonlinear cable model is adopted, applicable to taut cables such as on cable-stayed bridges, that allows for cable inclination, small sag (such that the vibration modes are similar to those of a taut string), multiple modes in both planes and end motion and/or external forcing close to any natural frequency. Based on the method of scaling and averaging it is found that, for sinusoidal inputs and positive damping, non-zero steady state responses can only occur in the modes in each plane with natural frequencies close to the excitation frequency and those with natural frequencies close to half this frequency. Analytical solutions, in the form of non-dimensional polynomial equations, are derived for the steady state vibration amplitudes in up to three modes simultaneously: the directly excited mode, the corresponding nonlinearly coupled mode in the orthogonal plane and a parametrically excited mode with half the natural frequency. The stability of the solutions is also identified. The outputs of the equations are consistent with previous results, where available. Example results from the analytical solutions are presented for a typical inclined bridge cable subject to vertical excitation of the lower end, and they are validated by numerical integration of the equations of motion and against some previous experimental results. It is shown that the modal interactions and sag (although very small) affect the responses significantly.

  8. N-H stretching modes of adenosine monomer in solution studied by ultrafast nonlinear infrared spectroscopy and ab initio calculations.

    PubMed

    Greve, Christian; Preketes, Nicholas K; Costard, Rene; Koeppe, Benjamin; Fidder, Henk; Nibbering, Erik T J; Temps, Friedrich; Mukamel, Shaul; Elsaesser, Thomas

    2012-07-26

    The N-H stretching vibrations of adenine, one of the building blocks of DNA, are studied by combining infrared absorption and nonlinear two-dimensional infrared spectroscopy with ab initio calculations. We determine diagonal and off-diagonal anharmonicities of N-H stretching vibrations in chemically modified adenosine monomer dissolved in chloroform. For the single-quantum excitation manifold, the normal mode picture with symmetric and asymmetric NH(2) stretching vibrations is fully appropriate. For the two-quantum excitation manifold, however, the interplay between intermode coupling and frequency shifts due to a large diagonal anharmonicity leads to a situation where strong mixing does not occur. We compare our findings with previously reported values obtained on overtone spectroscopy of coupled hydrogen stretching oscillators.

  9. Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow.

    PubMed

    Deng, Mingge; Grinberg, Leopold; Caswell, Bruce; Karniadakis, George Em

    2015-06-28

    We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a dissipative particle dynamics (DPD) method. Unlike previous works, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance.

  10. Generalized Grueneisen tensor from solid nonlinearity parameters

    NASA Technical Reports Server (NTRS)

    Cantrell, J. H., Jr.

    1980-01-01

    Anharmonic effects in solids are often described in terms of generalized Grueneisen parameters which measure the strain dependence of the lattice vibrational frequencies. The relationship between these parameters and the solid nonlinearity parameters measured directly in ultrasonic harmonic generation experiments is derived using an approach valid for normal-mode elastic wave propagation in any crystalline direction. The resulting generalized Grueneisen parameters are purely isentropic in contrast to the Brugger-Grueneisen parameters which are of a mixed thermodynamic state. Experimental data comparing the isentropic generalized Grueneisen parameters and the Brugger-Grueneisen parameters are presented.

  11. KAM for Beating Solutions of the Quintic NLS

    NASA Astrophysics Data System (ADS)

    Haus, E.; Procesi, M.

    2017-09-01

    We consider the nonlinear Schrödinger equation of degree five on the circle T= R / 2π}. We prove the existence of quasi-periodic solutions with four frequencies which bifurcate from "resonant" solutions [studied in Grébert and Thomann (Ann Inst Henri Poincaré Anal Non Linéaire 29(3):455-477, 2012)] of the system obtained by truncating the Hamiltonian after one step of Birkhoff normal form, exhibiting recurrent exchange of energy between some Fourier modes. The existence of these quasi-periodic solutions is a purely nonlinear effect.

  12. Turbulence and mixing from optimal perturbations to a stratified shear layer

    NASA Astrophysics Data System (ADS)

    Kaminski, Alexis; Caulfield, C. P.; Taylor, John

    2014-11-01

    The stability and mixing of stratified shear layers is a canonical problem in fluid dynamics with relevance to flows in the ocean and atmosphere. The Miles-Howard theorem states that a necessary condition for normal-mode instability in parallel, inviscid, steady stratified shear flows is that the gradient Richardson number, Rig is less than 1/4 somewhere in the flow. However, substantial transient growth of non-normal modes may be possible at finite times even when Rig > 1 / 4 everywhere in the flow. We have calculated the ``optimal perturbations'' associated with maximum perturbation energy gain for a stably-stratified shear layer. These optimal perturbations are then used to initialize direct numerical simulations. For small but finite perturbation amplitudes, the optimal perturbations grow at the predicted linear rate initially, but then experience sufficient transient growth to become nonlinear and susceptible to secondary instabilities, which then break down into turbulence. Remarkably, this occurs even in flows for which Rig > 1 / 4 everywhere. We will describe the nonlinear evolution of the optimal perturbations and characterize the resulting turbulence and mixing.

  13. DNS of Laminar-Turbulent Transition in Swept-Wing Boundary Layers

    NASA Technical Reports Server (NTRS)

    Duan, L.; Choudhari, M.; Li, F.

    2014-01-01

    Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing and the mode selected for forcing corresponds to the most amplified secondary instability mode that, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. An inlet boundary condition is carefully designed to allow for accurate injection of instability wave modes and minimize acoustic reflections at numerical boundaries. Nonlinear parabolized stability equation (PSE) predictions compare well with the DNS in terms of modal amplitudes and modal shape during the strongly nonlinear phase of the secondary instability mode. During the transition process, the skin friction coefficient rises rather rapidly and the wall-shear distribution shows a sawtooth pattern that is analogous to the previously documented surface flow visualizations of transition due to stationary crossflow instability. Fully turbulent features are observed in the downstream region of the flow.

  14. Kinematic parameters of second-mode internal waves in the South China Sea

    NASA Astrophysics Data System (ADS)

    Kurkina, Oxana; Talipova, Tatiana; Kurkin, Andrey; Naumov, Alexander; Rybin, Artem

    2017-04-01

    Kinematic parameters of second-mode internal waves (in the framework of weakly nonlinear model of the Gardner equation) are calculated for the region of the South China Sea on a base of GDEM climatology. The prognostic parameters of the model include phase speed of long linear waves, coefficients of dispersion, quadratic and cubic nonlinearity, location (in vertical) of minimum, zero and maximum of the second vertical baroclinic mode and the ratio of its maximal and minimal values. All the parameters are presented in the form of geographical maps for winter (January) and summer (July) seasons. Frequence (in the sense of occurrence) histograms and scatter plots with depth are also given for all the parameters. Special attention is paid to the conditions of normalizing for internal waves of the second mode, as it possesses two extremes. Here some freedom exists, but for correct further modeling of internal waves within the Gardner model one has to fix and keep the same normalization (at maximum or at minimum) for whole a basin. Constructed arrays of prognostic parameters of second-mode internal waves are necessary for the estimations of shape and width (at fixed amplitude) of internal solitary and breather-like waves, limiting amplitudes of internal solitary waves of different families, for assessment of near-bed and near-surface flows induced by such waves, and for evaluation of transport distance for dissolved and suspended matter. The presented results of research are obtained with the support of the Russian Foundation for Basic Research grant 16-05-00049.

  15. Mid-infrared high birefringence As2Se3-based PCF with large nonlinearity and distinctive dispersion by using asymmetric elliptical air hole cladding

    NASA Astrophysics Data System (ADS)

    Hui, Zhanqiang; Yang, Min; Zhang, Youkun; Zhang, Meizhi

    2018-01-01

    A novel high birefringence As2Se3-based hexagonal lattice photonic crystal fiber (PCF) is proposed. In the structure, a central defect core and three kinds of elliptical air holes with different major axes length and ellipticity are introduced in the cladding. The finite difference time domain (FDTD) method with perfectly matched layer (PML) absorption boundary conditions are used to simulate the guided modes of the designed PCF. The properties of this PCF are investigated in detail including the birefringence, beat length, dispersion, nonlinearity and polarization mode dispersion in the 2-5 μm mid-infrared range. The results show that for the optimized structure parameters of Λ = 1.6μm, a = 0.4μm, b = 0.1μm, a1 = 0.6μm, b1 = 0.04μm, a2 = 0.8μm, b2 = 0.06μm, the high birefringence of 0.1192 and beat length of 41.93 μm are obtained. The maximum nonlinearity coefficient of 10,050 w-1km-1 and 15,200 w-1km-1 for x- and y-polarization modes are achieved. The distinctive dispersion is analyzed, which is all-normal in x-polarization direction while it has two zero dispersion points at 3.18 μm and 3.65 μm in y-polarization direction. The designed PCF with high birefringence, large nonlinearity and distinctive dispersion will be beneficial for mid-infrared fiber sensing, mid-infrared spectroscopy and nonlinear optics applications.

  16. Nonlinear hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure

    NASA Astrophysics Data System (ADS)

    Huang, Xing-Rong; Jézéquel, Louis; Besset, Sébastien; Li, Lin; Sauvage, Olivier

    2018-01-01

    This paper describes a simple and fast numerical procedure to study the steady state responses of assembled structures with nonlinearities along continuous interfaces. The proposed strategy is based on a generalized nonlinear modal superposition approach supplemented by a double modal synthesis strategy. The reduced nonlinear modes are derived by combining a single nonlinear mode method with reduction techniques relying on branch modes. The modal parameters containing essential nonlinear information are determined and then employed to calculate the stationary responses of the nonlinear system subjected to various types of excitation. The advantages of the proposed nonlinear modal synthesis are mainly derived in three ways: (1) computational costs are considerably reduced, when analyzing large assembled systems with weak nonlinearities, through the use of reduced nonlinear modes; (2) based on the interpolation models of nonlinear modal parameters, the nonlinear modes introduced during the first step can be employed to analyze the same system under various external loads without having to reanalyze the entire system; and (3) the nonlinear effects can be investigated from a modal point of view by analyzing these nonlinear modal parameters. The proposed strategy is applied to an assembled system composed of plates and nonlinear rubber interfaces. Simulation results have proven the efficiency of this hybrid nonlinear modal synthesis, and the computation time has also been significantly reduced.

  17. Response functions for dimers and square-symmetric molecules in four-wave-mixing experiments with polarized light

    NASA Astrophysics Data System (ADS)

    Smith, Eric Ryan; Farrow, Darcie A.; Jonas, David M.

    2005-07-01

    Four-wave-mixing nonlinear-response functions are given for intermolecular and intramolecular vibrations of a perpendicular dimer and intramolecular vibrations of a square-symmetric molecule containing a doubly degenerate state. A two-dimensional particle-in-a-box model is used to approximate the electronic wave functions and obtain harmonic potentials for nuclear motion. Vibronic interactions due to symmetry-lowering distortions along Jahn-Teller active normal modes are discussed. Electronic dephasing due to nuclear motion along both symmetric and asymmetric normal modes is included in these response functions, but population transfer between states is not. As an illustration, these response functions are used to predict the pump-probe polarization anisotropy in the limit of impulsive excitation.

  18. Nonlinear VLF Wave Physics in the Radiation Belts

    NASA Astrophysics Data System (ADS)

    Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.

    2014-12-01

    Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function [Storey and Lefeuvre, 1979] to yield the power distribution as a function of wave-normal angle and local azimuthal angle. We have validated this technique in the NRL space chamber and applied this methodology to Van Allen probe data to demonstrate that traditional wave-normal analaysis can give misleading results when multiple waves are present.

  19. A comparative numerical analysis of linear and nonlinear aerodynamic sound generation by vortex disturbances in homentropic constant shear flows

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hau, Jan-Niklas, E-mail: hau@fdy.tu-darmstadt.de; Oberlack, Martin; GSC CE, Technische Universität Darmstadt, Dolivostraße 15, 64293 Darmstadt

    2015-12-15

    Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, “Linear mechanism of wave emergence from vortices in smooth shear flows,” Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, “Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow,” Phys.more » Fluids 12, 3021-3028 (2000); N. A. Bakas, “Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow,” J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, “Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow,” Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber plane, which results in highly directional linear sound radiation, whereas the nonlinearly generated waves are almost omni-directional. As part of this analysis, we compare the effectiveness of the linear and nonlinear mechanisms of wave generation within the range of validity of the rapid distortion theory and show the dominance of the linear aerodynamic sound generation. Finally, topological differences between the linear source term of the acoustic analogy equation and of the anisotropic non-normality induced linear mechanism of wave generation are found.« less

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

    NASA Astrophysics Data System (ADS)

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

    2017-08-01

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

  1. Dynamics of Aqueous Foam Drops

    NASA Technical Reports Server (NTRS)

    Akhatov, Iskander; McDaniel, J. Gregory; Holt, R. Glynn

    2001-01-01

    We develop a model for the nonlinear oscillations of spherical drops composed of aqueous foam. Beginning with a simple mixture law, and utilizing a mass-conserving bubble-in-cell scheme, we obtain a Rayleigh-Plesset-like equation for the dynamics of bubbles in a foam mixture. The dispersion relation for sound waves in a bubbly liquid is then coupled with a normal modes expansion to derive expressions for the frequencies of eigenmodal oscillations. These eigenmodal (breathing plus higher-order shape modes) frequencies are elicited as a function of the void fraction of the foam. A Mathieu-like equation is obtained for the dynamics of the higher-order shape modes and their parametric coupling to the breathing mode. The proposed model is used to explain recently obtained experimental data.

  2. Dark solitons in laser radiation build-up dynamics.

    PubMed

    Woodward, R I; Kelleher, E J R

    2016-03-01

    We reveal the existence of slowly decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schrödinger equation. The evolution of noise perturbations to quasistationary dark solitons is examined, and the significance of background shape and soliton-soliton collisions on the eventual soliton decay is established. We demonstrate the role of a restoring force in extending soliton interactions in conservative systems to include the effects of dissipation, as encountered in laser cavities, and generalize our observations to other nonlinear systems.

  3. Nonlinear hybridization of the fundamental eigenmodes of microscopic ferromagnetic ellipses.

    PubMed

    Demidov, V E; Buchmeier, M; Rott, K; Krzysteczko, P; Münchenberger, J; Reiss, G; Demokritov, S O

    2010-05-28

    We have studied experimentally with high spatial resolution the nonlinear eigenmodes of microscopic Permalloy elliptical elements. We show that the nonlinearity affects the frequencies of the edge and the center modes in an essentially different way. This leads to repulsion of corresponding resonances and to nonlinear mode hybridization resulting in qualitative modifications of the spatial characteristics of the modes. We find that the nonlinear counterparts of the edge and the center modes simultaneously exhibit features specific for both their linear analogues.

  4. Nature of the wiggle instability of galactic spiral shocks

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kim, Woong-Tae; Kim, Yonghwi; Kim, Jeong-Gyu, E-mail: wkim@astro.snu.ac.kr, E-mail: kimyh@astro.snu.ac.kr, E-mail: jgkim@astro.snu.ac.kr

    Gas in disk galaxies interacts nonlinearly with an underlying stellar spiral potential to form galactic spiral shocks. While numerical simulations typically show that spiral shocks are unstable to wiggle instability (WI) even in the absence of magnetic fields and self-gravity, its physical nature has remained uncertain. To clarify the mechanism behind the WI, we conduct a normal-mode linear stability analysis and nonlinear simulations assuming that the disk is isothermal and infinitesimally thin. We find that the WI is physical, originating from the generation of potential vorticity at a deformed shock front, rather than Kelvin-Helmholtz instabilities as previously thought. Since gasmore » in galaxy rotation periodically passes through the shocks multiple times, the potential vorticity can accumulate successively, setting up a normal mode that grows exponentially with time. Eigenfunctions of the WI decay exponentially downstream from the shock front. Both shock compression of acoustic waves and a discontinuity of shear across the shock stabilize the WI. The wavelength and growth time of the WI depend on the arm strength quite sensitively. When the stellar-arm forcing is moderate at 5%, the wavelength of the most unstable mode is about 0.07 times the arm-to-arm spacing, with the growth rate comparable to the orbital angular frequency, which is found to be in good agreement with the results of numerical simulations.« less

  5. Nonlinear modes of snap-through motions of a shallow arch

    NASA Astrophysics Data System (ADS)

    Breslavsky, I.; Avramov, K. V.; Mikhlin, Yu.; Kochurov, R.

    2008-03-01

    Nonlinear modes of snap-through motions of a shallow arch are analyzed. Dynamics of shallow arch is modeled by a two-degree-of-freedom system. Two nonlinear modes of this discrete system are treated. The methods of Ince algebraization and Hill determinants are used to study stability of nonlinear modes. The analytical results are compared with the data of the numerical simulations.

  6. Characteristic Exponent of Normal and Oblique Rolls in Homeotropically Aligned Nematic Liquid Crystal

    NASA Astrophysics Data System (ADS)

    Saraswati, V.; Nugroho, F.

    2018-04-01

    Soft-mode turbulence (SMT) is one of an experimental example of spatiotemporal chaos, observed in electroconvection system of homeotropically aligned nematic liquid crystal (NLC), due to a non-linear interaction between Nambu-Goldstone mode denoted by the C(r)- director and the convective mode q(r). There are two types of stripe patterns in the SMT, namely normal rolls (NR) and oblique rolls (OR) which separated by a point of applied frequency, called the Lifshitz frequency (f L ). We report a study of the phase transition from normal to oblique rolls by observing the patterns with an applied frequency below and beyond of fL . The temporal fluctuations of the pattern images had been analyzed using autocorrelation function. It fits with Kohlrausch Williams Watts (KWW) function, showing there is a dynamical glass-forming liquid in the transition of NR-OR regime. Also, we found a new type of defect in the NR regime which never been reported before, a dynamic defect which takes the shape of a ring first to a spot in the end.

  7. Effects of Thermal Noise on the Transitional Dynamics of an Inextensible Elastic Filament in Stagnation Flow

    PubMed Central

    Deng, Mingge; Grinberg, Leopold; Caswell, Bruce

    2015-01-01

    We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a Dissipative Particle Dynamics (DPD) method. Unlike previous works1, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance. PMID:26023834

  8. Towards a better understanding of critical gradients and near-marginal turbulence in burning plasma conditions

    NASA Astrophysics Data System (ADS)

    Holland, C.; Candy, J.; Howard, N. T.

    2017-10-01

    Developing accurate predictive transport models of burning plasma conditions is essential for confident prediction and optimization of next step experiments such as ITER and DEMO. Core transport in these plasmas is expected to be very small in gyroBohm-normalized units, such that the plasma should lie close to the critical gradients for onset of microturbulence instabilities. We present recent results investigating the scaling of linear critical gradients of ITG, TEM, and ETG modes as a function of parameters such as safety factor, magnetic shear, and collisionality for nominal conditions and geometry expected in ITER H-mode plasmas. A subset of these results is then compared against predictions from nonlinear gyrokinetic simulations, to quantify differences between linear and nonlinear thresholds. As part of this study, linear and nonlinear results from both GYRO and CGYRO codes will be compared against each other, as well as to predictions from the quasilinear TGLF model. Challenges arising from near-marginal turbulence dynamics are addressed. This work was supported by the US Department of Energy under US DE-SC0006957.

  9. Nonlinear surface elastic modes in crystals

    NASA Astrophysics Data System (ADS)

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

    1990-03-01

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

  10. Principal dynamic mode analysis of neural mass model for the identification of epileptic states

    NASA Astrophysics Data System (ADS)

    Cao, Yuzhen; Jin, Liu; Su, Fei; Wang, Jiang; Deng, Bin

    2016-11-01

    The detection of epileptic seizures in Electroencephalography (EEG) signals is significant for the diagnosis and treatment of epilepsy. In this paper, in order to obtain characteristics of various epileptiform EEGs that may differentiate different states of epilepsy, the concept of Principal Dynamic Modes (PDMs) was incorporated to an autoregressive model framework. First, the neural mass model was used to simulate the required intracerebral EEG signals of various epileptiform activities. Then, the PDMs estimated from the nonlinear autoregressive Volterra models, as well as the corresponding Associated Nonlinear Functions (ANFs), were used for the modeling of epileptic EEGs. The efficient PDM modeling approach provided physiological interpretation of the system. Results revealed that the ANFs of the 1st and 2nd PDMs for the auto-regressive input exhibited evident differences among different states of epilepsy, where the ANFs of the sustained spikes' activity encountered at seizure onset or during a seizure were the most differentiable from that of the normal state. Therefore, the ANFs may be characteristics for the classification of normal and seizure states in the clinical detection of seizures and thus provide assistance for the diagnosis of epilepsy.

  11. Nonlinear Pressurization and Modal Analysis Procedure for Dynamic Modeling of Inflatable Structures

    NASA Technical Reports Server (NTRS)

    Smalley, Kurt B.; Tinker, Michael L.; Saxon, Jeff (Technical Monitor)

    2002-01-01

    An introduction and set of guidelines for finite element dynamic modeling of nonrigidized inflatable structures is provided. A two-step approach is presented, involving 1) nonlinear static pressurization of the structure and updating of the stiffness matrix and 2) hear normal modes analysis using the updated stiffness. Advantages of this approach are that it provides physical realism in modeling of pressure stiffening, and it maintains the analytical convenience of a standard bear eigensolution once the stiffness has been modified. Demonstration of the approach is accomplished through the creation and test verification of an inflated cylinder model using a large commercial finite element code. Good frequency and mode shape comparisons are obtained with test data and previous modeling efforts, verifying the accuracy of the technique. Problems encountered in the application of the approach, as well as their solutions, are discussed in detail.

  12. Nonextensive GES instability with nonlinear pressure effects

    NASA Astrophysics Data System (ADS)

    Gohain, Munmi; Karmakar, Pralay Kumar

    2018-03-01

    We herein analyze the instability dynamics associated with the nonextensive nonthermal gravito-electrostatic sheath (GES) model for the perturbed solar plasma portraiture. The usual neutral gas approximation is herewith judiciously relaxed and the laboratory plasma-wall interaction physics is procedurally incorporated amid barotropic nonlinearity. The main motivation here stems from the true nature of the solar plasma system as a set of concentric nonlocal nonthermal sub-layers as evidenced from different multi-space satellite probes and missions. The formalism couples the solar interior plasma (SIP, bounded) and solar wind plasma (SWP, unbounded) via the diffused solar surface boundary (SSB) formed due to an exact long-range gravito-electrostatic force-equilibration. A linear normal mode ansatz reveals both dispersive and non-dispersive features of the modified GES collective wave excitations. It is seen that the thermostatistical GES stability depends solely on the electron-to-ion temperature ratio. The damping behavior on both the scales is more pronounced in the acoustic domain, K → ∞ , than the gravitational domain, K → 0 ; where, K is the Jeans-normalized angular wave number. It offers a unique quasi-linear coupling of the gravitational and acoustic fluctuations amid the GES force action. The results may be useful to see the excitation dynamics of natural normal modes in bounded nonextensive astero-environs from a new viewpoint of the plasma-wall coupling mechanism.

  13. The nonlinear dynamics of a spacecraft coupled to the vibration of a contained fluid

    NASA Technical Reports Server (NTRS)

    Peterson, Lee D.; Crawley, Edward F.; Hansman, R. John

    1988-01-01

    The dynamics of a linear spacecraft mode coupled to a nonlinear low gravity slosh of a fluid in a cylindrical tank is investigated. Coupled, nonlinear equations of motion for the fluid-spacecraft dynamics are derived through an assumed mode Lagrangian method. Unlike linear fluid slosh models, this nonlinear slosh model retains two fundamental slosh modes and three secondary modes. An approximate perturbation solution of the equations of motion indicates that the nonlinear coupled system response involves fluid-spacecraft modal resonances not predicted by either a linear, or a nonlinear, uncoupled slosh analysis. Experimental results substantiate the analytical predictions.

  14. Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D

    DOE PAGES

    Liu, Feng; Huijsmans, G. T. A.; Loarte, A.; ...

    2015-09-04

    In the Quiescent H-mode (QH-mode) regime, the edge harmonic oscillation (EHO), thought to be a saturated kink-peeling mode (KPM) driven unstable by current and rotation, is found in experiment to provide sufficient stationary edge particle transport to avoid the periodic expulsion of particles and energy by edge localized modes (ELMs). In this article, both linear and nonlinear MHD modelling of QH-mode plasmas from the DIII-D tokamak have been investigated to understand the mechanism leading to the appearance of the EHO in QH-mode plasmas. For the first time nonlinear MHD simulations with low-n modes both with ideal wall and resistive wallmore » boundary conditions have been carried out with 3-D non-linear MHD code JOREK. The results show, in agreement with the original conjectures, that in the nonlinear phase, kink peeling modes are the main unstable modes in QH-mode plasmas of DIIID and that the kink-peeling modes saturate non-linearly leading to a 3-D stationary state. The characteristics of the kink-peeling modes, in terms of mode structure and associated decrease of the edge plasma density associated with them, are in good agreement with experimental measurements of the EHO in DIII-D. Finally, the effect of plasma resistivity, the role of plasma parallel rotation as well as the effect of the conductivity of the vacuum vessel wall on the destabilization and saturation of kink-peeling modes have been evaluated for experimental QH-mode plasma conditions in DIII-D.« less

  15. A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nash, Patrick L.

    2008-01-10

    Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation {delta}{sub perpendicular} {sup FDA} of 1/r ({partial_derivative})/({partial_derivative}r) r({partial_derivative})/({partial_derivative}r) that possesses an associated exact unitary representation of e{sup i/2{lambda}}{sup {delta}{sub perpendicular}{sup FDA}}. The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown tomore » be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium.« less

  16. Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation.

    PubMed

    Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon

    2016-01-25

    Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η(2) for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr's hydrodynamic theory.

  17. Experimental Observation of Bohr’s Nonlinear Fluidic Surface Oscillation

    PubMed Central

    Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon

    2016-01-01

    Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory. PMID:26803911

  18. Immiscible three-dimensional fingering in porous media: A weakly nonlinear analysis

    NASA Astrophysics Data System (ADS)

    Brandão, Rodolfo; Dias, Eduardo O.; Miranda, José A.

    2018-03-01

    We present a weakly nonlinear theory for the development of fingering instabilities that arise at the interface between two immiscible viscous fluids flowing radially outward in a uniform three-dimensional (3D) porous medium. By employing a perturbative second-order mode-coupling scheme, we investigate the linear stability of the system as well as the emergence of intrinsically nonlinear finger branching events in this 3D environment. At the linear stage, we find several differences between the 3D radial fingering and its 2D counterpart (usual Saffman-Taylor flow in radial Hele-Shaw cells). These include the algebraic growth of disturbances and the existence of regions of absolute stability for finite values of viscosity contrast and capillary number in the 3D system. On the nonlinear level, our main focus is to get analytical insight into the physical mechanism resulting in the occurrence of finger tip-splitting phenomena. In this context, we show that the underlying mechanism leading to 3D tip splitting relies on the coupling between the fundamental interface modes and their first harmonics. However, we find that in three dimensions, in contrast to the usual 2D fingering structures normally encountered in radial Hele-Shaw flows, tip splitting into three branches can also be observed.

  19. Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

    NASA Technical Reports Server (NTRS)

    Przekop, Adam; Rizzi, Stephen A.

    2006-01-01

    The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

  20. Nonlinear Reduced Order Random Response Analysis of Structures With Shallow Curvature

    NASA Technical Reports Server (NTRS)

    Przekop, Adam; Rizzi, Stephen A.

    2005-01-01

    The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

  1. Tunable all-fiber dissipative-soliton laser with a multimode interference filter.

    PubMed

    Zhang, Lei; Hu, Jinmeng; Wang, Jianhua; Feng, Yan

    2012-09-15

    We report on a tunable all-fiber dissipative-soliton laser with a multimode interference filter that consists of a multimode fiber spliced between two single-mode fibers. By carefully selecting the fiber parameters, a filter with a central wavelength at 1032 nm and a bandwidth of 7.6 nm is constructed and used for spectral filtering in an all-normal-dispersion mode-locked ytterbium-doped fiber laser based on nonlinear polarization evolution. The laser delivers 31 mW of average output power with positively chirped 7 ps pulses. The repetition rate of the pulses is 15.3 MHz, and pulse energy is 2.1 nJ. Tunable dissipative-soliton over 12 nm is achieved by applying tension to the single-mode-multimode-single-mode filter.

  2. Surface normal coupling to multiple-slot and cover-slotted silicon nanocrystalline waveguides and ring resonators

    NASA Astrophysics Data System (ADS)

    Covey, John; Chen, Ray T.

    2014-03-01

    Grating couplers are ideal for coupling into the tightly confined propagation modes of semiconductor waveguides. In addition, nonlinear optics has benefited from the sub-diffraction limit confinement of horizontal slot waveguides. By combining these two advancements, slot-based nonlinear optics with mode areas less than 0.02 μm2 can become as routine as twisting fiber connectors together. Surface normal fiber alignment to a chip is also highly desirable from time, cost, and manufacturing considerations. To meet these considerable design challenges, a custom genetic algorithm is created which, starting from purely random designs, creates a unique four stage grating coupler for two novel horizontal slot waveguide platforms. For horizontal multiple-slot waveguides filled with silicon nanocrystal, a theoretical fiber-towaveguide coupling efficiency of 68% is obtained. For thin silicon waveguides clad with optically active silicon nanocrystal, known as cover-slot waveguides, a theoretical fiber-to-waveguide coupling efficiency of 47% is obtained, and 1 dB and 3 dB theoretical bandwidths of 70 nm and 150 nm are obtained, respectively. Both waveguide platforms are fabricated from scratch, and their respective on-chip grating couplers are experimentally measured from a standard single mode fiber array that is mounted surface normally. The horizontal multiple-slot grating coupler achieved an experimental 60% coupling efficiency, and the horizontal cover-slot grating coupler achieved an experimental 38.7% coupling efficiency, with an extrapolated 1 dB bandwidth of 66 nm. This report demonstrates the promise of genetic algorithm-based design by reducing to practice the first large bandwidth vertical grating coupler to a novel silicon nanocrystal horizontal cover-slot waveguide.

  3. Amplitude-dependent topological edge states in nonlinear phononic lattices

    NASA Astrophysics Data System (ADS)

    Pal, Raj Kumar; Vila, Javier; Leamy, Michael; Ruzzene, Massimo

    2018-03-01

    This work investigates the effect of nonlinearities on topologically protected edge states in one- and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are inverted copies of each other. Explicit expressions derived for the frequencies of the localized modes guide the study of the effect of cubic nonlinearities on the resonant characteristics of the interface, which are shown to be described by a Duffing-like equation. Nonlinearities produce amplitude-dependent frequency shifts, which in the case of a softening nonlinearity cause the localized mode to migrate to the bulk spectrum. The case of a hexagonal lattice implementing a phononic analog of a crystal exhibiting the quantum spin Hall effect is also investigated in the presence of weakly nonlinear cubic springs. An asymptotic analysis provides estimates of the amplitude dependence of the localized modes, while numerical simulations illustrate how the lattice response transitions from bulk-to-edge mode-dominated by varying the excitation amplitude. In contrast with the interface mode of the first example studies, this occurs both for hardening and softening springs. The results of this study provide a theoretical framework for the investigation of nonlinear effects that induce and control topologically protected wave modes through nonlinear interactions and amplitude tuning.

  4. Nonlinear interaction in differential mode delay managed mode-division multiplexed transmission systems.

    PubMed

    Rademacher, Georg; Warm, Stefan; Petermann, Klaus

    2015-01-12

    We analyze the impact of Differential Mode Delay (DMD) Management on the nonlinear impairments in mode-division multiplexed transmission systems. It is found out that DMD Management can lead to a degraded performance, due to enhanced intermodal nonlinear interaction. This can be attributed to an increased correlation of co-propagating channels, similar to the effects that show up in dispersion managed single-mode systems.

  5. Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

    NASA Astrophysics Data System (ADS)

    Saksida, Pavle

    2018-01-01

    We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

  6. Nonlinear dynamics and control of a vibrating rectangular plate

    NASA Technical Reports Server (NTRS)

    Shebalin, J. V.

    1983-01-01

    The von Karman equations of nonlinear elasticity are solved for the case of a vibrating rectangular plate by meams of a Fourier spectral transform method. The amplification of a particular Fourier mode by nonlinear transfer of energy is demonstrated for this conservative system. The multi-mode system is reduced to a minimal (two mode) system, retaining the qualitative features of the multi-mode system. The effect of a modal control law on the dynamics of this minimal nonlinear elastic system is examined.

  7. Pulse generation without gain-bandwidth limitation in a laser with self-similar evolution.

    PubMed

    Chong, A; Liu, H; Nie, B; Bale, B G; Wabnitz, S; Renninger, W H; Dantus, M; Wise, F W

    2012-06-18

    With existing techniques for mode-locking, the bandwidth of ultrashort pulses from a laser is determined primarily by the spectrum of the gain medium. Lasers with self-similar evolution of the pulse in the gain medium can tolerate strong spectral breathing, which is stabilized by nonlinear attraction to the parabolic self-similar pulse. Here we show that this property can be exploited in a fiber laser to eliminate the gain-bandwidth limitation to the pulse duration. Broad (∼200 nm) spectra are generated through passive nonlinear propagation in a normal-dispersion laser, and these can be dechirped to ∼20-fs duration.

  8. Magnetotail dynamics under isobaric constraints

    NASA Technical Reports Server (NTRS)

    Birn, Joachim; Schindler, Karl; Janicke, Lutz; Hesse, Michael

    1994-01-01

    Using linear theory and nonlinear MHD simulations, we investigate the resistive and ideal MHD stability of two-dimensional plasma configurations under the isobaric constraint dP/dt = 0, which in ideal MHD is equivalent to conserving the pressure function P = P(A), where A denotes the magnetic flux. This constraint is satisfied for incompressible modes, such as Alfven waves, and for systems undergoing energy losses. The linear stability analysis leads to a Schroedinger equation, which can be investigated by standard quantum mechanics procedures. We present an application to a typical stretched magnetotail configuration. For a one-dimensional sheet equilibrium characteristic properties of tearing instability are rediscovered. However, the maximum growth rate scales with the 1/7 power of the resistivity, which implies much faster growth than for the standard tearing mode (assuming that the resistivity is small). The same basic eigen-mode is found also for weakly two-dimensional equilibria, even in the ideal MHD limit. In this case the growth rate scales with the 1/4 power of the normal magnetic field. The results of the linear stability analysis are confirmed qualitatively by nonlinear dynamic MHD simulations. These results suggest the interesting possibility that substorm onset, or the thinning in the late growth phase, is caused by the release of a thermodynamic constraint without the (immediate) necessity of releasing the ideal MHD constraint. In the nonlinear regime the resistive and ideal developments differ in that the ideal mode does not lead to neutral line formation without the further release of the ideal MHD constraint; instead a thin current sheet forms. The isobaric constraint is critically discussed. Under perhaps more realistic adiabatic conditions the ideal mode appears to be stable but could be driven by external perturbations and thus generate the thin current sheet in the late growth phase, before a nonideal instability sets in.

  9. Nonlinear optical whispering gallery mode resonators

    NASA Technical Reports Server (NTRS)

    Ilchenko, Vladimir (Inventor); Matsko, Andrey B. (Inventor); Savchenkov, Anatoliy (Inventor); Maleki, Lutfollah (Inventor)

    2005-01-01

    Whispering gallery mode (WGM) optical resonators comprising nonlinear optical materials, where the nonlinear optical material of a WGM resonator includes a plurality of sectors within the optical resonator and nonlinear coefficients of two adjacent sectors are oppositely poled.

  10. Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades

    NASA Technical Reports Server (NTRS)

    Subrahmanyam, K. B.; Kaza, K. R. V.

    1986-01-01

    The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.

  11. Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

    NASA Technical Reports Server (NTRS)

    Tkalcevic, S.

    1982-01-01

    The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.

  12. Symmetry properties of second harmonics generated by antisymmetric Lamb waves

    NASA Astrophysics Data System (ADS)

    Zhu, Wujun; Xiang, Yanxun; Liu, Chang-Jun; Deng, Mingxi; Xuan, Fu-Zhen

    2018-03-01

    Symmetry properties of second harmonics generated by antisymmetric primary Lamb waves are systematically studied in this work. In theory, the acoustic field of second harmonic Lamb waves is obtained by using the perturbation approximation and normal modal method, and the energy flux transfer from the primary Lamb waves to second harmonics is mainly explored. Symmetry analyses indicate that either the symmetric or antisymmetric Lamb waves can merely generate the symmetric second harmonics. Finite element simulations are performed on the nonlinear Lamb wave propagation of the antisymmetric A0 mode in the low frequency region. The signals of the second harmonics and the symmetric second harmonic s0 mode are found to be exactly equivalent in the time domain. The relative acoustic nonlinearity parameter A2/A12 oscillates with the propagation distance, and the oscillation amplitude and spatial period are well consistent with the theoretical prediction of the A0-s0 mode pair, which means that only the second harmonic s0 mode is generated by the antisymmetric primary A0 mode. Experiments are further conducted to examine the cumulative generation of symmetric second harmonics for the antisymmetric-symmetric mode pair A3-s6. Results show that A2/A12 increases linearly with the propagation distance, which means that the symmetric second harmonic s6 mode is generated cumulatively by the antisymmetric primary A3 mode. The present investigation systematically corroborates the proposed theory that only symmetric second harmonics can be generated accompanying the propagation of antisymmetric primary Lamb waves in a plate.

  13. A femtosecond Yb-doped fiber laser with generalized vector vortex beams output (Conference Presentation)

    NASA Astrophysics Data System (ADS)

    Huo, Tiancheng; Qi, Li; Zhang, Buyun; Chen, Zhongping

    2017-03-01

    Light carries both spin and orbital angular momentum (OAM) and the superpositions of these two dynamical properties have found many applications. Many techniques exist to create such light sources but none allow their creation at the femtosecond fiber laser. Here we report on a novel mode-locked Ytterbium-doped fiber laser that generates femtosecond pulses with generalized vector vortex states. The controlled generation of such pulses such as azimuthally and radially polarized light with definite orbital angular momentum modes are demonstrated. A unidirectional ring cavity constructed with the Yb-doped fiber placed at the end of the fiber section to reduces unnecessary nonlinear effects is employed for self-starting operation. Pairs of diffraction gratings are used for compensating the normal group velocity dispersion of the fiber and other elements. Mode-locked operation is achieved based on nonlinear polarization evolution, which is mainly implemented with the single mode fiber, the bulk wave plates and the variable spiral plates (q-plate with topological charge q=0.5). The conversion from spin angular momentum to the OAM and reverse inside the laser cavity are realized by means of a quarter-wave plate and a q-plate so that the polarization control was mapped to OAM mode control. The fiber laser is diode pumped by a wavelength-division multiplexing coupler, which leads to excellent stability and portability.

  14. Delocalized periodic vibrations in nonlinear LC and LCR electrical chains

    NASA Astrophysics Data System (ADS)

    Chechin, G. M.; Shcherbinin, S. A.

    2015-05-01

    We consider electrical LC- and LCR-chains consisting of N cells. In the LC-chain each cell contains a linear inductor L and a nonlinear capacitor C, while the cell in the LCR-chain include additionally a resistor R and an voltage source. It is assumed that voltage dependence of capacitors represents an even function. Such capacitors have implemented by some experimental groups studying propagation of electrical signals in the lines constructed on MOS and CMOS substrates. In these chains, we study dynamical regimes representing nonlinear normal modes (NNMs) by Rosenberg. We prove that maximum possible number of symmetry-determined NNMs which can be excited in the considered chains is equal to 5. The stability of these modes for different N is studied with the aid of the group-theoretical method [Physical Review E 73 (2006) 36216] which allows to simplify radically the variational systems appearing in the Floquet stability analysis. For NNMs in LC-chain, the scaling of the voltage stability threshold in the thermodynamic limit (N → ∞) is determined. It is shown that the above group theoretical method can be also used for studying stability of NNMs in the LCR-chains.

  15. A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes

    NASA Astrophysics Data System (ADS)

    Ferhatoglu, Erhan; Cigeroglu, Ender; Özgüven, H. Nevzat

    2018-07-01

    In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the nonlinear system is bounded by the confinement of these linear systems. In this study, a modal superposition method utilizing novel hybrid mode shapes which are defined as linear combinations of the modal vectors of the limiting linear systems is proposed to determine periodic response of nonlinear systems. In this method the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system. This provides decrease of the number of modes that should be retained for an accurate solution, which in turn reduces the number of nonlinear equations to be solved. In this way, computational time for response calculation is directly curtailed. In the solution, the equations of motion are converted to a set of nonlinear algebraic equations by using describing function approach, and the numerical solution is obtained by using Newton's method with arc-length continuation. The method developed is applied on two different systems: a lumped parameter model and a finite element model. Several case studies are performed and the accuracy and computational efficiency of the proposed modal superposition method with hybrid mode shapes are compared with those of the classical modal superposition method which utilizes the mode shapes of the underlying linear system.

  16. Optimal second order sliding mode control for nonlinear uncertain systems.

    PubMed

    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. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  17. Magnetic Helicity of Alfven Simple Waves

    NASA Technical Reports Server (NTRS)

    Webb, Gary M.; Hu, Q.; Dasgupta, B.; Zank, G. P.; Roberts, D.

    2010-01-01

    The magnetic helicity of fully nonlinear, multi-dimensional Alfven simple waves are investigated, by using relative helicity formulae and also by using an approach involving poloidal and toroidal decomposition of the magnetic field and magnetic vector potential. Different methods to calculate the magnetic vector potential are used, including the homotopy and Biot-Savart formulas. Two basic Alfven modes are identified: (a) the plane 1D Alfven simple wave given in standard texts, in which the Alfven wave propagates along the z-axis, with wave phase varphi=k_0(z-lambda t), where k_0 is the wave number and lambda is the group velocity of the wave, and (b)\\ the generalized Barnes (1976) simple Alfven wave in which the wave normal {bf n} moves in a circle in the xy-plane perpendicular to the mean field, which is directed along the z-axis. The plane Alfven wave (a) is analogous to the slab Alfven mode and the generalized Barnes solution (b) is analogous to the 2D mode in Alfvenic, incompressible turbulence. The helicity characteristics of these two basic Alfven modes are distinct. The helicity characteristics of more general multi-dimensional simple Alfven waves are also investigated. Applications to nonlinear Aifvenic fluctuations and structures observed in the solar wind are discussed.

  18. A minimization principle for the description of modes associated with finite-time instabilities

    PubMed Central

    Babaee, H.

    2016-01-01

    We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have finite lifetime, they can play a crucial role either by altering the system dynamics through the activation of other instabilities or by creating sudden nonlinear energy transfers that lead to extreme responses. However, their essentially transient character makes their description a particularly challenging task. We develop a minimization framework that focuses on the optimal approximation of the system dynamics in the neighbourhood of the system state. This minimization formulation results in differential equations that evolve a time-dependent basis so that it optimally approximates the most unstable directions. We demonstrate the capability of the method for two families of problems: (i) linear systems, including the advection–diffusion operator in a strongly non-normal regime as well as the Orr–Sommerfeld/Squire operator, and (ii) nonlinear problems, including a low-dimensional system with transient instabilities and the vertical jet in cross-flow. We demonstrate that the time-dependent subspace captures the strongly transient non-normal energy growth (in the short-time regime), while for longer times the modes capture the expected asymptotic behaviour. PMID:27118900

  19. Energy transfer in mesoscopic vibrational systems enabled by eigenfrequency fluctuations

    NASA Astrophysics Data System (ADS)

    Atalaya, Juan

    Energy transfer between low-frequency vibrational modes can be achieved by means of nonlinear coupling if their eigenfrequencies fulfill certain nonlinear resonance conditions. Because of the discreteness of the vibrational spectrum at low frequencies, such conditions may be difficult to satisfy for most low-frequency modes in typical mesoscopic vibrational systems. Fluctuations of the vibrational eigenfrequencies can also be relatively strong in such systems. We show that energy transfer between modes can occur in the absence of nonlinear resonance if frequency fluctuations are allowed. The case of three modes with cubic nonlinear coupling and no damping is particularly interesting. It is found that the system has a non-thermal equilibrium state which depends only on the initial conditions. The rate at which the system approaches to such state is determined by the parameters such as the noise strength and correlation time, the nonlinearity strength and the detuning from exact nonlinear resonance. We also discuss the case of many weakly coupled modes. Our results shed light on the problem of energy relaxation of low-frequency vibrational modes into the continuum of high-frequency vibrational modes. The results have been obtained with Mark Dykman. Alternative email: jatalaya2012@gmail.com.

  20. Effect of P T symmetry on nonlinear waves for three-wave interaction models in the quadratic nonlinear media

    NASA Astrophysics Data System (ADS)

    Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao

    2018-04-01

    We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.

  1. Analysis of calibration data for the uranium active neutron coincidence counting collar with attention to errors in the measured neutron coincidence rate

    DOE PAGES

    Croft, Stephen; Burr, Thomas Lee; Favalli, Andrea; ...

    2015-12-10

    We report that the declared linear density of 238U and 235U in fresh low enriched uranium light water reactor fuel assemblies can be verified for nuclear safeguards purposes using a neutron coincidence counter collar in passive and active mode, respectively. The active mode calibration of the Uranium Neutron Collar – Light water reactor fuel (UNCL) instrument is normally performed using a non-linear fitting technique. The fitting technique relates the measured neutron coincidence rate (the predictor) to the linear density of 235U (the response) in order to estimate model parameters of the nonlinear Padé equation, which traditionally is used to modelmore » the calibration data. Alternatively, following a simple data transformation, the fitting can also be performed using standard linear fitting methods. This paper compares performance of the nonlinear technique to the linear technique, using a range of possible error variance magnitudes in the measured neutron coincidence rate. We develop the required formalism and then apply the traditional (nonlinear) and alternative approaches (linear) to the same experimental and corresponding simulated representative datasets. Lastly, we find that, in this context, because of the magnitude of the errors in the predictor, it is preferable not to transform to a linear model, and it is preferable not to adjust for the errors in the predictor when inferring the model parameters« less

  2. NONLINEAR AND FIBER OPTICS: Influence of nonlinearity of the parameters of guided modes in fiber waveguides

    NASA Astrophysics Data System (ADS)

    Goncharenko, I. A.

    1990-04-01

    The shift formula method is used to obtain analytic expressions which provide estimates of the influence of nonlinearity on the parameters of fiber waveguide modes. Depending on the sign of the nonlinear susceptibility of the waveguide core, the nonlinearity can improve or impair (right down to complete loss) the waveguiding properties of fibers. The optical power at which a fiber loses its guiding properties is constant far from the cutoff, but rises steeply near the critical cutoff frequency. The nonlinearity can be used to vary the zero dispersion wavelength and the range of single-mode operation of a fiber waveguide.

  3. Identification of Dynamic Patterns of Speech-Evoked Auditory Brainstem Response Based on Ensemble Empirical Mode Decomposition and Nonlinear Time Series Analysis Methods

    NASA Astrophysics Data System (ADS)

    Mozaffarilegha, Marjan; Esteki, Ali; Ahadi, Mohsen; Nazeri, Ahmadreza

    The speech-evoked auditory brainstem response (sABR) shows how complex sounds such as speech and music are processed in the auditory system. Speech-ABR could be used to evaluate particular impairments and improvements in auditory processing system. Many researchers used linear approaches for characterizing different components of sABR signal, whereas nonlinear techniques are not applied so commonly. The primary aim of the present study is to examine the underlying dynamics of normal sABR signals. The secondary goal is to evaluate whether some chaotic features exist in this signal. We have presented a methodology for determining various components of sABR signals, by performing Ensemble Empirical Mode Decomposition (EEMD) to get the intrinsic mode functions (IMFs). Then, composite multiscale entropy (CMSE), the largest Lyapunov exponent (LLE) and deterministic nonlinear prediction are computed for each extracted IMF. EEMD decomposes sABR signal into five modes and a residue. The CMSE results of sABR signals obtained from 40 healthy people showed that 1st, and 2nd IMFs were similar to the white noise, IMF-3 with synthetic chaotic time series and 4th, and 5th IMFs with sine waveform. LLE analysis showed positive values for 3rd IMFs. Moreover, 1st, and 2nd IMFs showed overlaps with surrogate data and 3rd, 4th and 5th IMFs showed no overlap with corresponding surrogate data. Results showed the presence of noisy, chaotic and deterministic components in the signal which respectively corresponded to 1st, and 2nd IMFs, IMF-3, and 4th and 5th IMFs. While these findings provide supportive evidence of the chaos conjecture for the 3rd IMF, they do not confirm any such claims. However, they provide a first step towards an understanding of nonlinear behavior of auditory system dynamics in brainstem level.

  4. Nonlinear cellular dynamics of keratinocytes in normal and psoriatic epidermis under action of UV radiation

    NASA Astrophysics Data System (ADS)

    Stolnitz, Mikhail M.; Medvedev, Boris A.; Gribko, Tatyana V.

    2004-05-01

    The semi-phenomenological model of epidermal cell dynamics is submitted. The model takes into account three types of basal layer keratinocytes (stem, transient amplifying, terminally differentiated), distribution of first two types cells on mitotic cycle stages and resting states, keratinocytes-lymphocytes interactions that provide a positive feedback loop, influence of more differentiated cells on their progenitors that provide a negative feedback loop. Simplified model are developed and its stationary solutions are received. The opportunity of interpretation of some received modes as corresponding to various stages of psoriasis is discussed. Influence of UV-radiation on transitions between various modes of epidermis functioning is qualitatively analyzed.

  5. Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

    PubMed Central

    Mitran, Sorin M.; Forest, M. Gregory; Yao, Lingxing; Lindley, Brandon; Hill, David B.

    2009-01-01

    The classical oscillatory shear wave model of Ferry et al. [J. Polym. Sci. 2:593-611, (1947)] is extended for active linear and nonlinear microrheology. In the Ferry protocol, oscillation and attenuation lengths of the shear wave measured from strobe photographs determine storage and loss moduli at each frequency of plate oscillation. The microliter volumes typical in biology require modifications of experimental method and theory. Microbead tracking replaces strobe photographs. Reflection from the top boundary yields counterpropagating modes which are modeled here for linear and nonlinear viscoelastic constitutive laws. Furthermore, bulk imposed strain is easily controlled, and we explore the onset of normal stress generation and shear thinning using nonlinear viscoelastic models. For this paper, we present the theory, exact linear and nonlinear solutions where possible, and simulation tools more generally. We then illustrate errors in inverse characterization by application of the Ferry formulas, due to both suppression of wave reflection and nonlinearity, even if there were no experimental error. This shear wave method presents an active and nonlinear analog of the two-point microrheology of Crocker et al. [Phys. Rev. Lett. 85: 888 - 891 (2000)]. Nonlocal (spatially extended) deformations and stresses are propagated through a small volume sample, on wavelengths long relative to bead size. The setup is ideal for exploration of nonlinear threshold behavior. PMID:20011614

  6. Monolithic integration of active and second-order nonlinear functionality in Bragg reflection waveguides

    NASA Astrophysics Data System (ADS)

    Bijlani, Bhavin J.

    2011-07-01

    This thesis explored the theory, design, fabrication and characterization of AlGaAs Bragg reflection waveguides (BRW) towards the goal of a platform for monolithic integration of active and optically nonlinear devices. Through integration of a diode laser and nonlinear phase-matched cavity, the possibility of on-chip nonlinear frequency generation was explored. Such integrated devices would be highly useful as a robust, alignment free, small footprint and electrically injected alternative to bulk optic systems. A theoretical framework for modal analysis of arbitrary 1-D photonic crystal defect waveguides is developed. This method relies on the transverse resonance condition. It is then demonstrated in the context of several types of Bragg reflection waveguides. The framework is then extended to phase-match second-order nonlinearities and incorporating quantum-wells for diode lasers. Experiments within a slab and ridge waveguide demonstrated phase-matched Type-I second harmonic generation at fundamental wavelength of 1587 and 1600 nm, respectively; a first for this type of waveguide. For the slab waveguide, conversion efficiency was 0.1 %/W. In the more strongly confined ridge waveguides, efficiency increased to 8.6 %/W owing to the increased intensity. The normalized conversion efficiency was estimated to be at 600 %/Wcm2. Diode lasers emitting at 980 nm in the BRW mode were also fabricated. Verification of the Bragg mode was performed through imaging the near- field of the mode. Propagation loss of this type of mode was measured directly for the first time at ≈ 14 cm-1. The lasers were found to be very insensitive with characteristic temperature at 215 K. Two designs incorporating both laser and phase-matched nonlinearity within the same cavity were fabricated, for degenerate and non-degenerate down-conversion. Though the lasers were sub-optimal, a parametric fluorescence signal was readily detected. Fluorescence power as high as 4 nW for the degenerate design and 5 nW for the non-degenerate design were detected. The conversion efficiency was 4176 %/Wcm2 and 874 %/Wcm2, respectively. Neither design was found to emit near the design wavelength. In general, the signal is between 1600-1800 nm and the idler is between 2200-2400 nm. Improvements in laser performance are expected to drastically increase the conversion efficiency.

  7. Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems.

    PubMed

    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. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

  8. Nonlinear Decay of Alfvén Waves Driven by Interplaying Two- and Three-dimensional Nonlinear Interactions

    NASA Astrophysics Data System (ADS)

    Zhao, J. S.; Voitenko, Y.; De Keyser, J.; Wu, D. J.

    2018-04-01

    We study the decay of Alfvén waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfvén and slow waves. These interactions have previously been studied separately in long- and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfvén waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 × 10‑4 ≲ ρ i k 0⊥ ≲ 1, where the decay is essentially 3D and nonlocal, generating product Alfvén and slow waves around the ion gyroscale. Here ρ i is the ion gyroradius, and k 0⊥ is the pump Alfvén wavenumber. It appears that, except for the smallest wavenumbers at and below {ρ }i{k}0\\perp ∼ {10}-4 in Channel I, the nonlinear decay of magnetohydrodynamic Alfvén waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfvén waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfvén waves can still be approximately described as normal Alfvénic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    White, A. E., E-mail: whitea@mit.edu; Howard, N. T.; Creely, A. J.

    2015-05-15

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

  10. Escape time, relaxation, and sticky states of a softened Henon-Heiles model: Low-frequency vibrational mode effects and glass relaxation

    NASA Astrophysics Data System (ADS)

    Toledo-Marín, J. Quetzalcóatl; Naumis, Gerardo G.

    2018-04-01

    Here we study the relaxation of a chain consisting of three masses joined by nonlinear springs and periodic conditions when the stiffness is weakened. This system, when expressed in their normal coordinates, yields a softened Henon-Heiles system. By reducing the stiffness of one low-frequency vibrational mode, a faster relaxation is enabled. This is due to a reduction of the energy barrier heights along the softened normal mode as well as for a widening of the opening channels of the energy landscape in configurational space. The relaxation is for the most part exponential, and can be explained by a simple flux equation. Yet, for some initial conditions the relaxation follows as a power law, and in many cases there is a regime change from exponential to power-law decay. We pinpoint the initial conditions for the power-law decay, finding two regions of sticky states. For such states, quasiperiodic orbits are found since almost for all components of the initial momentum orientation, the system is trapped inside two pockets of configurational space. The softened Henon-Heiles model presented here is intended as the simplest model in order to understand the interplay of rigidity, nonlinear interactions and relaxation for nonequilibrium systems such as glass-forming melts or soft matter. Our softened system can be applied to model β relaxation in glasses and suggest that local reorientational jumps can have an exponential and a nonexponential contribution for relaxation, the latter due to asymmetric molecules sticking in cages for certain orientations.

  11. The Effect of Basis Selection on Static and Random Acoustic Response Prediction Using a Nonlinear Modal Simulation

    NASA Technical Reports Server (NTRS)

    Rizzi, Stephen A.; Przekop, Adam

    2005-01-01

    An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.

  12. Nonlinear dynamics of toroidal Alfvén eigenmodes in presence of tearing modes

    NASA Astrophysics Data System (ADS)

    Zhu, Jia; Ma, Zhiwei; Wang, Sheng; Zhang, Wei

    2016-10-01

    A new hybrid kinetic-MHD code CLT-K is developed to study nonlinear dynamics of n =1 toroidal Alfvén eigenmodes (TAEs) with the m/n =2/1 tearing mode. It is found that the n =1 TAE is first excited by isotropic energetic particles in the earlier stage and reaches the steady state due to wave-particle interaction. After the saturation of the n =1 TAE, the tearing mode intervenes and triggers the second growth of the mode. The modes goes into the second steady state due to multiple tearing mode-mode nonlinear coupling. Both wave-particle and wave-wave interactions are observed in our hybrid simulation.

  13. Nonlinear characterization of a bolted, industrial structure using a modal framework

    NASA Astrophysics Data System (ADS)

    Roettgen, Daniel R.; Allen, Matthew S.

    2017-02-01

    This article presents measurements from a sub assembly of an off-the-shelf automotive exhaust system containing a bolted-flange connection and uses a recently proposed modal framework to develop a nonlinear dynamic model for the structure. The nonlinear identification and characterization methods used are reviewed to highlight the strengths of the current approach and the areas where further development is needed. This marks the first use of these new testing and nonlinear identification tools, and the associated modal framework, on production hardware with a realistic joint and realistic torque levels. To screen the measurements for nonlinearities, we make use of a time frequency analysis routine designed for transient responses called the zeroed early-time fast Fourier transform (ZEFFT). This tool typically reveals the small frequency shifts and distortions that tend to occur near each mode that is affected by the nonlinearity. The damping in this structure is found to be significantly nonlinear and a Hilbert transform is used to characterize the damping versus amplitude behavior. A model is presented that captures these effects for each mode individually (e.g. assuming negligible nonlinear coupling between modes), treating each mode as a single degree-of-freedom oscillator with a spring and viscous damping element in parallel with a four parameter Iwan model. The parameters of this model are identified for each of the structure's modes that exhibited nonlinearity and the resulting nonlinear model is shown to capture the stiffness and damping accurately over a large range of response amplitudes.

  14. Distributed Adaptive Containment Control for a Class of Nonlinear Multiagent Systems With Input Quantization.

    PubMed

    Wang, Chenliang; Wen, Changyun; Hu, Qinglei; Wang, Wei; Zhang, Xiuyu

    2018-06-01

    This paper is devoted to distributed adaptive containment control for a class of nonlinear multiagent systems with input quantization. By employing a matrix factorization and a novel matrix normalization technique, some assumptions involving control gain matrices in existing results are relaxed. By fusing the techniques of sliding mode control and backstepping control, a two-step design method is proposed to construct controllers and, with the aid of neural networks, all system nonlinearities are allowed to be unknown. Moreover, a linear time-varying model and a similarity transformation are introduced to circumvent the obstacle brought by quantization, and the controllers need no information about the quantizer parameters. The proposed scheme is able to ensure the boundedness of all closed-loop signals and steer the containment errors into an arbitrarily small residual set. The simulation results illustrate the effectiveness of the scheme.

  15. Dissipative vector soliton in a dispersion-managed fiber laser with normal dispersion.

    PubMed

    Wang, Siming; Fan, Xuliang; Zhao, Luming; Wang, Yong; Tang, Dingyuan; Shen, Deyuan

    2014-12-10

    We numerically study the vector dynamics of dissipative solitons (DSs) in a 2 μm dispersion-managed fiber laser mode locked by a semiconductor saturable absorber mirror and operated in the normal dispersion regime. It is shown that the effective gain bandwidth is crucial for the DS generation. The steep spectral edges of DSs are the consequence of the interaction among the normal dispersion, fiber nonlinearity, gain and loss, and gain dispersion effect, etc. We numerically duplicate the experimental results and further explore the vector features of the generated DSs. Two DSs formed along the two orthogonal polarization directions which, incoherently coupled with each other, could propagate in the birefringent cavity with the same group velocity.

  16. Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios

    NASA Astrophysics Data System (ADS)

    Liu, F.; Huijsmans, G. T. A.; Loarte, A.; Garofalo, A. M.; Solomon, W. M.; Hoelzl, M.; Nkonga, B.; Pamela, S.; Becoulet, M.; Orain, F.; Van Vugt, D.

    2018-01-01

    In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated kink-peeling mode. The features of the dominant saturated KPMs, which are localised toroidally by nonlinear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the edge harmonic oscillation typically present in DIII-D QH-mode experiments. The nonlinear evolution of MHD modes including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E × B flow and its shear on the QH-mode plasma has been investigated. E × B flow shear has a strong stabilisation effect on the medium to high-n modes but is destabilising for the n = 2 mode. The QH-mode extrapolation results of an ITER Q = 10 plasma show that the pedestal currents are large enough to destabilise n = 1-5 KPMs, leading to a stationary saturated kink-peeling mode.

  17. Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method

    NASA Technical Reports Server (NTRS)

    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.

  18. All-Optical Control of Linear and Nonlinear Energy Transfer via the Zeno Effect

    NASA Astrophysics Data System (ADS)

    Guo, Xiang; Zou, Chang-Ling; Jiang, Liang; Tang, Hong X.

    2018-05-01

    Microresonator-based nonlinear processes are fundamental to applications including microcomb generation, parametric frequency conversion, and harmonics generation. While nonlinear processes involving either second- (χ(2 )) or third- (χ(3 )) order nonlinearity have been extensively studied, the interaction between these two basic nonlinear processes has seldom been reported. In this paper we demonstrate a coherent interplay between second- and third- order nonlinear processes. The parametric (χ(2 ) ) coupling to a lossy ancillary mode shortens the lifetime of the target photonic mode and suppresses its density of states, preventing the photon emissions into the target photonic mode via the Zeno effect. Such an effect is then used to control the stimulated four-wave mixing process and realize a suppression ratio of 34.5.

  19. Elastic Nonlinear Response in Granular Media Under Resonance Conditions

    NASA Astrophysics Data System (ADS)

    Jia, X.; Johnson, P. A.

    2004-12-01

    We are studying the elastic linear and nonlinear behavior of granular media using dynamic wave methods. In the work presented here, our goal is to quantify the elastic nonlinear response by applying wave resonance. Resonance studies are desirable because they provide the means to easily study amplitude dependencies of elastic nonlinear behavior and thus to characterize the physical nature of the elastic nonlinearity. This work has implications for a variety of topics, in particular, the in situ nonlinear response of surface sediments. For this work we constructed an experimental cell in which high sensitivity dynamic resonance studies were conducted using granular media under controlled effective pressure. We limit our studies here to bulk modes but have the capability to employ shear waves as well. The granular media are composed of glass beads held under pressure by a piston, while applying resonance waves from transducers as both the excitation and the material probe. The container is closed with two fitted pistons and a normal load is applied to the granular sample across the top piston. Force and displacement are measured directly. Resonant frequency sweeps with frequencies corresponding to the fundamental bulk mode are applied to the longitudinal source transducer. The pore pressure in the system is 1 atm. The glass beads used in our experiments are of diameter 0.5 mm, randomly deposited in a duralumin cylinder of diameter 30 mm and height of 15 mm. This corresponds to a granular skeleton acoustic wave velocity of v ª 750m/s under 50 N of force [0.07 Mpa]. The loaded system gives fundamental mode resonances in the audio frequency band at half a wavelength where resonance frequency is effective-pressure dependent. The volume fraction of glass beads thus obtained is found to be 0.63 ± 0.01. Plane-wave generating and detecting transducers of diameter 30 mm are placed on axis at the top and bottom of the cylindrical container in direct contact with the glass beads. The wave signals are detected using a lock-in amplifier, and frequency and amplitude are recorded on computer. Drive frequency is swept from below to above the resonance mode. A typical frequency sweep is 3 kHz in width with a frequency sampling of 6 Hz. Frequency sweeps are applied at progressively increasing drive voltages to test for nonlinear-dynamical induced modulus softening. The resonance frequency at peak amplitude corresponds directly to modulus. We find significant elastic nonlinearity at all effective pressures, manifest by the fundamental-mode resonance curves decreasing progressively, at progressively increasing drive level. This is equivalent to progressive material softening with wave amplitude, meaning the wavespeed and modulus diminish. The wave dissipation simultaneously increases (Johnson and Sutin 2004). For example, at 0.11 Mpa effective pressure the observed change in resonance frequency of about 2.6% corresponds to a material bulk modulus decrease of about 5.2%. Strain amplitudes are 10-7-10-6. Thus, we would predict that surface sediments should have significant elastic nonlinear response beginning at about 10-6 strain amplitude. reference: Johnson, P. and A. Sutin, Slow dynamics in diverse solids, J. Acoust. Soc Am., in press (2004).

  20. Research on the Diesel Engine with Sliding Mode Variable Structure Theory

    NASA Astrophysics Data System (ADS)

    Ma, Zhexuan; Mao, Xiaobing; Cai, Le

    2018-05-01

    This study constructed the nonlinear mathematical model of the diesel engine high-pressure common rail (HPCR) system through two polynomial fitting which was treated as a kind of affine nonlinear system. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for affine nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrated that sliding-mode variable structure control algorithm shows favourable control performances which are overcoming the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

  1. Ytterbium-doped fiber laser passively mode locked by few-layer Molybdenum Disulfide (MoS2) saturable absorber functioned with evanescent field interaction

    PubMed Central

    Du, Juan; Wang, Qingkai; Jiang, Guobao; Xu, Changwen; Zhao, Chujun; Xiang, Yuanjiang; Chen, Yu; Wen, Shuangchun; Zhang, Han

    2014-01-01

    By coupling few-layer Molybdenum Disulfide (MoS2) with fiber-taper evanescent light field, a new type of MoS2 based nonlinear optical modulating element had been successfully fabricated as a two-dimensional layered saturable absorber with strong light-matter interaction. This MoS2-taper-fiber device is not only capable of passively mode-locking an all-normal-dispersion ytterbium-doped fiber laser and enduring high power laser excitation (up to 1 W), but also functions as a polarization sensitive optical modulating component (that is, different polarized light can induce different nonlinear optical response). Thanks to the combined advantages from the strong nonlinear optical response in MoS2 together with the sufficiently-long-range interaction between light and MoS2, this device allows for the generation of high power stable dissipative solitons at 1042.6 nm with pulse duration of 656 ps and a repetition rate of 6.74 MHz at a pump power of 210 mW. Our work may also constitute the first example of MoS2-enabled wave-guiding photonic device, and potentially give some new insights into two-dimensional layered materials related photonics. PMID:25213108

  2. When linear stability does not exclude nonlinear instability

    DOE PAGES

    Kevrekidis, P. G.; Pelinovsky, D. E.; Saxena, A.

    2015-05-29

    We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. In this study, this instability is due to the nonlinearity-induced coupling of the linearization’s internal modes of negative energy with the continuous spectrum. In a broad class of nonlinear Schrödinger equations considered, the presence of such internal modes guarantees the nonlinear instability of the stationary states in the evolution dynamics. To corroborate this idea, we explore three prototypical case examples: (a) an antisymmetric soliton in a double-well potential, (b) a twisted localized mode in a one-dimensionalmore » lattice with cubic nonlinearity, and (c) a discrete vortex in a two-dimensional saturable lattice. In all cases, we observe a weak nonlinear instability, despite the linear stability of the respective states.« less

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

    NASA Astrophysics Data System (ADS)

    Liu, Z. X.; Xu, X. Q.; Gao, X.; Xia, T. Y.; Joseph, I.; Meyer, W. H.; Liu, S. C.; Xu, G. S.; Shao, L. M.; Ding, S. Y.; Li, G. Q.; Li, J. G.

    2014-09-01

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

  4. Bearing Fault Diagnosis by a Robust Higher-Order Super-Twisting Sliding Mode Observer

    PubMed Central

    Kim, Jong-Myon

    2018-01-01

    An effective bearing fault detection and diagnosis (FDD) model is important for ensuring the normal and safe operation of machines. This paper presents a reliable model-reference observer technique for FDD based on modeling of a bearing’s vibration data by analyzing the dynamic properties of the bearing and a higher-order super-twisting sliding mode observation (HOSTSMO) technique for making diagnostic decisions using these data models. The HOSTSMO technique can adaptively improve the performance of estimating nonlinear failures in rolling element bearings (REBs) over a linear approach by modeling 5 degrees of freedom under normal and faulty conditions. The effectiveness of the proposed technique is evaluated using a vibration dataset provided by Case Western Reserve University, which consists of vibration acceleration signals recorded for REBs with inner, outer, ball, and no faults, i.e., normal. Experimental results indicate that the proposed technique outperforms the ARX-Laguerre proportional integral observation (ALPIO) technique, yielding 18.82%, 16.825%, and 17.44% performance improvements for three levels of crack severity of 0.007, 0.014, and 0.021 inches, respectively. PMID:29642459

  5. Bearing Fault Diagnosis by a Robust Higher-Order Super-Twisting Sliding Mode Observer.

    PubMed

    Piltan, Farzin; Kim, Jong-Myon

    2018-04-07

    An effective bearing fault detection and diagnosis (FDD) model is important for ensuring the normal and safe operation of machines. This paper presents a reliable model-reference observer technique for FDD based on modeling of a bearing's vibration data by analyzing the dynamic properties of the bearing and a higher-order super-twisting sliding mode observation (HOSTSMO) technique for making diagnostic decisions using these data models. The HOSTSMO technique can adaptively improve the performance of estimating nonlinear failures in rolling element bearings (REBs) over a linear approach by modeling 5 degrees of freedom under normal and faulty conditions. The effectiveness of the proposed technique is evaluated using a vibration dataset provided by Case Western Reserve University, which consists of vibration acceleration signals recorded for REBs with inner, outer, ball, and no faults, i.e., normal. Experimental results indicate that the proposed technique outperforms the ARX-Laguerre proportional integral observation (ALPIO) technique, yielding 18.82%, 16.825%, and 17.44% performance improvements for three levels of crack severity of 0.007, 0.014, and 0.021 inches, respectively.

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

    PubMed

    Kim, Sangbum; Kim, Kihong

    2017-12-11

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

  7. Theoretical analysis on lower band cascade as a mechanism for multiband chorus in the Earth's magnetosphere

    NASA Astrophysics Data System (ADS)

    Gao, Xinliang; Lu, Quanming; Wang, Shaojie; Wang, Shui

    2018-05-01

    Whistler-mode waves play a crucial role in controlling electron dynamics in the Earth's Van Allen radiation belt, which is increasingly important for spacecraft safety. Using THEMIS waveform data, Gao et al. [X. L. Gao, Q. Lu, J. Bortnik, W. Li, L. Chen, and S. Wang, Geophys. Res. Lett., 43, 2343-2350, 2016] have reported two multiband chorus events, wherein upper-band chorus appears at harmonics of lower-band chorus. They proposed that upper-band harmonic waves are excited through the nonlinear coupling between the electromagnetic and electrostatic components of lower-band chorus, a second-order effect called "lower band cascade". However, the theoretical explanation of lower band cascade was not thoroughly explained in the earlier work. In this paper, based on a cold plasma assumption, we have obtained the explicit nonlinear driven force of lower band cascade through a full nonlinear theoretical analysis, which includes both the ponderomotive force and coupling between electrostatic and electromagnetic components of the pump whistler wave. Moreover, we discover the existence of an efficient energy-transfer (E-t) channel from lower-band to upper-band whistler-mode waves during lower band cascade for the first time, which is also confirmed by PIC simulations. For lower-band whistler-mode waves with a small wave normal angle (WNA), the E-t channel is detected when the driven upper-band wave nearly satisfies the linear dispersion relation of whistler mode. While, for lower-band waves with a large WNA, the E-t channel is found when the lower-band wave is close to its resonant frequency, and the driven upper-band wave becomes quasi-electrostatic. Through this efficient channel, the harmonic upper band of whistler waves is generated through energy cascade from the lower band, and the two-band spectral structure of whistler waves is then formed. Both two types of banded whistler-mode spectrum have also been successfully reproduced by PIC simulations.

  8. Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com

    2014-07-15

    The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the Lmore » and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.« less

  9. Optimal Averages for Nonlinear Signal Decompositions - Another Alternative for Empirical Mode Decomposition

    DTIC Science & Technology

    2014-10-01

    nonlinear and non-stationary signals. It aims at decomposing a signal, via an iterative sifting procedure, into several intrinsic mode functions ...stationary signals. It aims at decomposing a signal, via an iterative sifting procedure into several intrinsic mode functions (IMFs), and each of the... function , optimization. 1 Introduction It is well known that nonlinear and non-stationary signal analysis is important and difficult. His- torically

  10. Nonlinear study of the parallel velocity/tearing instability using an implicit, nonlinear resistive MHD solver

    NASA Astrophysics Data System (ADS)

    Chacon, L.; Finn, J. M.; Knoll, D. A.

    2000-10-01

    Recently, a new parallel velocity instability has been found.(J. M. Finn, Phys. Plasmas), 2, 12 (1995) This mode is a tearing mode driven unstable by curvature effects and sound wave coupling in the presence of parallel velocity shear. Under such conditions, linear theory predicts that tearing instabilities will grow even in situations in which the classical tearing mode is stable. This could then be a viable seed mechanism for the neoclassical tearing mode, and hence a non-linear study is of interest. Here, the linear and non-linear stages of this instability are explored using a fully implicit, fully nonlinear 2D reduced resistive MHD code,(L. Chacon et al), ``Implicit, Jacobian-free Newton-Krylov 2D reduced resistive MHD nonlinear solver,'' submitted to J. Comput. Phys. (2000) including viscosity and particle transport effects. The nonlinear implicit time integration is performed using the Newton-Raphson iterative algorithm. Krylov iterative techniques are employed for the required algebraic matrix inversions, implemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix), and preconditioned with a ``physics-based'' preconditioner. Nonlinear results indicate that, for large total plasma beta and large parallel velocity shear, the instability results in the generation of large poloidal shear flows and large magnetic islands even in regimes when the classical tearing mode is absolutely stable. For small viscosity, the time asymptotic state can be turbulent.

  11. Multi-pulse operation of a dissipative soliton fibre laser based on nonlinear polarisation rotation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yu, H L; Wang, X L; Zhou, P

    We report an experimental observation of multiple dissipative soliton (DS) operation states in an all-normal-dispersion passively mode-locked Yb-doped fibre laser, including DS bound and oscillating states. In the bound state, multiple DSs up to 11 can coexist in the cavity. In the oscillating state, the DSs' movements are not purely random and three typical states are generalised and illustrated. A single-pulse mode-locked state is established at a high pump power by carefully adjusting the polarisation controllers. The broad spectrum indicates that it may be noise-like pulses, which can serve as a pump to generate a supercontinuum. (control of laser radiationmore » parameters)« less

  12. Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

    NASA Technical Reports Server (NTRS)

    Barnes, A.

    1983-01-01

    An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.

  13. Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices

    DOE PAGES

    Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Pelinovsky, Dmitry E.

    2016-08-01

    Here, we explore the possibility of multi-site breather states in a nonlinear Klein–Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the Klein–Gordon lattice with a soft (Morse) and amore » hard (Φ 4) potential. Compared to the case of the nonlinear Schrödinger lattice, the Krein signature of the internal mode relative to that of the wave continuum may change depending on the period of the multi-site breather state. For the periods for which the Krein signatures of the internal mode and the wave continuum coincide, multi-site breather states are observed to be nonlinearly stable.« less

  14. Multiple-mode nonlinear free and forced vibrations of beams using finite element method

    NASA Technical Reports Server (NTRS)

    Mei, Chuh; Decha-Umphai, Kamolphan

    1987-01-01

    Multiple-mode nonlinear free and forced vibration of a beam is analyzed by the finite element method. The geometric nonlinearity is investigated. Inplane displacement and inertia (IDI) are also considered in the formulation. Harmonic force matrix is derived and explained. Nonlinear free vibration can be simply treated as a special case of the general forced vibration by setting the harmonic force matrix equal to zero. The effect of the higher modes is more pronouced for the clamped supported beam than the simply supported one. Beams without IDI yield more effect of the higher modes than the one with IDI. The effects of IDI are to reduce nonlinearity. For beams with end supports restrained from axial movement (immovable cases), only the hardening type nonlinearity is observed. However, beams of small slenderness ratio (L/R = 20) with movable end supports, the softening type nonlinearity is found. The concentrated force case yields a more severe response than the uniformly distributed force case. Finite element results are in good agreement with the solution of simple elliptic response, harmonic balance method, and Runge-Kutte method and experiment.

  15. Nonlinear pulse shaping and polarization dynamics in mode-locked fiber lasers

    NASA Astrophysics Data System (ADS)

    Boscolo, Sonia; Sergeyev, Sergey V.; Mou, Chengbo; Tsatourian, Veronika; Turitsyn, Sergei; Finot, Christophe; Mikhailov, Vitaly; Rabin, Bryan; Westbrook, Paul S.

    2014-03-01

    We review our recent progress on the study of new nonlinear mechanisms of pulse shaping in passively mode-locked fiber lasers. These include a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on our recent experimental studies unveiling new types of vector solitons with processing states of polarization for multi-pulse and tightly bound-state soliton (soliton molecule) operations in a carbon nanotube (CNT) mode-locked fiber laser with anomalous dispersion cavity.

  16. Geometrically nonlinear analysis of adhesively bonded joints

    NASA Technical Reports Server (NTRS)

    Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.

    1982-01-01

    A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-relase rates (G1/G2) was found to be strongly affected by he adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.

  17. Experimental identification of nonlinear coupling between (intermediate, small)-scale microturbulence and an MHD mode in the core of a superconducting tokamak

    NASA Astrophysics Data System (ADS)

    Sun, P. J.; Li, Y. D.; Ren, Y.; Zhang, X. D.; Wu, G. J.; Xu, L. Q.; Chen, R.; Li, Q.; Zhao, H. L.; Zhang, J. Z.; Shi, T. H.; Wang, Y. M.; Lyu, B.; Hu, L. Q.; Li, J.; The EAST Team

    2018-01-01

    In this paper, we present clear experimental evidence of core region nonlinear coupling between (intermediate, small)-scale microturbulence and an magnetohydrodynamics (MHD) mode during the current ramp-down phase in a set of L-mode plasma discharges in the experimental advanced superconducting tokamak (EAST, Wan et al (2006 Plasma Sci. Technol. 8 253)). Density fluctuations of broadband microturbulence (k\\perpρi˜2{-}5.2 ) and the MHD mode (toroidal mode number m = -1 , poloidal mode number n = 1 ) are measured simultaneously, using a four-channel tangential CO2 laser collective scattering diagnostic in core plasmas. The nonlinear coupling between the broadband microturbulence and the MHD mode is directly demonstrated by showing a statistically significant bicoherence and modulation of turbulent density fluctuation amplitude by the MHD mode.

  18. Finite-time synchronization for second-order nonlinear multi-agent system via pinning exponent sliding mode control.

    PubMed

    Hou, Huazhou; Zhang, Qingling

    2016-11-01

    In this paper we investigate the finite-time synchronization for second-order multi-agent system via pinning exponent sliding mode control. Firstly, for the nonlinear multi-agent system, differential mean value theorem is employed to transfer the nonlinear system into linear system, then, by pinning only one node in the system with novel exponent sliding mode control, we can achieve synchronization in finite time. Secondly, considering the 3-DOF helicopter system with nonlinear dynamics and disturbances, the novel exponent sliding mode control protocol is applied to only one node to achieve the synchronization. Finally, the simulation results show the effectiveness and the advantages of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  19. Feedback and Control of Linear and Nonlinear Global MHD Modes in Rotating Plasmas

    NASA Astrophysics Data System (ADS)

    Finn, J. M.; Chacon, L.

    2002-11-01

    We present studies of feedback applied to resistive wall modes in the presence of plasma rotation. The main tool used is a Newton-Krylov nonlinear reduced resistive MHD code with completely implicit time stepping[1]. The effects of proportional and derivative gain and toroidal phase shift are investigated. In addition to studying the complete stabilization of the resistive wall mode, we present results on controlling the amplitude of nonlinear modes locked to the wall but propagating slowly; we also show results on reducing the hysteresis in the locking-unlocking bifurcation diagram. [1] L. Chacon, D. A. Knoll and J. M. Finn, "An implicit, nonlinear reduced resistive MHD solver", J. Comp. Phys. v. 178, pp 15-36 (2002).

  20. q Breathers in Finite Lattices: Nonlinearity and Weak Disorder

    NASA Astrophysics Data System (ADS)

    Ivanchenko, M. V.

    2009-05-01

    Nonlinearity and disorder are the recognized ingredients of the lattice vibrational dynamics, the factors that could be diminished, but never excluded. We generalize the concept of q breathers—periodic orbits in nonlinear lattices, exponentially localized in the linear mode space—to the case of weak disorder, taking the Fermi-Pasta-Ulan chain as an example. We show that these nonlinear vibrational modes remain exponentially localized near the central mode and stable, provided the disorder is sufficiently small. The instability threshold depends sensitively on a particular realization of disorder and can be modified by specifically designed impurities. Based on this sensitivity, an approach to controlling the energy flow between the modes is proposed. The relevance to other model lattices and experimental miniature arrays is discussed.

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

    NASA Astrophysics Data System (ADS)

    Dhote, Sharvari; Zu, Jean; Zhu, Yang

    2015-04-01

    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.

  2. Sliding mode control for a two-joint coupling nonlinear system based on extended state observer.

    PubMed

    Zhao, Ling; Cheng, Haiyan; Wang, Tao

    2018-02-01

    A two-joint coupling nonlinear system driven by pneumatic artificial muscles is introduced in this paper. A sliding mode controller with extended state observer is proposed to cope with nonlinearities and disturbances for the two-joint coupling nonlinear system. In addition, convergence of the extended state observer is presented and stability analysis of the closed-loop system is also demonstrated with the sliding mode controller. Lastly, some experiments are carried out to show the reality effectiveness of the proposed method. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

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

    PubMed

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

    2006-02-06

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

  4. Hybrid simulation of fishbone instabilities in the EAST tokamak

    DOE PAGES

    Shen, Wei; Wang, Feng; Fu, G. Y.; ...

    2017-08-11

    Hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in the experimental advanced superconducting tokamak (EAST) experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. Our results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a beta-induced Alfvenmore » eigenmode (BAE) with much higher frequency. This BAE is driven by higher energy beam ions. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. Furthermore, for the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution.« less

  5. A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

    PubMed

    Xu, Zhengfu; Bao, Gang

    2010-11-01

    A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

  6. Electromagnetic eigenmodes of collisional and collisionless plasmas and their stability to stimulated Brillouin scattering

    NASA Astrophysics Data System (ADS)

    Pathak, Vishwa Bandhu; Tripathi, V. K.

    2007-02-01

    Nonlinear electromagnetic eigenmodes of collisional and collisionless plasmas, when the temporal extent of the modes is longer than the ambipolar diffusion time, have been investigated. The nonlinearity in a collisionless plasma arises through ponderomotive force, whereas in collisional plasmas Ohmic nonlinearity prevails. The mode structure in both cases, representing a balance between the nonlinearity-induced self-convergence and diffraction-induced divergence, closely resembles Gaussian form. The spot size of the mode decreases with the increasing axial amplitude of the laser, attains a minimum, and then rises very gradually. The modes are susceptible to stimulated Brillouin backscattering. The growth rate of the Brillouin process initially increases with mode amplitude, attains a maximum, and then decreases. The reduction in the growth rate is caused by strong electron evacuation from the axial region by the ponderomotive force and thermal pressure gradient force created by nonuniform Ohmic heating.

  7. Harmonic generation of Lamb waves

    NASA Astrophysics Data System (ADS)

    Ing, Ros Kiri

    2002-11-01

    Lamb waves are dispersive waves that propagate following a number of distinct modes that depend on the values of the central frequency and frequency band. According to such properties and using the time-reversal process, it is shown that the hyperfocusing effect may be experienced [R. K. Ing and M. Fink, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1032-1043 (1998)]. Such a focusing effect both relates the time recompression of the dispersive Lamb waves and constructive interference on the focus point of the modes involved. The hyperfocusing effect is interesting because it allows the amplitude of the Lamb waves to reach huge values on the focus point. In our experiments, Lamb waves with normal amplitudes of micrometer values have been achieved on the free surface of a Duralumin plate of 3 mm thickness. By analyzing the Lamb waves in the neighborhood of the focus point using the 2-D Fourier transform technique, a nonlinear process of harmonic generation is then observed--the fundamental frequency component is centered at 1.5 MHz. This nonlinear process is under study and quantified.

  8. Electrocardiogram signal denoising based on empirical mode decomposition technique: an overview

    NASA Astrophysics Data System (ADS)

    Han, G.; Lin, B.; Xu, Z.

    2017-03-01

    Electrocardiogram (ECG) signal is nonlinear and non-stationary weak signal which reflects whether the heart is functioning normally or abnormally. ECG signal is susceptible to various kinds of noises such as high/low frequency noises, powerline interference and baseline wander. Hence, the removal of noises from ECG signal becomes a vital link in the ECG signal processing and plays a significant role in the detection and diagnosis of heart diseases. The review will describe the recent developments of ECG signal denoising based on Empirical Mode Decomposition (EMD) technique including high frequency noise removal, powerline interference separation, baseline wander correction, the combining of EMD and Other Methods, EEMD technique. EMD technique is a quite potential and prospective but not perfect method in the application of processing nonlinear and non-stationary signal like ECG signal. The EMD combined with other algorithms is a good solution to improve the performance of noise cancellation. The pros and cons of EMD technique in ECG signal denoising are discussed in detail. Finally, the future work and challenges in ECG signal denoising based on EMD technique are clarified.

  9. A predication model for combustion modes of the scramjet-powered aerospace vehicle based on the nonlinear features of the isolator flow field

    NASA Astrophysics Data System (ADS)

    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.

  10. Fluctuation Reduction in a Si Micromechanical Resonator Tuned to Nonlinear Internal Resonance

    NASA Astrophysics Data System (ADS)

    Strachan, B. Scott; Czaplewski, David; Chen, Changyao; Dykman, Mark; Lopez, Daniel; Shaw, Steven

    2015-03-01

    We describe experimental and theoretical results on an unusual behavior of fluctuations when the system exhibits internal resonance. We study the fundamental flexural mode (FFM) of a Si microbeam. The FFM is electrically actuated and detected. It is resonantly nonlinearly coupled to another mode, which is not directly accessible and has a frequency nearly three times the FFM frequency. Both the FFM and the passive mode have long lifetimes. We find that the passive mode can be a ``sink'' for fluctuations of the FFM. This explains the recently observed dramatic decrease of these fluctuations at nonlinear resonance. The re-distribution of the vibration amplitudes and the fluctuations is reminiscent of what happens at level anti-crossing in quantum mechanics. However, here it is different because of interplay of the dependence of the vibration frequency of the FFM on its amplitude due to internal nonlinearity and the nonlinear resonance with the passive mode. We study both the response of the system to external resonant driving and also the behavior of the system in the presence of a feedback loop. The experimental and theoretical results are in good agreement.

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

    NASA Astrophysics Data System (ADS)

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

    2017-06-01

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

  12. On the asymptotic stability of nonlinear mechanical switched systems

    NASA Astrophysics Data System (ADS)

    Platonov, A. V.

    2018-05-01

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

  13. Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio

    2004-03-01

    Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [F. Dell'Anno, S. De Siena, and F. Illuminati, Phys. Rev. A 69, 033812 (2004)], we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of Hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing nondegenerate and degenerate multiphoton processes. We determine the coherent states associated with the canonical transformations, which generalize the nondegenerate two-photon squeezed states. Such heterodyne multiphoton squeezed states are defined asmore » the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non-Gaussian, highly nonclassical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two-mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.« less

  14. Structure of multiphoton quantum optics. II. Bipartite systems, physical processes, and heterodyne squeezed states

    NASA Astrophysics Data System (ADS)

    dell'Anno, Fabio; de Siena, Silvio; Illuminati, Fabrizio

    2004-03-01

    Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper [

    F. Dell’Anno, S. De Siena, and F. Illuminati, Phys. Rev. A 69, 033812 (2004)
    ], we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of Hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing nondegenerate and degenerate multiphoton processes. We determine the coherent states associated with the canonical transformations, which generalize the nondegenerate two-photon squeezed states. Such heterodyne multiphoton squeezed states are defined as the simultaneous eigenstates of the transformed, coupled annihilation operators. They are generated by nonlinear unitary evolutions acting on two-mode squeezed states. They are non-Gaussian, highly nonclassical, entangled states. For a quadratic nonlinearity the heterodyne multiphoton squeezed states define two-mode cubic phase states. The statistical properties of these states can be widely adjusted by tuning the heterodyne mixing angles, the phases of the nonlinear couplings, as well as the strength of the nonlinearity. For quadratic nonlinearity, we study the higher-order contributions to the susceptibility in nonlinear media and we suggest possible experimental realizations of multiphoton conversion processes generating the cubic-phase heterodyne squeezed states.

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

    PubMed

    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.

  16. Improved nonlinear plasmonic slot waveguide: a full study

    NASA Astrophysics Data System (ADS)

    Elsawy, Mahmoud M. R.; Nazabal, Virginie; Chauvet, Mathieu; Renversez, Gilles

    2016-04-01

    We present a full study of an improved nonlinear plasmonic slot waveguides (NPSWs) in which buffer linear dielectric layers are added between the Kerr type nonlinear dielectric core and the two semi-infinite metal regions. Our approach computes the stationary solutions using the fixed power algorithm, in which for a given structure the wave power is an input parameter and the outputs are the propagation constant and the corresponding field components. For TM polarized waves, the inclusion of these supplementary layers have two consequences. First, they reduced the overall losses. Secondly, they modify the types of solutions that propagate in the NPSWs adding new profiles enlarging the possibilities offered by these nonlinear waveguides. In addition to the symmetric linear plasmonic profile obtained in the simple plasmonic structure with linear core such that its effective index is above the linear core refractive index, we obtained a new field profile which is more localized in the core with an effective index below the core linear refractive index. In the nonlinear case, if the effective index of the symmetric linear mode is above the core linear refractive index, the mode field profiles now exhibit a spatial transition from a plasmonic type profile to a solitonic type one. Our structure also provides longer propagation length due to the decrease of the losses compared to the simple nonlinear slot waveguide and exhibits, for well-chosen refractive index or thickness of the buffer layer, a spatial transition of its main modes that can be controlled by the power. We provide a full phase diagram of the TM wave operating regimes of these improved NPSWs. The stability of the main TM modes is then demonstrated numerically using the FDTD. We also demonstrate the existence of TE waves for both linear and nonlinear cases (for some configurations) in which the maximum intensity is located in the middle of the waveguide. We indicate the bifurcation of the nonlinear asymmetric TE mode from the symmetric nonlinear one through the Hopf bifurcation. This kind of bifurcation is similar to the ones already obtained in TM case for our improved structure, and also for the simple NPSWs. At high power, above the bifurcation threshold, the fundamental symmetric nonlinear TE mode moves gradually to new nonlinear mode in which the soliton peak displays two peaks in the core. The losses of the TE modes decrease with the power for all the cases. This kind of structures could be fabricated and characterized experimentally due to the realistic parameters chosen to model them.

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

    NASA Astrophysics Data System (ADS)

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

    2018-05-01

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

  18. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Rey, Michaël, E-mail: michael.rey@univ-reims.fr; Tyuterev, Vladimir G.; Nikitin, Andrei V.

    Accurate variational high-resolution spectra calculations in the range 0-8000 cm{sup −1} are reported for the first time for the monodeutered methane ({sup 12}CH{sub 3}D). Global calculations were performed by using recent ab initio surfaces for line positions and line intensities derived from the main isotopologue {sup 12}CH{sub 4}. Calculation of excited vibrational levels and high-J rovibrational states is described by using the normal mode Eckart-Watson Hamiltonian combined with irreducible tensor formalism and appropriate numerical procedures for solving the quantum nuclear motion problem. The isotopic H→D substitution is studied in details by means of symmetry and nonlinear normal mode coordinate transformations.more » Theoretical spectra predictions are given up to J = 25 and compared with the HITRAN 2012 database representing a compilation of line lists derived from analyses of experimental spectra. The results are in very good agreement with available empirical data suggesting that a large number of yet unassigned lines in observed spectra could be identified and modeled using the present approach.« less

  19. Vibration measurement by atomic force microscopy with laser readout

    NASA Astrophysics Data System (ADS)

    Snitka, Valentinas J.; Mizariene, Vida; Kalinauskas, Margiris; Lucinskas, Paulius

    1998-06-01

    Micromachined cantilever beams are widely used for different microengineering and nanotechnology actuators and sensors applications. The micromechanical cantilever tip-based data storage devices with reading real data at the rates exceeding 1Mbit/s have been demonstrated. The vibrational noise spectrum of a cantilever limits the data storage resolution. Therefore the possibility to measure the microvibrations and acoustic fields in different micromachined devices are of great interest. We describe a method to study a micromechanical cantilever and surface vibrations based on laser beam deflection measurements. The influence of piezoelectric plate vibrations and the tip- surface contact condition on the cantilever vibrations were investigated in the frequency range of 1-200 kHz. The experiments were performed using the measurement results. The V-shaped cantilevers exited by the normal vibrations due to the non-linearity at the tip-surface contact vibrates with a complex motion and has a lateral vibration mode coupled with normal vibration mode. The possibility to use laser deflection technique for the vibration measurements in micromachined structures with nano resolution is shown.

  20. A Comparison of the Bounded Derivative and the Normal Mode Initialization Methods Using Real Data

    NASA Technical Reports Server (NTRS)

    Semazzi, F. H. M.; Navon, I. M.

    1985-01-01

    Browning et al. (1980) proposed an initialization method called the bounded derivative method (BDI). They used analytical data to test the new method. Kasahara (1982) theoretically demonstrated the equivalence between BDI and the well known nonlinear normal mode initialization method (NMI). The purposes of this study are the extension of the application of BDI to real data and comparison with NMI. The unbalanced initial state (UBD) is data of January, 1979 OOZ which were interpolated from the adjacent sigma levels of the GLAS GCM to the 300 mb surface. The global barotropic model described by Takacs and Balgovind (1983) is used. Orographic forcing is explicitly included in the model. Many comparisons are performed between various quantities. However, we only present a comparison of the time evolution at two grid points A(50 S, 90 E) and B(10 S, 20 E) which represent low and middle latitude locations. To facilitate a more complete comparison an initialization experiment based on the classical balance equation (CBE) was also included.

  1. A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Friedman, B., E-mail: friedman11@llnl.gov; Lawrence Livermore National Laboratory, Livermore, California 94550; Carter, T. A.

    2015-01-15

    Linear eigenmode analysis often fails to describe turbulence in model systems that have non-normal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account non-modal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. We define such amore » non-modal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on cross-phases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as delta-function-like, periodic forces that randomize the state variables once every eddy turnover time. Furthermore, we estimate the eddy turnover time to be the inverse of the least stable eigenmode frequency or growth rate, which allows for prediction without nonlinear numerical simulation. We test this procedure on the 2D and 3D Hasegawa-Wakatani model [A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)] and find that the non-modal growth rate is a good predictor of energy injection rates, especially in the strongly non-normal, fully developed turbulence regime.« less

  2. A non-modal analytical method to predict turbulent properties applied to the Hasegawa-Wakatani model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Friedman, B.; Carter, T. A.

    2015-01-15

    Linear eigenmode analysis often fails to describe turbulence in model systems that have non-normal linear operators and thus nonorthogonal eigenmodes, which can cause fluctuations to transiently grow faster than expected from eigenmode analysis. When combined with energetically conservative nonlinear mode mixing, transient growth can lead to sustained turbulence even in the absence of eigenmode instability. Since linear operators ultimately provide the turbulent fluctuations with energy, it is useful to define a growth rate that takes into account non-modal effects, allowing for prediction of energy injection, transport levels, and possibly even turbulent onset in the subcritical regime. Here, we define suchmore » a non-modal growth rate using a relatively simple model of the statistical effect that the nonlinearities have on cross-phases and amplitude ratios of the system state variables. In particular, we model the nonlinearities as delta-function-like, periodic forces that randomize the state variables once every eddy turnover time. Furthermore, we estimate the eddy turnover time to be the inverse of the least stable eigenmode frequency or growth rate, which allows for prediction without nonlinear numerical simulation. Also, we test this procedure on the 2D and 3D Hasegawa-Wakatani model [A. Hasegawa and M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)] and find that the non-modal growth rate is a good predictor of energy injection rates, especially in the strongly non-normal, fully developed turbulence regime.« less

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

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

    Data-driven modeling of climate requires adequate principal variables extracted from observed high-dimensional data. For constructing such variables it is needed to find spatial-temporal patterns explaining a substantial part of the variability and comprising all dynamically related time series from the data. The difficulties of this task rise from the nonlinearity and non-stationarity of the climate dynamical system. The nonlinearity leads to insufficiency of linear methods of data decomposition for separating different processes entangled in the observed time series. On the other hand, various forcings, both anthropogenic and natural, make the dynamics non-stationary, and we should be able to describe the response of the system to such forcings in order to separate the modes explaining the internal variability. The method we present is aimed to overcome both these problems. The method is based on the Nonlinear Dynamical Mode (NDM) decomposition [1,2], but takes into account external forcing signals. An each mode depends on hidden, unknown a priori, time series which, together with external forcing time series, are mapped onto data space. Finding both the hidden signals and the mapping allows us to study the evolution of the modes' structure in changing external conditions and to compare the roles of the internal variability and forcing in the observed behavior. The method is used for extracting of the principal modes of SST variability on inter-annual and multidecadal time scales accounting the external forcings such as CO2, variations of the solar activity and volcanic activity. The structure of the revealed teleconnection patterns as well as their forecast under different CO2 emission scenarios are discussed.[1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101.

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

    PubMed

    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.

  5. Lagrangian space consistency relation for large scale structure

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Horn, Bart; Hui, Lam; Xiao, Xiao

    Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » Furthermore, the simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less

  6. Lagrangian space consistency relation for large scale structure

    DOE PAGES

    Horn, Bart; Hui, Lam; Xiao, Xiao

    2015-09-29

    Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » Furthermore, the simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less

  7. Real-time, ultrahigh-resolution, optical coherence tomography with an all-fiber, femtosecond fiber laser continuum at 1.5 microm.

    PubMed

    Nishizawa, N; Chen, Y; Hsiung, P; Ippen, E P; Fujimoto, J G

    2004-12-15

    Real-time, ultrahigh-resolution optical coherence tomography (OCT) is demonstrated in the 1.4-1.7-microm wavelength region with a stretched-pulse, passively mode-locked, Er-doped fiber laser and highly nonlinear fiber. The fiber laser generates 100-mW, linearly chirped pulses at a 51-MHz repetition rate. The pulses are compressed and then coupled into a normally dispersive highly nonlinear fiber to generate a low-noise supercontinuum with a 180-nm FWHM bandwidth and 38 mW of output power. This light source is stable, compact, and broadband, permitting high-speed, real-time, high-resolution OCT imaging. In vivo high-speed OCT imaging of human skin with approximately 5.5-microm resolution and 99-dB sensitivity is demonstrated.

  8. Adding In-Plane Flexibility to the Equations of Motion of a Single Rotor Helicopter

    NASA Technical Reports Server (NTRS)

    Curtiss, H. C., Jr.

    2000-01-01

    This report describes a way to add the effects of main rotor blade flexibility in the in- plane or lead-lag direction to a large set of non-linear equations of motion for a single rotor helicopter with rigid blades(l). Differences between the frequency of the regressing lag mode predicted by the equations of (1) and that measured in flight (2) for a UH-60 helicopter indicate that some element is missing from the analytical model of (1) which assumes rigid blades. A previous study (3) noted a similar discrepancy for the CH-53 helicopter. Using a relatively simple analytical model in (3), compared to (1), it was shown that a mechanical lag damper increases significantly the coupling between the rigid lag mode and the first flexible mode. This increased coupling due to a powerful lag damper produces an increase in the lowest lag frequency when viewed in a frame rotating with the blade. Flight test measurements normally indicate the frequency of this mode in a non-rotating or fixed frame. This report presents the additions necessary to the full equations of motion, to include main rotor blade lag flexibility. Since these additions are made to a very complex nonlinear dynamic model, in order to provide physical insight, a discussion of the results obtained from a simplified set of equations of motion is included. The reduced model illustrates the physics involved in the coupling and should indicate trends in the full model.

  9. Hybrid simulation of fishbone instabilities in the EAST tokamak

    NASA Astrophysics Data System (ADS)

    Shen, Wei; Fu, Guoyong; Wang, Feng; Xu, Liqing; Li, Guoqiang; Liu, Chengyue; EAST Team

    2017-10-01

    Hybrid simulations with the global kinetic- MHD code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of beam-driven fishbone in EAST experiment. Linear simulations show that a low frequency fishbone instability is excited at experimental value of beam ion pressure. The mode is mainly driven by low energy beam ions via precessional resonance. The results are consistent with the experimental measurement with respect to mode frequency and mode structure. When the beam ion pressure is increased to exceed a critical value, the low frequency mode transits to a BAE with much higher frequency. Nonlinear simulations show that the frequency of the low frequency fishbone chirps up and down with corresponding hole-clump structures in phase space, consistent with the Berk-Breizman theory. In addition to the low frequency mode, the high frequency BAE is excited during the nonlinear evolution. For the transient case of beam pressure fraction where the low and high frequency modes are simultaneously excited in the linear phase, only one dominant mode appears in the nonlinear phase with frequency jumps up and down during nonlinear evolution. This work is supported by the National Natural Science Foundation of China under Grant Nos. 11605245 and 11505022, and the CASHIPS Director's Fund under Grant No. YZJJ201510, and the Department of Energy Scientific Discovery through Advanced Computing (SciDAC) under Grant No. DE-AC02-09CH11466.

  10. Measurement of the Raman scattering cross section of the breathing mode in KDP and DKDP crystals.

    PubMed

    Demos, Stavros G; Raman, Rajesh N; Yang, Steven T; Negres, Raluca A; Schaffers, Kathleen I; Henesian, Mark A

    2011-10-10

    The spontaneous Raman scattering cross sections of the main peaks (related to the A1 vibrational mode) in rapid and conventional grown potassium dihydrogen phosphate and deuterated crystals are measured at 532 nm, 355 nm, and 266 nm. The measurement involves the use of the Raman line of water centered at 3400 cm-1 as a reference to obtain relative values of the cross sections which are subsequently normalized against the known absolute value for water as a function of excitation wavelength. This measurement enables the estimation of the transverse stimulated Raman scattering gain of these nonlinear optical materials in various configurations suitable for frequency conversion and beam control in high-power, large-aperture laser systems.

  11. Core-pumped mode-locked ytterbium-doped fiber laser operating around 980 nm

    NASA Astrophysics Data System (ADS)

    Zhou, Yue; Dai, Yitang; Li, Jianqiang; Yin, Feifei; Dai, Jian; Zhang, Tian; Xu, Kun

    2018-07-01

    In this letter, we first demonstrate a core-pumped passively mode-locked all-normal-dispersion ytterbium-doped fiber oscillator based on nonlinear polarization evolution operating around 980 nm. The dissipative soliton fiber laser pulse can be compressed down to 250 fs with 1 nJ pulse energy, and the slope efficiency of the oscillator can be as high as 19%. To improve the dissipative soliton laser output spectrum smoothness, we replace the birefringent plate based intracavity filter with a diffraction-grating based filter. The output pulse duration can then be further compressed down to 180 fs with improved spectral-smoothness. These schemes have potential applications in seeding cryogenic Yb:YLF amplifiers and underwater exploration of marine resources.

  12. All-fiber broadband supercontinuum generation in a single-mode high nonlinear silica fiber

    NASA Astrophysics Data System (ADS)

    Gao, Weiqing; Liao, Meisong; Yang, Lingzhen; Yan, Xin; Suzuki, Takenobu; Ohishi, Yasutake

    2012-06-01

    We demonstrate an all-fiber broadband supercontinuum (SC) source with high efficiency in a single-mode high nonlinear silica fiber. The SC is pumped by the 1557 nm sub-picosecond pulse, which is generated by a homemade passively mode-locked fiber laser, amplified by an EDFA and compressed to 600 fs. The high nonlinear fiber used in experiments has the zero-dispersion wavelength of 1584 nm with low dispersion slope. The pump pulse is in the normal dispersion region and the SC generation is initiated by the SPM effect. When the long-wave band of the spectrum is extended to the anomalous dispersion region, the soliton effects and intra-pulse Raman effects extend the spectrum further. Meanwhile, the dispersive waves shorter than 1100 nm begin to emerge because the phase matching condition is satisfied and the intensity increases with increasing the pump intensity. The broad SC spectrum with the spectral range from 840 to 2390 nm is obtained at the pump peak power of 46.71 kW, and the 10 dB bandwidth from 1120 nm to 2245 nm of the SC covers one octave assuming the peak near 1550 nm is filtered. The temporal trace of the SC has the repetition rate of 16.7 MHz, and some satellite pulses are generated during the nonlinear process. The SC source system is constructed by all-fiber components, which can be fusion spliced together directly with low loss less than 0.1 dB and improves the energy transfer efficiency from the pump source to the SC greatly. The maximum SC average power of 332 mW is obtained for the total spectral range, and the slop efficiency to the pump source is about 70.3%, which will be lower when the peaks near 1550 nm are filtered, but is higher than those in PCFs. The spectral density for the 10 dB bandwidth is in the range from -17.3 to -7.3 dBm/nm.

  13. Nonlinear optics and crystalline whispering gallery mode resonators

    NASA Technical Reports Server (NTRS)

    Matsko, Andrey; Savchenkov, Anatoliy; Ilchenko, Vladimir S.; Maleki, Lute

    2004-01-01

    We report on our recent results concerning fabrication of high-Q whispering gallery mode crystalline resonaors, and discuss some possible applications of lithium niobate WGM resonators in nonlinear optics and photonics.

  14. Investigation on the Nonlinear Control System of High-Pressure Common Rail (HPCR) System in a Diesel Engine

    NASA Astrophysics Data System (ADS)

    Cai, Le; Mao, Xiaobing; Ma, Zhexuan

    2018-02-01

    This study first constructed the nonlinear mathematical model of the high-pressure common rail (HPCR) system in the diesel engine. Then, the nonlinear state transformation was performed using the flow’s calculation and the standard state space equation was acquired. Based on sliding-mode variable structure control (SMVSC) theory, a sliding-mode controller for nonlinear systems was designed for achieving the control of common rail pressure and the diesel engine’s rotational speed. Finally, on the simulation platform of MATLAB, the designed nonlinear HPCR system was simulated. The simulation results demonstrate that sliding-mode variable structure control algorithm shows favorable control performances and overcome the shortcomings of traditional PID control in overshoot, parameter adjustment, system precision, adjustment time and ascending time.

  15. Multipolar second-harmonic generation by Mie-resonant dielectric nanoparticles

    NASA Astrophysics Data System (ADS)

    Smirnova, Daria; Smirnov, Alexander I.; Kivshar, Yuri S.

    2018-01-01

    By combining analytical and numerical approaches, we study resonantly enhanced second-harmonic generation by individual high-index dielectric nanoparticles made of centrosymmetric materials. Considering both bulk and surface nonlinearities, we describe second-harmonic nonlinear scattering from a silicon nanoparticle optically excited in the vicinity of the magnetic and electric dipolar resonances. We discuss the contributions of different nonlinear sources and the effect of the low-order optical Mie modes on the characteristics of the generated far field. We demonstrate that the multipolar expansion of the radiated field is dominated by dipolar and quadrupolar modes (two axially symmetric electric quadrupoles, an electric dipole, and a magnetic quadrupole) and the interference of these modes can ensure directivity of the nonlinear scattering. The developed multipolar analysis can be instructive for interpreting the far-field measurements of the nonlinear scattering and it provides prospective insights into a design of complementary metal-oxide-semiconductor compatible nonlinear nanoantennas fully integrated with silicon-based photonic circuits, as well as methods of nonlinear diagnostics.

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

    PubMed

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

    2017-05-02

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

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dhote, Sharvari, E-mail: sharvari.dhote@mail.utoronto.ca; Zu, Jean; Zhu, Yang

    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 threemore » 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.« less

  18. Nonlinear fishbone dynamics in spherical tokamaks

    DOE Data Explorer

    Wang, Feng [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Dalian Univ Technol, Sch Phys & Optoelect Technol, Minist Educ, Key Lab Mat Modificat Laser Ion & Electron Beams, Dalian 116024, Peoples R China.; Fu, G.Y. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Institute for Fusion Theory and Simulation and Department of Physics Hangzhou, Zhejiang University, Hangzhou, 310027, People's Republic of China; Shen, Wei [Institute of Plasma Physics, Chinese Academy of Science, Hefei 230031, People's Republic of China

    2017-01-01

    Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. The results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturates due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. A substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.

  19. Nonlinear fishbone dynamics in spherical tokamaks

    DOE PAGES

    Wang, Feng; Fu, G. Y.; Shen, Wei

    2016-11-22

    Linear and nonlinear kinetic-MHD hybrid simulations have been carried out to investigate linear stability and nonlinear dynamics of beam-driven fishbone instability in spherical tokamak plasmas. Realistic NSTX parameters with finite toroidal rotation were used. Our results show that the fishbone is driven by both trapped and passing particles. The instability drive of passing particles is comparable to that of trapped particles in the linear regime. The effects of rotation are destabilizing and a new region of instability appears at higher q min (>1.5) values, q min being the minimum of safety factor profile. In the nonlinear regime, the mode saturatesmore » due to flattening of beam ion distribution, and this persists after initial saturation while mode frequency chirps down in such a way that the resonant trapped particles move out radially and keep in resonance with the mode. Correspondingly, the flattening region of beam ion distribution expands radially outward. Furthermore, a substantial fraction of initially non-resonant trapped particles become resonant around the time of mode saturation and keep in resonance with the mode as frequency chirps down. On the other hand, the fraction of resonant passing particles is significantly smaller than that of trapped particles. Finally, our analysis shows that trapped particles provide the main drive to the mode in the nonlinear regime.« less

  20. Analog nonlinear MIMO receiver for optical mode division multiplexing transmission.

    PubMed

    Spalvieri, Arnaldo; Boffi, Pierpaolo; Pecorino, Simone; Barletta, Luca; Magarini, Maurizio; Gatto, Alberto; Martelli, Paolo; Martinelli, Mario

    2013-10-21

    The complexity and the power consumption of digital signal processing are crucial issues in optical transmission systems based on mode division multiplexing and coherent multiple-input multiple-output (MIMO) processing at the receiver. In this paper the inherent characteristic of spatial separation between fiber modes is exploited, getting a MIMO system where joint demultiplexing and detection is based on spatially separated photodetectors. After photodetection, one has a MIMO system with nonlinear crosstalk between modes. The paper shows that the nonlinear crosstalk can be dealt with by a low-complexity and non-adaptive detection scheme, at least in the cases presented in the paper.

  1. Nonlinear mode coupling theory of the lower-hybrid-drift instability

    NASA Technical Reports Server (NTRS)

    Drake, J. F.; Guzdar, P. N.; Hassam, A. B.; Huba, J. D.

    1984-01-01

    A nonlinear mode coupling theory of the lower-hybrid-drift instability is presented. A two-dimensional nonlinear wave equation is derived which describes lower-hybrid drift wave turbulence in the plane transverse to B (k.B = 0), and which is valid for finite beta, collisional and collisionless plasmas. The instability saturates by transferring energy from growing, long wavelength modes to damped, short wavelength modes. Detailed numerical results are presented which compare favorably to both recent computer simulations and experimental observations. Applications of this theory to space plasmas, the earth's magnetotail and the equatorial F region ionosphere, are discussed. Previously announced in STAR as N84-17734

  2. Fully nonlinear development of the most unstable goertler vortex in a three dimensional boundary layer

    NASA Technical Reports Server (NTRS)

    Otto, S. R.; Bassom, Andrew P.

    1992-01-01

    The nonlinear development is studied of the most unstable Gortler mode within a general 3-D boundary layer upon a suitably concave surface. The structure of this mode was first identified by Denier, Hall and Seddougui (1991) who demonstrated that the growth rate of this instability is O(G sup 3/5) where G is the Gortler number (taken to be large here), which is effectively a measure of the curvature of the surface. Previous researchers have described the fate of the most unstable mode within a 2-D boundary layer. Denier and Hall (1992) discussed the fully nonlinear development of the vortex in this case and showed that the nonlinearity causes a breakdown of the flow structure. The effect of crossflow and unsteadiness upon an infinitesimal unstable mode was elucidated by Bassom and Hall (1991). They demonstrated that crossflow tends to stabilize the most unstable Gortler mode, and for certain crossflow/frequency combinations the Gortler mode may be made neutrally stable. These vortex configurations naturally lend themselves to a weakly nonlinear stability analysis; work which is described in a previous article by the present author. Here we extend the ideas of Denier and Hall (1992) to the three-dimensional boundary layer problem. It is found that the numerical solution of the fully nonlinear equations is best conducted using a method which is essentially an adaption of that utilized by Denier and Hall (1992). The influence of crossflow and unsteadiness upon the breakdown of the flow is described.

  3. Derivation of regularized Grad's moment system from kinetic equations: modes, ghosts and non-Markov fluxes

    NASA Astrophysics Data System (ADS)

    Karlin, Ilya

    2018-04-01

    Derivation of the dynamic correction to Grad's moment system from kinetic equations (regularized Grad's 13 moment system, or R13) is revisited. The R13 distribution function is found as a superposition of eight modes. Three primary modes, known from the previous derivation (Karlin et al. 1998 Phys. Rev. E 57, 1668-1672. (doi:10.1103/PhysRevE.57.1668)), are extended into the nonlinear parameter domain. Three essentially nonlinear modes are identified, and two ghost modes which do not contribute to the R13 fluxes are revealed. The eight-mode structure of the R13 distribution function implies partition of R13 fluxes into two types of contributions: dissipative fluxes (both linear and nonlinear) and nonlinear streamline convective fluxes. Physical interpretation of the latter non-dissipative and non-local in time effect is discussed. A non-perturbative R13-type solution is demonstrated for a simple Lorentz scattering kinetic model. The results of this study clarify the intrinsic structure of the R13 system. This article is part of the theme issue `Hilbert's sixth problem'.

  4. Simulation of the oscillation regimes of bowed bars: a non-linear modal approach

    NASA Astrophysics Data System (ADS)

    Inácio, Octávio; Henrique, Luís.; Antunes, José

    2003-06-01

    It is still a challenge to properly simulate the complex stick-slip behavior of multi-degree-of-freedom systems. In the present paper we investigate the self-excited non-linear responses of bowed bars, using a time-domain modal approach, coupled with an explicit model for the frictional forces, which is able to emulate stick-slip behavior. This computational approach can provide very detailed simulations and is well suited to deal with systems presenting a dispersive behavior. The effects of the bar supporting fixture are included in the model, as well as a velocity-dependent friction coefficient. We present the results of numerical simulations, for representative ranges of the bowing velocity and normal force. Computations have been performed for constant-section aluminum bars, as well as for real vibraphone bars, which display a central undercutting, intended to help tuning the first modes. Our results show limiting values for the normal force FN and bowing velocity ẏbow for which the "musical" self-sustained solutions exist. Beyond this "playability space", double period and even chaotic regimes were found for specific ranges of the input parameters FN and ẏbow. As also displayed by bowed strings, the vibration amplitudes of bowed bars also increase with the bow velocity. However, in contrast to string instruments, bowed bars "slip" during most of the motion cycle. Another important difference is that, in bowed bars, the self-excited motions are dominated by the system's first mode. Our numerical results are qualitatively supported by preliminary experimental results.

  5. The Effect of Basis Selection on Thermal-Acoustic Random Response Prediction Using Nonlinear Modal Simulation

    NASA Technical Reports Server (NTRS)

    Rizzi, Stephen A.; Przekop, Adam

    2004-01-01

    The goal of this investigation is to further develop nonlinear modal numerical simulation methods for prediction of geometrically nonlinear response due to combined thermal-acoustic loadings. As with any such method, the accuracy of the solution is dictated by the selection of the modal basis, through which the nonlinear modal stiffness is determined. In this study, a suite of available bases are considered including (i) bending modes only; (ii) coupled bending and companion modes; (iii) uncoupled bending and companion modes; and (iv) bending and membrane modes. Comparison of these solutions with numerical simulation in physical degrees-of-freedom indicates that inclusion of any membrane mode variants (ii - iv) in the basis affects the bending displacement and stress response predictions. The most significant effect is on the membrane displacement, where it is shown that only the type (iv) basis accurately predicts its behavior. Results are presented for beam and plate structures in the thermally pre-buckled regime.

  6. A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.

    PubMed

    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. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  7. Scalar-vector soliton fiber laser mode-locked by nonlinear polarization rotation.

    PubMed

    Wu, Zhichao; Liu, Deming; Fu, Songnian; Li, Lei; Tang, Ming; Zhao, Luming

    2016-08-08

    We report a passively mode-locked fiber laser by nonlinear polarization rotation (NPR), where both vector and scalar soliton can co-exist within the laser cavity. The mode-locked pulse evolves as a vector soliton in the strong birefringent segment and is transformed into a regular scalar soliton after the polarizer within the laser cavity. The existence of solutions in a polarization-dependent cavity comprising a periodic combination of two distinct nonlinear waves is first demonstrated and likely to be applicable to various other nonlinear systems. For very large local birefringence, our laser approaches the operation regime of vector soliton lasers, while it approaches scalar soliton fiber lasers under the condition of very small birefringence.

  8. Mid-infrared supercontinuum generation in multimode step index chalcogenide fiber

    NASA Astrophysics Data System (ADS)

    Ben Khalifa, Ameni; Ben Salem, Amine; Cherif, Rim; Zghal, Mourad

    2016-09-01

    In this paper, we propose a design of a high numerical aperture multimode hybrid step-index fiber for mid-infrared (mid- IR) supercontinuum generation (SCG) where two chalcogenide glass compositions As40Se60 and Ge10As23.4Se66.6 for the core and the cladding are selected, respectively. Aiming to get accurate modeling of the SCG by the fundamental mode, we solve the multimode generalized nonlinear Schrödinger equations and demonstrate nonlinear coupling and energy transfer between high order modes. The proposed study points out the impact of nonlinear mode coupling that should be taken into account in order to successfully predict the mid-infrared supercontinuum generation in highly nonlinear multimode fibers.

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

    NASA Astrophysics Data System (ADS)

    Dumeige, Yannick; Féron, Patrice

    2011-10-01

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

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

    NASA Astrophysics Data System (ADS)

    Burdin, V.; Bourdine, A.

    2018-04-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

  12. A numerical study on weak-dissipative two-mode perturbed Burgers' and Ostrovsky models: right-left moving waves

    NASA Astrophysics Data System (ADS)

    Jaradat, Imad; Alquran, Marwan; Ali, Mohammed

    2018-04-01

    The purpose of this study is threefold. First, it derives newly developed two-mode nonlinear equations, two-mode perturbed Burgers' and two-mode Ostrovsky models. Second, it investigates the values of the nonlinearity and dispersion parameters that support the existence of two right-left (R-L) moving wave solutions to these models. Finally, it provides a graphical analysis of the "two-mode" concept and the impact of its phase velocity on the field function.

  13. Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer.

    PubMed

    Yang, Jiashi; Chen, Ziguang; Hu, Yuantai; Jiang, Shunong; Guo, Shaohua

    2007-04-01

    We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.

  14. A Locally Modal B-Spline Based Full-Vector Finite-Element Method with PML for Nonlinear and Lossy Plasmonic Waveguide

    NASA Astrophysics Data System (ADS)

    Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan

    2016-09-01

    In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.

  15. Rogue Wave Modes for the Long Wave-Short Wave Resonance and the Derivative Nonlinear Schrödinger Models

    NASA Astrophysics Data System (ADS)

    Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin

    2014-11-01

    Rogue waves are unexpectedly large displacements of the water surface and will obviously pose threat to maritime activities. Recently, the formation of rogue waves is correlated with the onset of modulation instabilities of plane waves of the system. The long wave-short wave resonance and the derivative nonlinear Schrödinger models are considered. They are relevant in a two-layer fluid and a fourth order perturbation expansion of free surface waves respectively. Analytical solutions of rogue wave modes for the two models are derived by the Hirota bilinear method. Properties and amplitudes of these rogue wave modes are investigated. Conditions for modulation instability of the plane waves are shown to be precisely the requirements for the occurrence of rogue waves. In contrast with the nonlinear Schrödinger equation, rogue wave modes for the derivative nonlinear Schrödinger model exist even if the dispersion and cubic nonlinearity are of the opposite signs, provided that a sufficiently strong self-steepening nonlinearity is present. Extensions to the coupled case (multiple waveguides) will be discussed. This work is partially supported by the Research Grants Council General Research Fund Contract HKU 711713E.

  16. Nonlinear Evolution of Counter-Propagating Whistler Mode Waves Excited by Anisotropic Electrons Within the Equatorial Source Region: 1-D PIC Simulations

    NASA Astrophysics Data System (ADS)

    Chen, Huayue; Gao, Xinliang; Lu, Quanming; Sun, Jicheng; Wang, Shui

    2018-02-01

    Nonlinear physical processes related to whistler mode waves are attracting more and more attention for their significant role in reshaping whistler mode spectra in the Earth's magnetosphere. Using a 1-D particle-in-cell simulation model, we have investigated the nonlinear evolution of parallel counter-propagating whistler mode waves excited by anisotropic electrons within the equatorial source region. In our simulations, after the linear phase of whistler mode instability, the strong electrostatic standing structures along the background magnetic field will be formed, resulting from the coupling between excited counter-propagating whistler mode waves. The wave numbers of electrostatic standing structures are about twice those of whistler mode waves generated by anisotropic hot electrons. Moreover, these electrostatic standing structures can further be coupled with either parallel or antiparallel propagating whistler mode waves to excite high-k modes in this plasma system. Compared with excited whistler mode waves, these high-k modes typically have 3 times wave number, same frequency, and about 2 orders of magnitude smaller amplitude. Our study may provide a fresh view on the evolution of whistler mode waves within their equatorial source regions in the Earth's magnetosphere.

  17. Decomposition of the complex system into nonlinear spatio-temporal modes: algorithm and application to climate data mining

    NASA Astrophysics Data System (ADS)

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

    2015-04-01

    Proper decomposition of the complex system into well separated "modes" is a way to reveal and understand the mechanisms governing the system behaviour as well as discover essential feedbacks and nonlinearities. The decomposition is also natural procedure that provides to construct adequate and concurrently simplest models of both corresponding sub-systems, and of the system in whole. In recent works two new methods of decomposition of the Earth's climate system into well separated modes were discussed. The first method [1-3] is based on the MSSA (Multichannel Singular Spectral Analysis) [4] for linear expanding vector (space-distributed) time series and makes allowance delayed correlations of the processes recorded in spatially separated points. The second one [5-7] allows to construct nonlinear dynamic modes, but neglects delay of correlations. It was demonstrated [1-3] that first method provides effective separation of different time scales, but prevent from correct reduction of data dimension: slope of variance spectrum of spatio-temporal empirical orthogonal functions that are "structural material" for linear spatio-temporal modes, is too flat. The second method overcomes this problem: variance spectrum of nonlinear modes falls essentially sharply [5-7]. However neglecting time-lag correlations brings error of mode selection that is uncontrolled and increases with growth of mode time scale. In the report we combine these two methods in such a way that the developed algorithm allows constructing nonlinear spatio-temporal modes. The algorithm is applied for decomposition of (i) multi hundreds years globally distributed data generated by the INM RAS Coupled Climate Model [8], and (ii) 156 years time series of SST anomalies distributed over the globe [9]. We compare efficiency of different methods of decomposition and discuss the abilities of nonlinear spatio-temporal modes for construction of adequate and concurrently simplest ("optimal") models of climate systems. 1. Feigin A.M., Mukhin D., Gavrilov A., Volodin E.M., and Loskutov E.M. (2013) "Separation of spatial-temporal patterns ("climatic modes") by combined analysis of really measured and generated numerically vector time series", AGU 2013 Fall Meeting, Abstract NG33A-1574. 2. Alexander Feigin, Dmitry Mukhin, Andrey Gavrilov, Evgeny Volodin, and Evgeny Loskutov (2014) "Approach to analysis of multiscale space-distributed time series: separation of spatio-temporal modes with essentially different time scales", Geophysical Research Abstracts, Vol. 16, EGU2014-6877. 3. Dmitry Mukhin, Dmitri Kondrashov, Evgeny Loskutov, Andrey Gavrilov, Alexander Feigin, and Michael Ghil (2014) "Predicting critical transitions in ENSO models, Part II: Spatially dependent models", Journal of Climate (accepted, doi: 10.1175/JCLI-D-14-00240.1). 4. Ghil, M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, et al. (2002) "Advanced spectral methods for climatic time series", Rev. Geophys. 40(1), 3.1-3.41. 5. Dmitry Mukhin, Andrey Gavrilov, Evgeny M Loskutov and Alexander M Feigin (2014) "Nonlinear Decomposition of Climate Data: a New Method for Reconstruction of Dynamical Modes", AGU 2014 Fall Meeting, Abstract NG43A-3752. 6. Andrey Gavrilov, Dmitry Mukhin, Evgeny Loskutov, and Alexander Feigin (2015) "Empirical decomposition of climate data into nonlinear dynamic modes", Geophysical Research Abstracts, Vol. 17, EGU2015-627. 7. Dmitry Mukhin, Andrey Gavrilov, Evgeny Loskutov, Alexander Feigin, and Juergen Kurths (2015) "Reconstruction of principal dynamical modes from climatic variability: nonlinear approach", Geophysical Research Abstracts, Vol. 17, EGU2015-5729. 8. http://83.149.207.89/GCM_DATA_PLOTTING/GCM_INM_DATA_XY_en.htm. 9. http://iridl.ldeo.columbia.edu/SOURCES/.KAPLAN/.EXTENDED/.v2/.ssta/.

  18. Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines

    NASA Astrophysics Data System (ADS)

    Eric, Tala-Tebue; Aurelien, Kenfack-Jiotsa; Marius Hervé, Tatchou-Ntemfack; Timoléon Crépin, Kofané

    2013-07-01

    In this work, we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines. Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch. Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing. On one hand, the difference between the two lines induced the fission for only one mode of propagation. This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton, leading to a possible increasing of the bit rate. On the other hand, the dissymmetry of the two lines converts the network into a good amplifier for the ω_ mode which corresponds to the regime admitting low frequencies.

  19. Nonlinear effects on the natural modes of oscillation of a finite length inviscid fluid column, supplement 2

    NASA Technical Reports Server (NTRS)

    Lyell, M. J.; Zhang, L.

    1994-01-01

    The aspects of nonlinear behavior of a finite length liquid column is investigated with an emphasis on bridge dynamics. The primary objectives are to determine the nonlinear corrections to the interface shape of a naturally oscillating finite length liquid column and to determine the nonlinear corrections to the oscillation frequencies for various modes of oscillation. Application of the Lindstedt-Poincare expansion in conjunction with the domain perturbation techniques results in an hierarchical system of equations.

  20. Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  1. On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

    NASA Technical Reports Server (NTRS)

    Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Huang; Peng, Chung Kang; hide

    2016-01-01

    The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

  2. On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

    PubMed Central

    Huang, Norden E.; Hu, Kun; Yang, Albert C. C.; Chang, Hsing-Chih; Jia, Deng; Liang, Wei-Kuang; Yeh, Jia Rong; Kao, Chu-Lan; Juan, Chi-Hung; Peng, Chung Kang; Meijer, Johanna H.; Wang, Yung-Hung; Long, Steven R.; Wu, Zhauhua

    2016-01-01

    The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities. PMID:26953180

  3. Effects of fast ions on interchange modes in the Large Helical Device plasmas

    NASA Astrophysics Data System (ADS)

    Pinon, Jonhathan; Todo, Yasushi; Wang, Hao

    2018-07-01

    Effects of fast ions on the magnetohydrodynamic (MHD) instabilities in a Large Helical Device (LHD) plasma with the central beta value (=pressure normalized by the magnetic pressure) 4% have been investigated with hybrid simulations for energetic particles interacting with an MHD fluid. When fast ions are neglected, it is found that the dominant instability is an ideal interchange mode with the dominant harmonic m/n = 2/1, where m, n are respectively the poloidal and toroidal numbers. The spatial peak location of the m/n = 2/1 harmonic is close to the ι = 1/2 magnetic surface located at r/a = 0.29, where ι is the rotational transform and r/a is the normalized radius. The second unstable mode is a resistive interchange mode with m/n =3/2 that peaks at r/a = 0.65 nearby the ι = 2/3 surface, which grows more slowly than the m/n = 2/1 mode. The nonlinear coupling of the m/n = 3/2 and 2/1 mode results in the growth of the m/n = 5/3 mode and other modes leading to the global reduction and flattening of the pressure profile. When fast ions are considered with the central beta value 0.2% and the total pressure profile is kept the same, the ideal interchange mode with m/n = 2/1 located close to the plasma center is stabilized while the resistive interchange mode with m/n = 3/2 located far from the plasma center is less affected. The stabilization is attributed to the reduction of bulk pressure gradient, which is the dilution of the free energy source, because the energy transfer between the fast ions and the interchange modes is found to be negligible. For higher fast-ion pressure, Alfvén eigenmodes are destabilized by fast ions.

  4. Algebra of Majorana doubling.

    PubMed

    Lee, Jaehoon; Wilczek, Frank

    2013-11-27

    Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.

  5. Elementary dispersion analysis of some mimetic discretizations on triangular C-grids

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Korn, P., E-mail: peter.korn@mpimet.mpg.de; Danilov, S.; A.M. Obukhov Institute of Atmospheric Physics, Moscow

    2017-02-01

    Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid discretization. The mimetic approach provides a discrete continuity equation which operates on an averaged combination of normal edge velocities instead of normal edge velocities proper. An elementary analysis of the wave dispersion of the new discretization for Poincaré, Rossby and Kelvin waves shows that, although spurious Poincaré modes are preserved, their frequency tends to zero in the limit of small wavenumbers, which removes the divergence noisemore » in this limit. However, the frequencies of spurious and physical modes become close on shorter scales indicating that spurious modes can be excited unless high-frequency short-scale motions are effectively filtered in numerical codes. We argue that filtering by viscous dissipation is more efficient in the mimetic approach than in the standard C-grid discretization. Lumping of mass matrices appearing with the velocity time derivative in the mimetic discretization only slightly reduces the accuracy of the wave dispersion and can be used in practice. Thus, the mimetic approach cures some difficulties of the traditional triangular C-grid discretization but may still need appropriately tuned viscosity to filter small scales and high frequencies in solutions of full primitive equations when these are excited by nonlinear dynamics.« less

  6. Nonlinear modal resonances in low-gravity slosh-spacecraft systems

    NASA Technical Reports Server (NTRS)

    Peterson, Lee D.

    1991-01-01

    Nonlinear models of low gravity slosh, when coupled to spacecraft vibrations, predict intense nonlinear eigenfrequency shifts at zero gravity. These nonlinear frequency shifts are due to internal quadratic and cubic resonances between fluid slosh modes and spacecraft vibration modes. Their existence has been verified experimentally, and they cannot be correctly modeled by approximate, uncoupled nonlinear models, such as pendulum mechanical analogs. These predictions mean that linear slosh assumptions for spacecraft vibration models can be invalid, and may lead to degraded control system stability and performance. However, a complete nonlinear modal analysis will predict the correct dynamic behavior. This paper presents the analytical basis for these results, and discusses the effect of internal resonances on the nonlinear coupled response at zero gravity.

  7. Resistive wall instabilities and tearing mode dynamics in the EXTRAP T2R thin shell reversed-field pinch

    NASA Astrophysics Data System (ADS)

    Malmberg, J.-A.; Brunsell, P. R.

    2002-01-01

    Observations of resistive wall instabilities and tearing mode dynamics in the EXTRAP T2R thin shell (τw=6 ms) reversed field pinch are described. A nonresonant mode (m=1,n=-10) with the same handedness as the internal field grows nearly exponentially with an average growth time of about 2.6 ms (less than 1/2 of the shell time) consistent with linear stability theory. The externally nonresonant unstable modes (m=1,n>0), predicted by linear stability theory, are observed to have only low amplitudes (in the normal low-Θ operation mode of the device). The radial field of the dominant internally resonant tearing modes (m=1,n=-15 to n=-12) remain low due to spontaneous fast mode rotation, corresponding to angular phase velocities up to 280 krad/s. Phase aligned mode structures are observed to rotate toroidally with an average angular velocity of 40 krad/s, in the opposite direction of the plasma current. Toward the end of the discharge, the radial field of the internally resonant modes grows as the modes slow down and become wall-locked, in agreement with nonlinear computations. Fast rotation of the internally resonant modes has been observed only recently and is attributed to a change of the front-end system (vacuum vessel, shell, and TF coil) of the device.

  8. Mode-Locking Behavior of Izhikevich Neuron Under Periodic External Forcing

    NASA Astrophysics Data System (ADS)

    Farokhniaee, Amirali; Large, Edward

    2015-03-01

    In this study we obtained the regions of existence of various mode-locked states on the periodic-strength plane, which are called Arnold Tongues, for Izhikevich neurons. The study is based on the new model for neurons by Izhikevich (2003) which is the normal form of Hodgkin-Huxley neuron. This model is much simpler in terms of the dimension of the coupled non-linear differential equations compared to other existing models, but excellent for generating the complex spiking patterns observed in real neurons. Many neurons in the auditory system of the brain must encode amplitude variations of a periodic signal. These neurons under periodic stimulation display rich dynamical states including mode-locking and chaotic responses. Periodic stimuli such as sinusoidal waves and amplitude modulated (AM) sounds can lead to various forms of n : m mode-locked states, similar to mode-locking phenomenon in a LASER resonance cavity. Obtaining Arnold tongues provides useful insight into the organization of mode-locking behavior of neurons under periodic forcing. Hence we can describe the construction of harmonic and sub-harmonic responses in the early processing stages of the auditory system, such as the auditory nerve and cochlear nucleus.

  9. Normal Stresses, Contraction, and Stiffening in Sheared Elastic Networks

    NASA Astrophysics Data System (ADS)

    Baumgarten, Karsten; Tighe, Brian P.

    2018-04-01

    When elastic solids are sheared, a nonlinear effect named after Poynting gives rise to normal stresses or changes in volume. We provide a novel relation between the Poynting effect and the microscopic Grüneisen parameter, which quantifies how stretching shifts vibrational modes. By applying this relation to random spring networks, a minimal model for, e.g., biopolymer gels and solid foams, we find that networks contract or develop tension because they vibrate faster when stretched. The amplitude of the Poynting effect is sensitive to the network's linear elastic moduli, which can be tuned via its preparation protocol and connectivity. Finally, we show that the Poynting effect can be used to predict the finite strain scale where the material stiffens under shear.

  10. Weak Nonlinearity Effects in TG and EAW Modes

    NASA Astrophysics Data System (ADS)

    Ashourvan, Arash; Dubin, Daniel H. E.

    2013-10-01

    We have studied the nonlinear coupling of Trivelpiece-Gould modes as well as EAW modes, in a cylindrically symmetric plasma with average density n0 and periodic boundary conditions at the axial ends of plasma. For Trivelpiece-Gould modes, the cold fluid formalism gives the slow time evolution of mode amplitudes due to nonlinear couplings. For EAW modes, the Vlasov-Poisson formalism is required. We analyze the coupling between mode mz = 2 with frequency ω2 and mode mz = 1 with frequency ω1, with initial density perturbations n2 (0) >>n1 (0) . For small detuning Δω ≡ 2ω1 -ω2 <<ω1n2 (0) /n0 , mode amplitude n1 grows exponentially in time due to resonant parametric interaction with mode mz = 2 , at a rate Γ which is linearly propotional to n2 (0) . For Δω >>ω1n2 (0) /n0 , mode amplitude n1 oscillates about its initial value, with frequency Δω and amplitude n1(2) ~n2 (0) n1 (0) . In both cases the theory is consistent with experiments. Work supported by PHY-0903877, DE-SC0002451, DE-SC0008693.

  11. Modified nonlinear amplifying loop mirror for mode-locked fibre oscillators with record-high energy and high-average-power pulsed output

    NASA Astrophysics Data System (ADS)

    Kobtsev, Sergey; Ivanenko, Alexey; Smirnov, Sergey; Kokhanovsky, Alexey

    2018-02-01

    The present work proposes and studies approaches for development of new modified non-linear amplifying loop mirror (NALM) allowing flexible and dynamic control of their non-linear properties within a relatively broad range of radiation powers. Using two independently pumped active media in the loop reflector constitutes one of the most promising approaches to development of better NALM with nonlinear properties controllable independently of the intra-cavity radiation power. This work reports on experimental and theoretical studies of the proposed redesigned NALM allowing both a higher level of energy parameters of output generated by mode-locked fibre oscillators and new possibilities of switching among different mode-locked regimes.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dumeige, Yannick; Feron, Patrice

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

  13. Nonlinear feedback in a six-dimensional Lorenz Model: impact of an additional heating term

    NASA Astrophysics Data System (ADS)

    Shen, B.-W.

    2015-03-01

    In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the steamfunction is referred to as a secondary streamfunction mode, while the two additional modes, that appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado. The implications of this and previous work, as well as future work, are also discussed.

  14. Nonlinear feedback in a six-dimensional Lorenz model: impact of an additional heating term

    NASA Astrophysics Data System (ADS)

    Shen, B.-W.

    2015-12-01

    In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the streamfunction is referred to as a secondary streamfunction mode, while the two additional modes, which appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): "If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado." The implications of this and previous work, as well as future work, are also discussed.

  15. Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

    NASA Technical Reports Server (NTRS)

    Gajjar, J. S. B.

    1993-01-01

    The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

  16. Transverse discrete breathers in unstrained graphene

    NASA Astrophysics Data System (ADS)

    Barani, Elham; Lobzenko, Ivan P.; Korznikova, Elena A.; Soboleva, Elvira G.; Dmitriev, Sergey V.; Zhou, Kun; Marjaneh, Aliakbar Moradi

    2017-02-01

    Discrete breathers (DB) are spatially localized vibrational modes of large amplitude in defect-free nonlinear lattices. The search for DBs in graphene is of high importance, taking into account that this one atom thick layer of carbon is promising for a number of applications. There exist several reports on successful excitation of DBs in graphene, based on molecular dynamics and ab initio simulations. In a recent work by Hizhnyakov with co-authors the possibility to excite a DB with atoms oscillating normal to the graphene sheet has been reported. In the present study we use a systematic approach for finding initial conditions to excite transverse DBs in graphene. The approach is based on the analysis of the frequency-amplitude dependence for a delocalized, short-wavelength vibrational mode. This mode is a symmetry-dictated exact solution to the dynamic equations of the atomic motion, regardless the mode amplitude and regardless the type of interatomic potentials used in the simulations. It is demonstrated that if the AIREBO potential is used, the mode frequency increases with the amplitude bifurcating from the upper edge of the phonon spectrum for out-of-plane phonons. Then a bell-shaped function is superimposed on this delocalized mode to obtain a spatially localized vibrational mode, i.e., a DB. Placing the center of the bell-shaped function at different positions with respect to the lattice sites, three different DBs are found. Typically, the degree of spatial localization of DBs increases with the DB amplitude, but the transverse DBs in graphene reported here demonstrate the opposite trend. The results are compared to those obtained with the use of the Savin interatomic potential and no transverse DBs are found in this case. The results of this study contribute to a better understanding of the nonlinear dynamics of graphene and they call for the ab initio simulations to verify which of the two potentials used in this study is more precise.

  17. MHD modeling of DIII-D QH-mode discharges and comparison to observations

    NASA Astrophysics Data System (ADS)

    King, Jacob

    2016-10-01

    MHD modeling of DIII-D QH-mode discharges and comparison to observations Nonlinear NIMROD simulations, initialized from a reconstruction of a DIII-D QH-mode discharge with broadband MHD, saturate into a turbulent state, but do not saturate when flow is not included. This is consistent with the experimental results of the quiescent regime observed on DIII-D with broadband MHD activity [Garofalo et al., PoP (2015) and refs. within]. These ELM-free discharges have the normalized pedestal-plasma confinement necessary for burning-plasma operation on ITER. Relative to QH-mode operation with more coherent MHD activity, operation with broadband MHD tends to occur at higher densities and lower rotation and thus may be more relevant to ITER. The nonlinear NIMROD simulations require highly accurate equilibrium reconstructions. Our equilibrium reconstructions include the scrape-off-layer profiles and the measured toroidal and poloidal rotation profiles. The simulation develops into a saturated turbulent state and the n=1 and 2 modes become dominant through an inverse cascade. Each toroidal mode in the range of n=1-5 is dominant at a different time. The perturbations are advected and sheared apart in the counter-clockwise direction consistent with the direction of the poloidal flow inside the LCFS. Work towards validation through comparison to magnetic coil and Doppler reflectometry measurements is presented. Consistent with experimental observations during QH-mode, the simulated state leads to large particle transport relative to the thermal transport. Analysis shows that the phase of the density and temperature perturbations differ resulting in greater convective particle transport relative to the convective thermal transport. This work supported by the U.S. Department of Energy Office of Science and the SciDAC Center for Extended MHD Modeling under Contract Numbers DE-FC02-06ER54875, DE-FC02-08ER54972 and DE-FC02-04ER54698.

  18. Analysis of wind-driven ambient noise in a shallow water environment with a sandy seabed.

    PubMed

    Knobles, D P; Joshi, S M; Gaul, R D; Graber, H C; Williams, N J

    2008-09-01

    On the New Jersey continental shelf ambient sound levels were recorded during tropical storm Ernesto that produced wind speeds up to 40 knots in early September 2006. The seabed at the position of the acoustic measurements can be approximately described as coarse sand. Differences between the ambient noise levels for the New Jersey shelf measurements and deep water reference measurements are modeled using both normal mode and ray methods. The analysis is consistent with a nonlinear frequency dependent seabed attenuation for the New Jersey site.

  19. Stable Spheromaks with Profile Control

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Fowler, T K; Jayakumar, R

    A spheromak equilibrium with zero edge current is shown to be stable to both ideal MHD and tearing modes that normally produce Taylor relaxation in gun-injected spheromaks. This stable equilibrium differs from the stable Taylor state in that the current density j falls to zero at the wall. Estimates indicate that this current profile could be sustained by non-inductive current drive at acceptable power levels. Stability is determined using the NIMROD code for linear stability analysis. Non-linear NIMROD calculations with non-inductive current drive could point the way to improved fusion reactors.

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

    PubMed

    Zhang, Zhen; Koroleva, I; Manevitch, L I; Bergman, L A; Vakakis, A F

    2016-09-01

    We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "NL pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the existence of nonreciprocal wave interaction phenomena in the form of irreversible targeted energy transfers from L waves to NL pulses during collisions of these two types of waves. Additional nonreciprocal acoustics are found in the form of complex "cascading processes, as well as nonreciprocal interactions between L waves and stationary discrete breathers. The computational studies confirm the theoretically predicted transition of the lattice dynamics to a low-energy state of nonlinear acoustic vacum with strong nonlocality.

  1. Applications of NASTRAN to nuclear problems

    NASA Technical Reports Server (NTRS)

    Spreeuw, E.

    1972-01-01

    The extent to which suitable solutions may be obtained for one physics problem and two engineering type problems is traced. NASTRAN appears to be a practical tool to solve one-group steady-state neutron diffusion equations. Transient diffusion analysis may be performed after new levels that allow time-dependent temperature calculations are developed. NASTRAN piecewise linear anlaysis may be applied to solve those plasticity problems for which a smooth stress-strain curve can be used to describe the nonlinear material behavior. The accuracy decreases when sharp transitions in the stress-strain relations are involved. Improved NASTRAN usefulness will be obtained when nonlinear material capabilities are extended to axisymmetric elements and to include provisions for time-dependent material properties and creep analysis. Rigid formats 3 and 5 proved to be very convenient for the buckling and normal-mode analysis of a nuclear fuel element.

  2. Lagrangian space consistency relation for large scale structure

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Horn, Bart; Hui, Lam; Xiao, Xiao, E-mail: bh2478@columbia.edu, E-mail: lh399@columbia.edu, E-mail: xx2146@columbia.edu

    Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias and Riotto and Peloso and Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present.more » The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.« less

  3. The nonlinear evolution of modes on unstable stratified shear layers

    NASA Technical Reports Server (NTRS)

    Blackaby, Nicholas; Dando, Andrew; Hall, Philip

    1993-01-01

    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.

  4. Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

    NASA Astrophysics Data System (ADS)

    Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

    2008-05-01

    The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

  5. A non-linear 4-wave resonant model for non-perturbative fast ion interactions with Alfv'enic modes in burning plasmas

    NASA Astrophysics Data System (ADS)

    Zonca, Fulvio; Chen, Liu

    2007-11-01

    We adopt the 4-wave modulation interaction model, introduced by Chen et al [1] for analyzing modulational instabilities of the radial envelope of Ion Temperature Gradient driven modes in toroidal geometry, extending it to the modulations on the fast particle distribution function due to nonlinear Alfv'enic mode dynamics, as proposed in Ref. [2]. In the case where the wave-particle interactions are non-perturbative and strongly influence the mode evolution, as in the case of Energetic Particle Modes (EPM) [3], radial distortions (redistributions) of the fast ion source dominate the mode nonlinear dynamics. In this work, we show that the resonant particle motion is secular with a time-scale inversely proportional to the mode amplitude [4] and that the time evolution of the EPM radial envelope can be cast into the form of a nonlinear Schr"odinger equation a la Ginzburg-Landau [5]. [1] L. Chen et al, Phys. Plasmas 7 3129 (2000) [2] F. Zonca et al, Theory of Fusion Plasmas (Bologna: SIF) 17 (2000) [3] L. Chen, Phys. Plasmas 1, 1519 (1994).[4] F. Zonca et al, Nucl. Fusion 45 477 (2005) [5] F. Zonca et al, Plasma Phys. Contr. Fusion 48 B15 (2006)

  6. Optical analogue of relativistic Dirac solitons in binary waveguide arrays

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tran, Truong X., E-mail: truong.tran@mpl.mpg.de; Max Planck Institute for the Science of Light, Günther-Scharowsky str. 1, 91058 Erlangen; Longhi, Stefano

    2014-01-15

    We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory. -- Highlights: •An opticalmore » analogue of Dirac solitons in nonlinear binary waveguide arrays is suggested. •Analytical solutions to pseudo-relativistic solitons are presented. •A correspondence of optical coupled-mode equations with the nonlinear relativistic Dirac equation is established.« less

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

    NASA Astrophysics Data System (ADS)

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

    2018-02-01

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

  8. Secondary Instability of Second Modes in Hypersonic Boundary Layers

    NASA Technical Reports Server (NTRS)

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

    2012-01-01

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

  9. Seasonal prediction for hydro-meteorological variables in the Korean Peninsula: Links with atmospheric teleconnections

    NASA Astrophysics Data System (ADS)

    Yoon, S.

    2016-12-01

    This study analyzes nonlinear behavior links with atmospheric teleconnections between hydrologic variables and climate indices using statistical models over the Korean Peninsula (KP). The ocean-related major climate factors such as the El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mode in the Tropical Ocean (TO) region were used to analyze the atmospheric teleconnections by principal component analysis (PCA) and a singular spectrum analysis (SSA). The nonlinear lag time correlations between climate indices and hydrological variables are calculated by the Mutual Information (MI) techniques. Results show that teleconnection based nonlinear correlation coefficients (CCs) were higher than linear CCs, ENSO shows a few months of lag time correlation with IOD, which has a direct influence on rainfall and streamflow anomalies in the KP. The precipitation and streamflow in KP shows a significant increasing and decreasing tendency during warm pool (WP) and cold tongue (CT) El Niño decaying years, respectively, while the La Niña year shows slightly above normal conditions. IOD events show significantly decreasing and increasing long-term normal conditions during positive and negative years, respectively. A better understanding of the relationship between climate indices and streamflow can help policy makers prepare for possible options in river discharge pattern changes. Furthermore, these results provide useful information for water managers and end-users to support long-range water resources prediction and water-related management plan.

  10. Dynamic analysis of rotor flex-structure based on nonlinear anisotropic shell models

    NASA Astrophysics Data System (ADS)

    Bauchau, Olivier A.; Chiang, Wuying

    1991-05-01

    In this paper an anisotropic shallow shell model is developed that accommodates transverse shearing deformations and arbitrarily large displacements and rotations, but strains are assumed to remain small. Two kinematic models are developed, the first using two DOF to locate the direction of the normal to the shell's midplane, the second using three. The latter model allows for an automatic compatibility of the shell model with beam models. The shell model is validated by comparing its predictions with several benchmark problems. In actual helicopter rotor blade problems, the shell model of the flex structure is shown to give very different results shown compared to beam models. The lead-lag and torsion modes in particular are strongly affected, whereas flapping modes seem to be less affected.

  11. Correlating non-linear properties with spectral states of RXTE data: possible observational evidences for four different accretion modes around compact objects

    NASA Astrophysics Data System (ADS)

    Adegoke, Oluwashina; Dhang, Prasun; Mukhopadhyay, Banibrata; Ramadevi, M. C.; Bhattacharya, Debbijoy

    2018-05-01

    By analysing the time series of RXTE/PCA data, the non-linear variabilities of compact sources have been repeatedly established. Depending on the variation in temporal classes, compact sources exhibit different non-linear features. Sometimes they show low correlation/fractal dimension, but in other classes or intervals of time they exhibit stochastic nature. This could be because the accretion flow around a compact object is a non-linear general relativistic system involving magnetohydrodynamics. However, the more conventional way of addressing a compact source is the analysis of its spectral state. Therefore, the question arises: What is the connection of non-linearity to the underlying spectral properties of the flow when the non-linear properties are related to the associated transport mechanisms describing the geometry of the flow? This work is aimed at addressing this question. Based on the connection between observed spectral and non-linear (time series) properties of two X-ray binaries: GRS 1915+105 and Sco X-1, we attempt to diagnose the underlying accretion modes of the sources in terms of known accretion classes, namely, Keplerian disc, slim disc, advection dominated accretion flow and general advective accretion flow. We explore the possible transition of the sources from one accretion mode to others with time. We further argue that the accretion rate must play an important role in transition between these modes.

  12. Nonlinear saturation amplitude of cylindrical Rayleigh—Taylor instability

    NASA Astrophysics Data System (ADS)

    Liu, Wan-Hai; Yu, Chang-Ping; Ye, Wen-Hua; Wang, Li-Feng

    2014-09-01

    The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh—Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the r0/λ (λ is the perturbation wavelength), the larger the NSA of the fundamental mode. When r0/λ is large enough (r0 ≫ λ), the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.

  13. Nonlinear reconnecting edge localized modes in current-carrying plasmas

    DOE PAGES

    Ebrahimi, F.

    2017-05-22

    Nonlinear edge localized modes in a tokamak are examined using global three-dimensional resistive magnetohydrodynamics simulations. Coherent current-carrying filament (ribbon-like) structures wrapped around the torus are nonlinearly formed due to nonaxisymmetric reconnecting current sheet instabilities, the so-called peeling-like edge localized modes. These fast growing modes saturate by breaking axisymmetric current layers isolated near the plasma edge and go through repetitive relaxation cycles by expelling current radially outward and relaxing it back. The local bidirectional fluctuation-induced electromotive force (emf) from the edge localized modes, the dynamo action, relaxes the axisymmetric current density and forms current holes near the edge. Furthermore, the three-dimensionalmore » coherent current-carrying filament structures (sometimes referred to as 3-D plasmoids) observed here should also have strong implications for solar and astrophysical reconnection.« less

  14. Analysis of originating ultra-short optical dissipative solitary pulses in the actively mode-locked semiconductor heterolasers with an external fiber cavity

    NASA Astrophysics Data System (ADS)

    Shcherbakov, Alexandre S.; Campos Acosta, Joaquin; Pons Aglio, Alicia; Moreno Zarate, Pedro; Mansurova, Svetlana

    2010-06-01

    We present an advanced approach to describing low-power trains of bright picosecond optical dissipative solitary pulses with an internal frequency modulation in practically important case of exploiting semiconductor heterolaser operating in near-infrared range in the active mode-locking regime. In the chosen schematic arrangement, process of the active mode-locking is caused by a hybrid nonlinear cavity consisting of this heterolaser and an external rather long single-mode optical fiber exhibiting square-law dispersion, cubic Kerr nonlinearity, and small linear optical losses. Our analysis of shaping dissipative solitary pulses includes three principal contributions associated with the modulated gain, total optical losses, as well as with linear and nonlinear phase shifts. In fact, various trains of the non-interacting to one another optical dissipative solitons appear within simultaneous balance between the second-order dispersion and cubic-law Kerr nonlinearity as well as between active medium gain and linear optical losses in a hybrid cavity. Our specific approach makes possible taking the modulating signals providing non-conventional composite regimes of a multi-pulse active mode-locking. Within our model, a contribution of the appearing nonlinear Ginzburg-Landau operator to the parameters of dissipative solitary pulses is described via exploiting an approximate variational procedure involving the technique of trial functions.

  15. Arbitrary amplitude nucleus-acoustic solitons in multi-ion quantum plasmas with relativistically degenerate electrons

    NASA Astrophysics Data System (ADS)

    Sultana, S.; Schlickeiser, R.

    2018-02-01

    A three component degenerate relativistic quantum plasma (consisting of relativistically degenerate electrons, nondegenerate inertial light nuclei, and stationary heavy nuclei) is considered to model the linear wave and also the electrostatic solitary waves in the light nuclei-scale length. A well-known normal mode analysis is employed to investigate the linear wave properties. A mechanical-motion analog (Sagdeev-type) pseudo-potential approach, which reveals the existence of large amplitude solitary excitations, is adopted to study the nonlinear wave properties. Only the positive potential solitary excitations are found to exist in the plasma medium under consideration. The basic properties of the arbitrary amplitude electrostatic acoustic modes in the light nuclei-scale length and their existence domain in terms of soliton speed (Mach number) are examined. The modifications of solitary wave characteristics and their existence domain with the variation of different key plasma configuration parameters (e.g., electrons degeneracy parameter, inertial light nuclei number density, and degenerate electron number density) are also analyzed. Our results, which may be helpful to explain the basic features of the nonlinear wave propagation in multi-component degenerate quantum plasmas, in connection with astrophysical compact objects (e.g., white dwarfs) are briefly discussed.

  16. Crossflow-Vortex Breakdown on Swept Wings: Correlation of Nonlinear Physics

    NASA Technical Reports Server (NTRS)

    Joslin, R. D.; Streett, C. L.

    1994-01-01

    The spatial evolution of cross flow-vortex packets in a laminar boundary layer on a swept wing are computed by the direct numerical simulation of the incompressible Navier- Stokes equations. A wall-normal velocity distribution of steady suction and blowing at the wing surface is used to generate a strip of equally spaced and periodic disturbances along the span. Three simulations are conducted to study the effect of initial amplitude on the disturbance evolution, to determine the role of traveling cross ow modes in transition, and to devise a correlation function to guide theories of transition prediction. In each simulation, the vortex packets first enter a chordwise region of linear independent growth, then, the individual packets coalesce downstream and interact with adjacent packets, and, finally, the vortex packets nonlinearly interact to generate inflectional velocity profiles. As the initial amplitude of the disturbance is increased, the length of the evolution to breakdown decreases. For this pressure gradient, stationary modes dominate the disturbance evolution. A two-coeffcient function was devised to correlate the simulation results. The coefficients, combined with a single simulation result, provide sufficient information to generate the evolution pattern for disturbances of any initial amplitude.

  17. Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

    2016-07-15

    Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

  18. Mode Identification of High-Amplitude Pressure Waves in Liquid Rocket Engines

    NASA Astrophysics Data System (ADS)

    EBRAHIMI, R.; MAZAHERI, K.; GHAFOURIAN, A.

    2000-01-01

    Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure amplitude histories and phase diagrams along the tube are computed. To determine the validity of the presented method for steep non-linear waves, the Euler equations are numerically solved for non-linear waves, and negligible interactions between these waves are observed. To show the applicability of this method, other's experimental results in which modes were identified are used. Results indicate that this simple method can be used in analyzing complicated pressure signal measurements.

  19. Universal fuzzy integral sliding-mode controllers for stochastic nonlinear systems.

    PubMed

    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.

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

    NASA Technical Reports Server (NTRS)

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

    2017-01-01

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

  1. Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

    NASA Technical Reports Server (NTRS)

    Jarrah, Yousef Mohd

    1989-01-01

    The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

  2. Spatiotemporal light-beam compression from nonlinear mode coupling

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  3. Nonlinear effects of electromagnetic forces on primary resonance of a levitated elastic bar supported by high- Tc superconducting bearings

    NASA Astrophysics Data System (ADS)

    Iori, T.; Ogawa, S.; Sugiura, T.

    2007-10-01

    This research investigates nonlinear dynamics of an elastic body supported at both its ends by electromagnetic forces between superconductors and magnets. We focus on the primary resonance of each eigenmode under vertical excitation of superconducting bulks. Experiment and numerical analysis show the softening tendency in the resonance of the 3rd mode consisting of mainly deflection and slightly translation. This nonlinear response can be theoretically explained only by nonlinear coupling between the 1st and 3rd modes through their quadratic terms.

  4. Integrability and correspondence of classical and quantum non-linear three-mode systems

    NASA Astrophysics Data System (ADS)

    Odzijewicz, A.; Wawreniuk, E.

    2018-04-01

    The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the quantum system are constructed. We find the explicit formulas for the reproducing measure for these states. Examples of some applications of the obtained results in non-linear quantum optics are presented.

  5. Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

    NASA Astrophysics Data System (ADS)

    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.

  6. Second harmonic generation in resonant optical structures

    DOEpatents

    Eichenfield, Matt; Moore, Jeremy; Friedmann, Thomas A.; Olsson, Roy H.; Wiwi, Michael; Padilla, Camille; Douglas, James Kenneth; Hattar, Khalid Mikhiel

    2018-01-09

    An optical second-harmonic generator (or spontaneous parametric down-converter) includes a microresonator formed of a nonlinear optical medium. The microresonator supports at least two modes that can be phase matched at different frequencies so that light can be converted between them: A first resonant mode having substantially radial polarization and a second resonant mode having substantially vertical polarization. The first and second modes have the same radial order. The thickness of the nonlinear medium is less than one-half the pump wavelength within the medium.

  7. Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk.

    PubMed

    Liu, Shijie; Zheng, Yuanlin; Chen, Xianfeng

    2017-09-15

    Whispering-gallery-mode (WGM) microcavities are very important in both fundamental science and practical applications, among which on-chip second-order nonlinear microresonators play an important role in integrated photonic functionalities. Here we demonstrate resonant second-harmonic generation (SHG) and cascaded third-harmonic generation (THG) in a lithium niobate-on-insulator (LNOI) microdisk resonator. Efficient SHG in the visible range was obtained with only several mW input powers at telecom wavelengths. THG was also observed through a cascading process, which reveals simultaneous phase matching and strong mode coupling in the resonator. Cascading of second-order nonlinear processes gives rise to an effectively large third-order nonlinearity, which makes on-chip second-order nonlinear microresonators a promising frequency converter for integrated nonlinear photonics.

  8. Switchable Q-switched and modelocked operation in ytterbium doped fiber laser under all-normal-dispersion configuration

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mukhopadhyay, Pranb K., E-mail: pkm@rrcat.gov.in; Gupta, Pradeep K.; Singh, Chandra Pal

    2015-03-15

    We have constructed an Yb-doped fiber laser in all-normal-dispersion configuration which can be independently operated in Q-switched or modelocked configuration with the help of a simple fiber optic ring resonator (FORR). In the presence of FORR, the laser operates in Q-switched mode producing stable pulses in the range of 1 μs-200 ns with repetition rate in the range of 45 kHz-82 kHz. On the other hand, the laser can be easily switched to mode-locked operation by disjoining the FORR loop producing train of ultrashort pulses of ∼5 ps duration (compressible to ∼150 fs) at ∼38 MHz repetition rate. The transmissionmore » characteristics of FORR in combination with the nonlinear polarization rotation for passive Q-switching operation is numerically investigated and experimentally verified. The laser can serve as a versatile seed source for power amplifier which can be easily configured for application in the fields that require different pulsed fiber lasers.« less

  9. A Criterion to Control Nonlinear Error in the Mixed-Mode Bending Test

    NASA Technical Reports Server (NTRS)

    Reeder, James R.

    2002-01-01

    The mixed-mode bending test ha: been widely used to measure delamination toughness and was recently standardized by ASTM as Standard Test Method D6671-01. This simple test is a combination of the standard Mode I (opening) test and a Mode II (sliding) test. This test uses a unidirectional composite test specimen with an artificial delamination subjected to bending loads to characterize when a delamination will extend. When the displacements become large, the linear theory used to analyze the results of the test yields errors in the calcu1ated toughness values. The current standard places no limit on the specimen loading and therefore test data can be created using the standard that are significantly in error. A method of limiting the error that can be incurred in the calculated toughness values is needed. In this paper, nonlinear models of the MMB test are refined. One of the nonlinear models is then used to develop a simple criterion for prescribing conditions where thc nonlinear error will remain below 5%.

  10. Stability of two-mode internal resonance in a nonlinear oscillator

    NASA Astrophysics Data System (ADS)

    Zanette, Damián H.

    2018-05-01

    We analyze the stability of synchronized periodic motion for two coupled oscillators, representing two interacting oscillation modes in a nonlinear vibrating beam. The main oscillation mode is governed by the forced Duffing equation, while the other mode is linear. By means of the multiple-scale approach, the system is studied in two situations: an open-loop configuration, where the excitation is an external force, and a closed-loop configuration, where the system is fed back with an excitation obtained from the oscillation itself. The latter is relevant to the functioning of time-keeping micromechanical devices. While the accessible amplitudes and frequencies of stationary oscillations are identical in the two situations, their stability properties are substantially different. Emphasis is put on resonant oscillations, where energy transfer between the two coupled modes is maximized and, consequently, the strong interdependence between frequency and amplitude caused by nonlinearity is largely suppressed.

  11. Finite time control for MIMO nonlinear system based on higher-order sliding mode.

    PubMed

    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. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Kinetic theory and Vlasov simulation of nonlinear ion-acoustic waves in multi-ion species plasmas.

    PubMed

    Chapman, T; Berger, R L; Brunner, S; Williams, E A

    2013-05-10

    The theory of damping and nonlinear frequency shifts from particles resonant with ion-acoustic waves (IAWs) is presented for multi-ion species plasma and compared to driven wave Vlasov simulations. Two distinct IAW modes may be supported in multi-ion species plasmas, broadly classified as fast and slow by their phase velocity relative to the constituent ion thermal velocities. In current fusion-relevant long pulse experiments, the ion to electron temperature ratio, T(i)/T(e), is expected to reach a level such that the least damped and thus more readily driven mode is the slow mode, with both linear and nonlinear properties that are shown to differ significantly from the fast mode. The lighter ion species of the slow mode is found to make no significant contribution to the IAW frequency shift despite typically being the dominant contributor to the Landau damping.

  13. Sliding Mode Thermal Control System for Space Station Furnace Facility

    NASA Technical Reports Server (NTRS)

    Jackson Mark E.; Shtessel, Yuri B.

    1998-01-01

    The decoupled control of the nonlinear, multiinput-multioutput, and highly coupled space station furnace facility (SSFF) thermal control system is addressed. Sliding mode control theory, a subset of variable-structure control theory, is employed to increase the performance, robustness, and reliability of the SSFF's currently designed control system. This paper presents the nonlinear thermal control system description and develops the sliding mode controllers that cause the interconnected subsystems to operate in their local sliding modes, resulting in control system invariance to plant uncertainties and external and interaction disturbances. The desired decoupled flow-rate tracking is achieved by optimization of the local linear sliding mode equations. The controllers are implemented digitally and extensive simulation results are presented to show the flow-rate tracking robustness and invariance to plant uncertainties, nonlinearities, external disturbances, and variations of the system pressure supplied to the controlled subsystems.

  14. Nonlinear network model analysis of vibrational energy transfer and localisation in the Fenna-Matthews-Olson complex

    NASA Astrophysics Data System (ADS)

    Morgan, Sarah E.; Cole, Daniel J.; Chin, Alex W.

    2016-11-01

    Collective protein modes are expected to be important for facilitating energy transfer in the Fenna-Matthews-Olson (FMO) complex of photosynthetic green sulphur bacteria, however to date little work has focussed on the microscopic details of these vibrations. The nonlinear network model (NNM) provides a computationally inexpensive approach to studying vibrational modes at the microscopic level in large protein structures, whilst incorporating anharmonicity in the inter-residue interactions which can influence protein dynamics. We apply the NNM to the entire trimeric FMO complex and find evidence for the existence of nonlinear discrete breather modes. These modes tend to transfer energy to the highly connected core pigments, potentially opening up alternative excitation energy transfer routes through their influence on pigment properties. Incorporating localised modes based on these discrete breathers in the optical spectra calculations for FMO using ab initio site energies and excitonic couplings can substantially improve their agreement with experimental results.

  15. An Aeroelastic Analysis of a Thin Flexible Membrane

    NASA Technical Reports Server (NTRS)

    Scott, Robert C.; Bartels, Robert E.; Kandil, Osama A.

    2007-01-01

    Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.

  16. Effect of Nozzle Nonlinearities upon Nonlinear Stability of Liquid Propellant Rocket Motors

    NASA Technical Reports Server (NTRS)

    Padmanabhan, M. S.; Powell, E. A.; Zinn, B. T.

    1975-01-01

    A three dimensional, nonlinear nozzle admittance relation is developed by solving the wave equation describing finite amplitude oscillatory flow inside the subsonic portion of a choked, slowly convergent axisymmetric nozzle. This nonlinear nozzle admittance relation is then used as a boundary condition in the analysis of nonlinear combustion instability in a cylindrical liquid rocket combustor. In both nozzle and chamber analyses solutions are obtained using the Galerkin method with a series expansion consisting of the first tangential, second tangential, and first radial modes. Using Crocco's time lag model to describe the distributed unsteady combustion process, combustion instability calculations are presented for different values of the following parameters: (1) time lag, (2) interaction index, (3) steady-state Mach number at the nozzle entrance, and (4) chamber length-to-diameter ratio. In each case, limit cycle pressure amplitudes and waveforms are shown for both linear and nonlinear nozzle admittance conditions. These results show that when the amplitudes of the second tangential and first radial modes are considerably smaller than the amplitude of the first tangential mode the inclusion of nozzle nonlinearities has no significant effect on the limiting amplitude and pressure waveforms.

  17. Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

    PubMed

    Chen, Yong; Yan, Zhenya

    2016-03-22

    Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

  18. Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials

    PubMed Central

    Chen, Yong; Yan, Zhenya

    2016-01-01

    Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543

  19. Simulation of Non-resonant Internal Kink Mode with Toroidal Rotation in NSTX

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Fu, Guoyong

    2013-07-16

    Plasmas in spherical and conventional tokamaks, with weakly reversed shear q pro le and minimum q above but close to unity, are susceptible to an non-resonant (m, n ) = (1, 1) internal kink mode. This mode can saturate and persist and can induce a (2; 1) seed island for Neoclassical Tearing Mode (NTMs)1 . The mode can also lead to large energetic particle transport and signi cant broadening of beam-driven current. Motivated by these important e ects, we have carried out extensive nonlinear simulations of the mode with nite toroidal rotation using parameters and pro les of an NTSXmore » plasma with a weakly reversed shear pro le. The numerical results show that, at the experimental level, plasma rotation has little e ect on either equilibrium or linear stability. However, rotation can signi cantly inuence the nonlinear dynamics of the (1, 1) mode and the the induced (2, 1) magnetic island. The simulation results show that a rotating helical equilibrium is formed and maintained in the nonlinear phase at nite plasma rotation. In contrast, for non-rotating cases, the nonlinear evolution exhibits dynamic oscillations between a quasi-2D state and a helical state. Furthermore, the e ects of rotation are found to greatly suppress the (2, 1) magnetic island even at a low level.« less

  20. Analysis of nonlinear axial vibration of single-walled carbon nanotubes using Homotopy perturbation method

    NASA Astrophysics Data System (ADS)

    Fatahi-Vajari, A.; Azimzadeh, Z.

    2018-05-01

    This paper investigates the nonlinear axial vibration of single-walled carbon nanotubes (SWCNTs) based on Homotopy perturbation method (HPM). A second order partial differential equation that governs the nonlinear axial vibration for such nanotubes is derived using doublet mechanics (DM) theory. To obtain the nonlinear natural frequency in axial vibration mode, this nonlinear equation is solved using HPM. The influences of some commonly used boundary conditions, amplitude of vibration, changes in vibration modes and variations of the nanotubes geometrical parameters on the nonlinear axial vibration characteristics of SWCNTs are discussed. It was shown that unlike the linear one, the nonlinear natural frequency is dependent to maximum vibration amplitude. Increasing the maximum vibration amplitude decreases the natural frequency of vibration compared to the predictions of the linear models. However, with increase in tube length, the effect of the amplitude on the natural frequency decreases. It was also shown that the amount and variation of nonlinear natural frequency is more apparent in higher mode vibration and two clamped boundary conditions. To show the accuracy and capability of this method, the results obtained herein were compared with the fourth order Runge-Kuta numerical results and good agreement was observed. It is notable that the results generated herein are new and can be served as a benchmark for future works.

  1. Strong Local-Field Enhancement of the Nonlinear Soft-Mode Response in a Molecular Crystal

    NASA Astrophysics Data System (ADS)

    Folpini, Giulia; Reimann, Klaus; Woerner, Michael; Elsaesser, Thomas; Hoja, Johannes; Tkatchenko, Alexandre

    2017-09-01

    The nonlinear response of soft-mode excitations in polycrystalline acetylsalicylic acid (aspirin) is studied with two-dimensional terahertz spectroscopy. We demonstrate that the correlation of CH3 rotational modes with collective oscillations of π electrons drives the system into the nonperturbative regime of light-matter interaction, even for a moderate strength of the THz driving field on the order of 50 kV /cm . Nonlinear absorption around 1.1 THz leads to a blueshifted coherent emission at 1.7 THz, revealing the dynamic breakup of the strong electron-phonon correlations. The observed behavior is reproduced by theoretical calculations including dynamic local-field correlations.

  2. All-fiber wavelength-tunable picosecond nonlinear reflectivity measurement setup for characterization of semiconductor saturable absorber mirrors

    NASA Astrophysics Data System (ADS)

    Viskontas, K.; Rusteika, N.

    2016-09-01

    Semiconductor saturable absorber mirror (SESAM) is the key component for many passively mode-locked ultrafast laser sources. Particular set of nonlinear parameters is required to achieve self-starting mode-locking or avoid undesirable q-switch mode-locking for the ultra-short pulse laser. In this paper, we introduce a novel all-fiber wavelength-tunable picosecond pulse duration setup for the measurement of nonlinear properties of saturable absorber mirrors at around 1 μm center wavelength. The main advantage of an all-fiber configuration is the simplicity of measuring the fiber-integrated or fiber-pigtailed saturable absorbers. A tunable picosecond fiber laser enables to investigate the nonlinear parameters at different wavelengths in ultrafast regime. To verify the capability of the setup, nonlinear parameters for different SESAMs with low and high modulation depth were measured. In the operating wavelength range 1020-1074 nm, <1% absolute nonlinear reflectivity accuracy was demonstrated. Achieved fluence range was from 100 nJ/cm2 to 2 mJ/cm2 with corresponding intensity from 10 kW/cm2 to 300 MW/cm2.

  3. Nonlinear ballooning modes in tokamaks: stability and saturation

    NASA Astrophysics Data System (ADS)

    Ham, C. J.; Cowley, S. C.; Brochard, G.; Wilson, H. R.

    2018-07-01

    The nonlinear dynamics of magneto-hydrodynamic ballooning mode perturbations is conjectured to be characterised by the motion of isolated elliptical flux tubes. The theory of stability, dynamics and saturation of such tubes in tokamaks is developed using a generalised Archimedes’ principle. The equation of motion for a tube moving against a drag force in a general axisymmetric equilibrium is derived and then applied to a simplified ‘s–α’ equilibrium. The perturbed nonlinear tube equilibrium (saturated) states are investigated in an ‘s–α’ equilibrium with specific pressure and magnetic shear profiles. The energy of these nonlinear (ballooning) saturated states is calculated. In some cases, particularly at low magnetic shear, these finitely displaced states can have a lower energy than the equilibrium state even if the profile is linearly stable to ballooning modes (infinitesimal tube displacements) at all radii. Thus nonlinear ballooning modes can be metastable. The amplitude of the saturated tube displacement in such cases can be as large as the pressure gradient scale length. We conjecture that triggering a transition into these filamentary states can lead to hard instability limits. A short survey of different pressure profiles is presented to illustrate the variety of behaviour of perturbed elliptical flux tubes.

  4. Ultrasonic nonlinear guided wave inspection of microscopic damage in a composite structure

    NASA Astrophysics Data System (ADS)

    Zhang, Li; Borigo, Cody; Owens, Steven; Lissenden, Clifford; Rose, Joseph; Hakoda, Chris

    2017-02-01

    Sudden structural failure is a severe safety threat to many types of military and industrial composite structures. Because sudden structural failure may occur in a composite structure shortly after macroscale damage initiates, reliable early diagnosis of microdamage formation in the composite structure is critical to ensure safe operation and to reduce maintenance costs. Ultrasonic guided waves have been widely used for long-range defect detection in various structures. When guided waves are generated under certain excitation conditions, in addition to the traditional linear wave mode (known as the fundamental harmonic wave mode), a number of nonlinear higher-order harmonic wave modes are also be generated. Research shows that the nonlinear parameters of a higher-order harmonic wave mode could have excellent sensitivity to microstructural changes in a material. In this work, we successfully employed a nonlinear guided wave structural health monitoring (SHM) method to detect microscopic impact damage in a 32-layer carbon/epoxy fiber-reinforced composite plate. Our effort has demonstrated that, utilizing appropriate transducer design, equipment, excitation signals, and signal processing techniques, nonlinear guided wave parameter measurements can be reliably used to monitor microdamage initiation and growth in composite structures.

  5. Three-dimensional boundary layer stability and transition

    NASA Technical Reports Server (NTRS)

    Malik, M. R.; Li, F.

    1992-01-01

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

  6. Study on Control Scheme for the Inverters in Low Voltage Microgrid with Nonlinear Loads

    NASA Astrophysics Data System (ADS)

    Xu, Jiqiang; Lu, Wenzhou; Wu, Lei

    2017-05-01

    There are a lot of nonlinear loads in real low voltage microgrid system. It will cause serious output voltage and grid current harmonic distortions problems in island and grid-connected modes, respectively. To solve this problem, this paper proposes a droop control scheme with quasi-proportion and resonant (quasi-PR) controller based on αβ stationary reference frame to make microgrid smoothly switch between grid-connected and island modes without changing control method. Moreover, in island mode, not only stable output voltage and frequency, but also reduced output voltage harmonics with added nonlinear loads can be achieved; In grid-connected mode, not only constant power, but also reduced grid current harmonics can be achieved. Simulation results verify the effectiveness of the proposed control scheme.

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

    NASA Astrophysics Data System (ADS)

    Chokani, Ndaona

    2005-01-01

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

  8. A Resonator for Low-Threshold Frequency Conversion

    NASA Technical Reports Server (NTRS)

    Iltchenko, Vladimir; Matsko, Andrey; Savchenkov, Anatoliy; Maleki, Lute

    2004-01-01

    A proposed toroidal or disklike dielectric optical resonator (dielectric optical cavity) would be made of an optically nonlinear material and would be optimized for use in parametric frequency conversion by imposition of a spatially periodic permanent electric polarization. The poling (see figure) would suppress dispersions caused by both the material and the geometry of the optical cavity, thereby effecting quasi-matching of the phases of high-resonance-quality (high-Q) whispering-gallery electromagnetic modes. The quasi-phase-matching of the modes would serve to maximize the interactions among them. Such a resonator might be a prototype of a family of compact, efficient nonlinear devices for operation over a broad range of optical wavelengths. A little background information is prerequisite to a meaningful description of this proposal: (1) Described in several prior NASA Tech Briefs articles, the whispering-gallery modes in a component of spheroidal, disklike, or toroidal shape are waveguide modes that propagate circumferentially and are concentrated in a narrow toroidal region centered on the equatorial plane and located near the outermost edge. (2) For the sake of completeness, it must be stated that even though optical resonators of the type considered here are solid dielectric objects and light is confined within them by total internal reflection at dielectric interfaces without need for mirrors, such components are sometimes traditionally called cavities because their effects upon the light propagating within them are similar to those of true cavities bounded by mirrors. (3) For a given set of electromagnetic modes interacting with each other in an optically nonlinear material (e.g., modes associated with the frequencies involved in a frequency-conversion scheme), the threshold power for oscillation depends on the mode volumes and the mode-overlap integral. (4) Whispering-gallery modes are attractive in nonlinear optics because they maximize the effects of nonlinearities by occupying small volumes and affording high Q values

  9. Nonlinear photothermal Mid-Infrared Microspectroscopy with Superresolution

    NASA Astrophysics Data System (ADS)

    Erramilli, Shyamsunder; Mertiri, Alket; Liu, Hui; Totachawattana, Atcha; Hong, Mi; Sander, Michelle

    2015-03-01

    We describe a nonlinear method for breaking the diffraction limit in mid-infrared microscopy using nonlinear photothermal microspectroscopy. A Quantum Cascade Laser (QCL) tuned to an infrared active vibrational molecular normal mode is used as the pump laser. A low-phase noise Erbium-doped fiber (EDFL) laser is used as the probe. When the incident intensity of the mid-infrared pump laser is increased past a critical threshold, a nanobubble is nucleated, strongly modulating the scatter of the probe beam, in agreement with prior work. Remarkably, we have also found that the photothermal spectral signature of the mid-infrared absorption bifurcates and is strongly narrowed, consistent with an effective ``mean-field'' theory of the observed pitchfork bifurcation. This ultrasharp narrowing can be exploited to obtain mid-infrared images with a resolution that breaks the diffraction limit, without the need of mechanical scanning near-field probes. The method provides a powerful new tool for hyperspectral label-free mid-infrared imaging and characterization of biological tissues and materials science and engineering. We thank our collaborators H. Altug, L. D. Ziegler, J. Mertz, for their advice and generous loan of equipment.

  10. Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

    NASA Astrophysics Data System (ADS)

    Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

    2000-04-01

    We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

  11. Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept.

    PubMed

    Mamatsashvili, G; Khujadze, G; Chagelishvili, G; Dong, S; Jiménez, J; Foysi, H

    2016-08-01

    To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86, and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.

  12. Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept

    NASA Astrophysics Data System (ADS)

    Mamatsashvili, G.; Khujadze, G.; Chagelishvili, G.; Dong, S.; Jiménez, J.; Foysi, H.

    2016-08-01

    To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86, and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.

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

    NASA Astrophysics Data System (ADS)

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

    2015-08-01

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

  14. Nonlinear interaction of strong S-waves with the rupture front in the shallow subsurface

    NASA Astrophysics Data System (ADS)

    Sleep, N. H.

    2017-12-01

    Shallow deformation in moderate to large earthquakes is sometimes distributed rather than being concentrated on a single fault plane. Strong high-frequency S-waves interact with the rupture front to produce this effect. For strike-slip faults, the rupture propagation velocity is a fraction of the S-wave velocity. The rupture propagation vector refracts essentially vertically in the low (S-wave) velocity shallow subsurface. So does the propagation direction of S-waves. The shallow rupture front is essentially mode 3 near the surface. Strong S-waves arrive before the rupture front. They continue to arrive for several seconds in a large event. There are simple scaling relationships. The dynamic Coulomb stress ratio of horizontal stress on horizontal planes from S-waves is the normalized acceleration in g's. For fractured rock and gravel, frictional failure occurs when the normalized acceleration exceeds the effective coefficient of friction. Acceleration tends to saturate at that level as the anelastic strain rate increases rapidly with stress. For muddy materials, failure begins at a low normalized acceleration but increases slowly with dynamic stress. Dynamic accelerations sometimes exceed 1 g. In both cases, the rupture tip finds the shallow subsurface already in nonlinear failure down to a few to tens of meters depth. The material does not distinguish between S-wave and rupture tip stresses. Both stresses add to the stress invariant and hence to the anelastic strain rate tensor. Surface anelastic strain from fault slip is thus distributed laterally over a distance scaling to the depth of nonlinearity from S-waves. The environs of the fault anelastically accommodate the fault slip at depth. This process differs from blind faults where the shallow coseismic strain is mostly elastic and interseismic anelastic processes accommodate the long-term shallow deformation.

  15. Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

    NASA Astrophysics Data System (ADS)

    Cummings, Patrick

    We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

  16. Observation of dynamic interactions between fundamental and second-harmonic modes in a high-power sub-terahertz gyrotron operating in regimes of soft and hard self-excitation.

    PubMed

    Saito, Teruo; Tatematsu, Yoshinori; Yamaguchi, Yuusuke; Ikeuchi, Shinji; Ogasawara, Shinya; Yamada, Naoki; Ikeda, Ryosuke; Ogawa, Isamu; Idehara, Toshitaka

    2012-10-12

    Dynamic mode interaction between fundamental and second-harmonic modes has been observed in high-power sub-terahertz gyrotrons [T. Notake et al., Phys. Rev. Lett. 103, 225002 (2009); T. Saito et al. Phys. Plasmas 19, 063106 (2012)]. Interaction takes place between a parasitic fundamental or first-harmonic (FH) mode and an operating second-harmonic (SH) mode, as well as among SH modes. In particular, nonlinear excitation of the parasitic FH mode in the hard self-excitation regime with assistance of a SH mode in the soft self-excitation regime was clearly observed. Moreover, both cases of stable two-mode oscillation and oscillation of the FH mode only were observed. These observations and theoretical analyses of the dynamic behavior of the mode interaction verify the nonlinear hard self-excitation of the FH mode.

  17. Nonlinearities in reservoir engineering: Enhancing quantum correlations

    NASA Astrophysics Data System (ADS)

    Hu, Xiangming; Hu, Qingping; Li, Lingchao; Huang, Chen; Rao, Shi

    2017-12-01

    There are two decisive factors for quantum correlations in reservoir engineering, but they are strongly reversely dependent on the atom-field nonlinearities. One is the squeezing parameter for the Bogoliubov modes-mediated collective interactions, while the other is the dissipative rates for the engineered collective dissipations. Exemplifying two-level atomic ensembles, we show that the moderate nonlinearities can compromise these two factors and thus enhance remarkably two-mode squeezing and entanglement of different spin atomic ensembles or different optical fields. This suggests that the moderate nonlinearities of the two-level systems are more advantageous for applications in quantum networks associated with reservoir engineering.

  18. Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD

    NASA Astrophysics Data System (ADS)

    Beidler, M. T.; Callen, J. D.; Hegna, C. C.; Sovinec, C. R.

    2017-05-01

    The nonlinear, extended-magnetohydrodynamic (MHD) code NIMROD is benchmarked with the theory of time-dependent forced magnetic reconnection induced by small resonant fields in slab geometry in the context of visco-resistive MHD modeling. Linear computations agree with time-asymptotic, linear theory of flow screening of externally applied fields. The inclusion of flow in nonlinear computations can result in mode penetration due to the balance between electromagnetic and viscous forces in the time-asymptotic state, which produces bifurcations from a high-slip state to a low-slip state as the external field is slowly increased. We reproduce mode penetration and unlocking transitions by employing time-dependent externally applied magnetic fields. Mode penetration and unlocking exhibit hysteresis and occur at different magnitudes of applied field. We also establish how nonlinearly determined flow screening of the resonant field is affected by the square of the magnitude of the externally applied field. These results emphasize that the inclusion of nonlinear physics is essential for accurate prediction of the reconnected field in a flowing plasma.

  19. Nonlinear Reduced-Order Simulation Using Stress-Free and Pre-Stressed Modal Bases

    NASA Technical Reports Server (NTRS)

    Przekop, Adam; Stover, Michael A.; Rizzi, Stephen A.

    2009-01-01

    A study is undertaken to determine the advantages and disadvantages associated with application of stress-free and pre-stressed modal bases in a reduced-order finite-element-based nonlinear simulation. A planar beam is chosen as an application example and its response due to combined thermal and random pressure loadings is examined. Combinations of two random pressure levels and two thermal conditions are investigated. The latter consists of an ambient temperature condition and an elevated temperature condition in the post-buckled regime. It is found that stress-free normal modes establish a broadly applicable modal basis yielding accurate results for all the loading regimes considered. In contrast, the range of applicability for a thermally pre-stressed modal basis is found to be limited. The behavior is explained by scrutinizing the coupling found in the linear stiffness and the effect this coupling has on the structural response characteristics under the range of loading conditions considered.

  20. Evaluation of the vibration-rotation-tunneling dynamics at the basis set superposition error corrected global minimum geometry of the ammonia dimer

    NASA Astrophysics Data System (ADS)

    Muguet, Francis F.; Robinson, G. Wilse; Bassez-Muguet, M. Palmyre

    1995-03-01

    With the help of a new scheme to correct for the basis set superposition error (BSSE), we find that an eclipsed nonlinear geometry becomes energetically favored over the eclipsed linear hydrogen-bonded geometry. From a normal mode analysis of the potential energy surface (PES) in the vicinity of the nonlinear geometry, we suggest that several dynamical interchange pathways must be taken into account. The minimal molecular symmetry group to be considered should be the double group of G36, but still larger multiple groups may be required. An interpretation of experimental vibration-rotation-tunneling (VRT) data in terms of the G144 group, which implies monomer inversions, may not be the only alternative. It appears that group theoretical considerations alone are insufficient for understanding the complex VRT dynamics of the ammonia dimer.

  1. Nonlinear motion of cantilevered SWNT and Its Meaning to Phonon Dynamics

    NASA Astrophysics Data System (ADS)

    Koh, Heeyuen; Cannon, James; Chiashi, Shohei; Shiomi, Junichiro; Maruyama, Shigeo

    2013-03-01

    Based on the finding that the lowest frequency mode of cantilevered SWNT is described by the continuum beam theory in frequency domain, we considered its effect of the symmetric structure for the coupling of orthogonal transverse modes to explain the nonlinear motion of free thermal vibration. This nonlinear motion calculated by our molecular dynamics simulation, once regarded as noise, is observed to have the periodic order with duffing and beating, which is dependent on aspect ratio and temperature. It could be dictated by the governing equation from the Green Lagrangian strain tensor. The nonlinear beam equation from strain tensor described the motion well for various models which has different aspect ratio in molecular dynamics simulation. Since this motion is nothing but the interaction between 2nd mode of radial, tangential mode and 1st longitudinal mode, it was found that Green Lagrangian strain tensor is capable to deal such coupling. The free thermal motion of suspended SWNT is also considered without temperature gradient. The Q factor measured by this theoretical analysis will be discussed. Part of this work was financially supported by Grant-in-Aid for Scientific Research (19054003 and 22226006), and Global COE Program 'Global Center for Excellence for Mechanical Systems Innovation'

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

    PubMed

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

    2014-11-15

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

  3. Wave-induced response of a floating two-dimensional body with a moonpool

    PubMed Central

    Fredriksen, Arnt G.; Kristiansen, Trygve; Faltinsen, Odd M.

    2015-01-01

    Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. PMID:25512594

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

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  5. Period doubling and other nonlinear phenomena in volcanic earthquakes and tremor

    USGS Publications Warehouse

    Julian, B.R.

    2000-01-01

    Evidence of subharmonic period-doubling cascades has recently been recognized in seismograms of volcanic tremor from several volcanoes. This phenomenon occurs only in nonlinear systems, and is the commonest route by which such systems change from periodic to chaotic behavior. It is predicted to occur in a model of volcanic tremor excitation by flow-induced vibration, and it might well also occur in other volcano-seismic source process. If the possibility of period doubling is not taken into account in interpreting spectra of tremor and long-period earthquakes, then low-frequency "sub-harmonic" oscillations may be mis-identified as normal modes of a linear acoustic resonator, leading to errors of an order of magnitude or more in inferred magma-body dimensions. This example illustrates the importance of nonlinear phenomena in attempts to understand volcano-seismic phenomena physically. Linear systems are fundamentally incapable of causing earthquakes or exciting tremor, so nonlinearity is essential to any theory of volcano-seismic phenomena. Nonlinear processes are in many respects qualitatively different from linear ones. A few of their characteristics that might be relevant in volcanoes include the possibility: (1) that damping might increase, rather than decrease, oscillation frequencies; and (2) that these frequencies might be functions of the amplitude of oscillation, so that temporal variations in spectral peak frequencies might not be manifestations of changes of conditions within the magmatic system.

  6. Wave theory of turbulence in compressible media

    NASA Technical Reports Server (NTRS)

    Kentzer, C. P.

    1975-01-01

    An acoustical theory of turbulence was developed to aid in the study of the generation of sound in turbulent flows. The statistical framework adopted is a quantum-like wave dynamical formulation in terms of complex distribution functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. This system of nonlinear equations is closed and complete. The technique of analysis was chosen such that direct applications to practical problems can be obtained with relative ease.

  7. Renormalized vibrations and normal energy transport in 1d FPU-like discrete nonlinear Schrödinger equations.

    PubMed

    Li, Simeng; Li, Nianbei

    2018-03-28

    For one-dimensional (1d) nonlinear atomic lattices, the models with on-site nonlinearities such as the Frenkel-Kontorova (FK) and ϕ 4 lattices have normal energy transport while the models with inter-site nonlinearities such as the Fermi-Pasta-Ulam-β (FPU-β) lattice exhibit anomalous energy transport. The 1d Discrete Nonlinear Schrödinger (DNLS) equations with on-site nonlinearities has been previously studied and normal energy transport has also been found. Here, we investigate the energy transport of 1d FPU-like DNLS equations with inter-site nonlinearities. Extended from the FPU-β lattice, the renormalized vibration theory is developed for the FPU-like DNLS models and the predicted renormalized vibrations are verified by direct numerical simulations same as the FPU-β lattice. However, the energy diffusion processes are explored and normal energy transport is observed for the 1d FPU-like DNLS models, which is different from their atomic lattice counterpart of FPU-β lattice. The reason might be that, unlike nonlinear atomic lattices where models with on-site nonlinearities have one less conserved quantities than the models with inter-site nonlinearities, the DNLS models with on-site or inter-site nonlinearities have the same number of conserved quantities as the result of gauge transformation.

  8. Cerebrovascular pattern improved by ozone autohemotherapy: an entropy-based study on multiple sclerosis patients.

    PubMed

    Molinari, Filippo; Rimini, Daniele; Liboni, William; Acharya, U Rajendra; Franzini, Marianno; Pandolfi, Sergio; Ricevuti, Giovanni; Vaiano, Francesco; Valdenassi, Luigi; Simonetti, Vincenzo

    2017-08-01

    Ozone major autohemotherapy is effective in reducing the symptoms of multiple sclerosis (MS) patients, but its effects on brain are still not clear. In this work, we have monitored the changes in the cerebrovascular pattern of MS patients and normal subjects during major ozone autohemotherapy by using near-infrared spectroscopy (NIRS) as functional and vascular technique. NIRS signals are analyzed using a combination of time, time-frequency analysis and nonlinear analysis of intrinsic mode function signals obtained from empirical mode decomposition technique. Our results show that there is an improvement in the cerebrovascular pattern of all subjects indicated by increasing the entropy of the NIRS signals. Hence, we can conclude that the ozone therapy increases the brain metabolism and helps to recover from the lower activity levels which is predominant in MS patients.

  9. Propagating Polaritons in III-Nitride Slab Waveguides

    NASA Astrophysics Data System (ADS)

    Ciers, J.; Roch, J. G.; Carlin, J.-F.; Jacopin, G.; Butté, R.; Grandjean, N.

    2017-03-01

    We report on III-nitride waveguides with c -plane GaN /(Al ,Ga )N quantum wells in the strong light-matter coupling regime supporting propagating polaritons. They feature a normal-mode splitting as large as 60 meV at low temperatures thanks to the large overlap between the optical mode and the active region, a polariton decay length up to 100 μ m for photonlike polaritons and a lifetime of 1 to 2 ps, with the latter values being essentially limited by residual absorption occurring in the waveguide. The fully lattice-matched nature of the structure allows for very low disorder and high in-plane homogeneity, which is an important asset for the realization of polaritonic integrated circuits that could support nonlinear polariton wave packets up to room temperature thanks to the large exciton binding energy of 40 meV.

  10. Femtosecond Optics: Advanced Devices and Ultrafast Phenomena

    DTIC Science & Technology

    2007-05-31

    repetition rate from a soliton fiber laser [6]. Because the mode- locking mechanism is passive, no external oscillator is required, leading to a more...nonlinearity, 1.8 m of LNL-SMF is included in the laser. Mode- locked operation of the laser was obtained through nonlinear polarization evolution [6]. For pump...Generation in Photonic Crystal Fibers for Optical Coherence Tomography H. Frequency Swept Lasers and Fourier Domain Mode Locking (FDML) I. Physics of

  11. Efficient computational nonlinear dynamic analysis using modal modification response technique

    NASA Astrophysics Data System (ADS)

    Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

    2012-08-01

    Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

  12. Generation of zonal magnetic fields by low-frequency dispersive electromagnetic waves in a nonuniform dusty magnetoplasma.

    PubMed

    Shukla, P K

    2004-04-01

    It is shown that zonal magnetic fields can be parametrically excited by low-frequency dispersive driftlike compressional electromagnetic (DDCEM) modes in a nonuniform dusty magnetoplasma. For this purpose, we derive a pair of coupled equations which exhibits the nonlinear coupling between DDCEM modes and zonal magnetic fields. The coupled mode equations are Fourier analyzed to derive a nonlinear dispersion relation. The latter depicts that zonal magnetic fields are nonlinearly generated at the expense of the low-frequency DDCEM wave energy. The relevance of our investigation to the transfer of energy from short scale DDCEM waves to long scale zonal magnetic field structures in dark molecular clouds is discussed.

  13. Stochasticity in numerical solutions of the nonlinear Schroedinger equation

    NASA Technical Reports Server (NTRS)

    Shen, Mei-Mei; Nicholson, D. R.

    1987-01-01

    The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.

  14. Qualitative analysis of ultra-short optical dissipative solitary pulses in the actively mode-locked semiconductor heterolasers with an external fiber cavity

    NASA Astrophysics Data System (ADS)

    Shcherbakov, Alexandre S.; Campos Acosta, Joaquin; Moreno Zarate, Pedro; Pons Aglio, Alicia

    2011-02-01

    An advanced qualitative characterization of simultaneously existing various low-power trains of ultra-short optical pulses with an internal frequency modulation in a distributed laser system based on semiconductor heterostructure is presented. The scheme represents a hybrid cavity consisting of a single-mode heterolaser operating in the active mode-locking regime and an external long single-mode optical fiber exhibiting square-law dispersion, cubic Kerr nonlinearity, and linear optical losses. In fact, we consider the trains of optical dissipative solitons, which appear within double balance between the second-order dispersion and cubic-law nonlinearity as well as between the active-medium gain and linear optical losses in a hybrid cavity. Moreover, we operate on specially designed modulating signals providing non-conventional composite regimes of simultaneous multi-pulse active mode-locking. As a result, the mode-locking process allows shaping regular trains of picosecond optical pulses excited by multi-pulse independent on each other sequences of periodic modulations. In so doing, we consider the arranged hybrid cavity as a combination of a quasi-linear part responsible for the active mode-locking by itself and a nonlinear part determining the regime of dissipative soliton propagation. Initially, these parts are analyzed individually, and then the primarily obtained data are coordinated with each other. Within this approach, a contribution of the appeared cubically nonlinear Ginzburg-Landau operator is analyzed via exploiting an approximate variational procedure involving the technique of trial functions.

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

    NASA Astrophysics Data System (ADS)

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

    2018-05-01

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

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

    PubMed

    Mobayen, Saleh

    2018-06-01

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

  17. Roles Played by Electrostatic Waves in Producing Radio Emissions

    NASA Technical Reports Server (NTRS)

    Cairns, Iver H.

    2000-01-01

    Processes in which electromagnetic radiation is produced directly or indirectly via intermediate waves are reviewed. It is shown that strict theoretical constraints exist for electrons to produce nonthermal levels of radiation directly by the Cerenkov or cyclotron resonances. In contrast, indirect emission processes in which intermediary plasma waves are converted into radiation are often favored on general and specific grounds. Four classes of mechanisms involving the conversion of electrostatic waves into radiation are linear mode conversion, hybrid linear/nonlinear mechanisms, nonlinear wave-wave and wave-particle processes, and radiation from localized wave packets. These processes are reviewed theoretically and observational evidence summarized for their occurrence. Strong evidence exists that specific nonlinear wave processes and mode conversion can explain quantitatively phenomena involving type III solar radio bursts and ionospheric emissions. On the other hand, no convincing evidence exists that magnetospheric continuum radiation is produced by mode conversion instead of nonlinear wave processes. Further research on these processes is needed.

  18. Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock

    NASA Astrophysics Data System (ADS)

    Chouvion, B.; McWilliam, S.; Popov, A. A.

    2018-06-01

    This paper investigates the dynamic behaviour of capacitive ring-based Coriolis Vibrating Gyroscopes (CVGs) under severe shock conditions. A general analytical model is developed for a multi-supported ring resonator by describing the in-plane ring response as a finite sum of modes of a perfect ring and the electrostatic force as a Taylor series expansion. It is shown that the supports can induce mode coupling and that mode coupling occurs when the shock is severe and the electrostatic forces are nonlinear. The influence of electrostatic nonlinearity is investigated by numerically simulating the governing equations of motion. For the severe shock cases investigated, when the electrode gap reduces by ∼ 60 % , it is found that three ring modes of vibration (1 θ, 2 θ and 3 θ) and a 9th order force expansion are needed to obtain converged results for the global shock behaviour. Numerical results when the 2 θ mode is driven at resonance indicate that electrostatic nonlinearity introduces mode coupling which has potential to reduce sensor performance under operating conditions. Under some circumstances it is also found that severe shocks can cause the vibrating response to jump to another stable state with much lower vibration amplitude. This behaviour is mainly a function of shock amplitude and rigid-body motion damping.

  19. Toward nonlinear magnonics: Intensity-dependent spin-wave switching in insulating side-coupled magnetic stripes

    NASA Astrophysics Data System (ADS)

    Sadovnikov, A. V.; Odintsov, S. A.; Beginin, E. N.; Sheshukova, S. E.; Sharaevskii, Yu. P.; Nikitov, S. A.

    2017-10-01

    We demonstrate that the nonlinear spin-wave transport in two laterally parallel magnetic stripes exhibit the intensity-dependent power exchange between the adjacent spin-wave channels. By the means of Brillouin light scattering technique, we investigate collective nonlinear spin-wave dynamics in the presence of magnetodipolar coupling. The nonlinear intensity-dependent effect reveals itself in the spin-wave mode transformation and differential nonlinear spin-wave phase shift in each adjacent magnetic stripe. The proposed analytical theory, based on the coupled Ginzburg-Landau equations, predicts the geometry design involving the reduction of power requirement to the all-magnonic switching. A very good agreement between calculation and experiment was found. In addition, a micromagnetic and finite-element approach has been independently used to study the nonlinear behavior of spin waves in adjacent stripes and the nonlinear transformation of spatial profiles of spin-wave modes. Our results show that the proposed spin-wave coupling mechanism provides the basis for nonlinear magnonic circuits and opens the perspectives for all-magnonic computing architecture.

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

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  1. The effects of suction on the nonlinear stability of the three-dimensional boundary layer above a rotating disc

    NASA Technical Reports Server (NTRS)

    Bassom, Andrew P.; Seddougui, Sharon O.

    1991-01-01

    There exist two types of stationary instability of the flow over a rotating disc corresponding to the upper branch, inviscid mode and the lower branch mode, which has a triple deck structure, of the neutral stability curve. A theoretical study of the linear problem and an account of the weakly nonlinear properties of the lower branch modes have been undertaken by Hall and MacKerrell respectively. Motivated by recent reports of experimental sightings of the lower branch mode and an examination of the role of suction on the linear stability properties of the flow here, the effects are studied of suction on the nonlinear disturbance described by MacKerrell. The additional analysis required in order to incorporate suction is relatively straightforward and enables the derivation of an amplitude equation which describes the evolution of the mode. For each value of the suction, a threshold value of the disturbance amplitude is obtained; modes of size greater than this threshold grow without limit as they develop away from the point of neutral stability.

  2. PV Degradation Curves: Non-Linearities and Failure Modes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jordan, Dirk C.; Silverman, Timothy J.; Sekulic, Bill

    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,more » 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.« less

  3. On the secondary instability of the most dangerous Goertler vortex

    NASA Technical Reports Server (NTRS)

    Otto, S. R.; Denier, James P.

    1993-01-01

    Recent studies have demonstrated the most unstable Goertler vortex mode is found in flows, both two and three-dimensional, with regions of (moderately) large body curvature and these modes reside within a thin layer situated at the base of the conventional boundary layer. Further work concerning the nonlinear development of the most dangerous mode demonstrates that the flow results in a self induced flow reversal. However, prior to the point at which flow reversal is encountered, the total streamwise velocity profile is found to be highly inflectional in nature. Previous work then suggests that the nonlinear vortex state will become unstable to secondary, inviscid, Rayleigh wave instabilities prior to the point of flow reversal. Our concern is with the secondary instability of the nonlinear vortex states, which result from the streamwise evolution of the most unstable Goertler vortex mode, with the aim of determining whether such modes can induce a transition to a fully turbulent state before separation is encountered.

  4. Frequency chirpings in Alfven continuum

    NASA Astrophysics Data System (ADS)

    Wang, Ge; Berk, Herb; Breizman, Boris; Zheng, Linjin

    2017-10-01

    We have used a self-consistent mapping technique to describe both the nonlinear wave-energetic particle resonant interaction and its spatial mode structure that depends upon the resonant energetic particle pressure. At the threshold for the onset of the energetic particle mode (EPM), strong chirping emerges in the lower continuum close to the TAE gap and then, driven by strong continuum damping, chirps rapidly to lower frequencies in the Alfven continuum. An adiabatic theory was developed that accurately replicated the results from the simulation where the nonlinearity was only due to the EPM resonant particles. The results show that the EPM-trapped particles have their action conserved during the time of rapid chirping. This adiabaticity enabled wave trapped particles to be confined within their separatrix, and produce even larger resonant structures, that can produce a large amplitude mode far from linearly predicted frequencies. In the present work we describe the effect of additional MHD nonlinearity to this calculation. We studied how the zonal flow component and its nonlinear feedback to the fundamental frequency and found that the MHD nonlinearity doesn't significantly alter the frequency chirping response that is predicted by the calculation that neglects the MHD nonlinearity.

  5. Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

    NASA Astrophysics Data System (ADS)

    Squire, J.; Quataert, E.; Kunz, M. W.

    2017-12-01

    In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the `parasitic instabilities' that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

  6. Sensitivity of a three-mirror cavity to thermal and nonlinear lensing: Gaussian-beam analysis.

    PubMed

    Anctil, G; McCarthy, N; Piché, M

    2000-12-20

    We consider a compact three-mirror cavity consisting of a flat output coupler, a curved folding mirror, and an active medium with one facet cut at the Brewster angle and the other facet coated for unit reflectivity. We examine the sensitivity to thermal lensing and to self-focusing in the active medium of the Gaussian beam that is circulating in that cavity. We use a simple thin-lens model; the astigmatism of the beam that is circulating in the cavity and the nonlinear coupling between the field distributions along the two orthogonal axes are taken into account. We find configurations in which beam ellipticity is compensated for at either end of the cavity in the presence of thermal lensing. We have derived an analytical criterion that predicts the sensitivity of the beam size to nonlinear lensing. The ability of the cavity to favor self-mode locking is found to be sensitive to the strength of thermal lensing. In the absence of thermal lensing, cavities operated as telescopic systems (C = 0) or self-imaging systems (B = 0) are most appropriate for achieving self-mode locking, with nonlinear mode selection accomplished through saturation of the spatially varying laser gain. We identify conditions for which self-mode locking can be produced by variable-reflectivity output couplers with either maximum or minimum reflectivity at the center of the coupler. We use our model to estimate the nonlinear gain produced in laser cavities equipped with such output couplers. We identify a cavity configuration for which nonlinear lensing can simultaneously produce mode locking and correction of beam ellipticity at the output coupler.

  7. Sensitivity of a Three-Mirror Cavity to Thermal and Nonlinear Lensing: Gaussian-Beam Analysis

    NASA Astrophysics Data System (ADS)

    Anctil, Geneviève; McCarthy, Nathalie; Piché, Michel

    2000-12-01

    We consider a compact three-mirror cavity consisting of a flat output coupler, a curved folding mirror, and an active medium with one facet cut at the Brewster angle and the other facet coated for unit reflectivity. We examine the sensitivity to thermal lensing and to self-focusing in the active medium of the Gaussian beam that is circulating in that cavity. We use a simple thin-lens model; the astigmatism of the beam that is circulating in the cavity and the nonlinear coupling between the field distributions along the two orthogonal axes are taken into account. We find configurations in which beam ellipticity is compensated for at either end of the cavity in the presence of thermal lensing. We have derived an analytical criterion that predicts the sensitivity of the beam size to nonlinear lensing. The ability of the cavity to favor self-mode locking is found to be sensitive to the strength of thermal lensing. In the absence of thermal lensing, cavities operated as telescopic systems ( C 0 ) or self-imaging systems ( B 0 ) are most appropriate for achieving self-mode locking, with nonlinear mode selection accomplished through saturation of the spatially varying laser gain. We identify conditions for which self-mode locking can be produced by variable-reflectivity output couplers with either maximum or minimum reflectivity at the center of the coupler. We use our model to estimate the nonlinear gain produced in laser cavities equipped with such output couplers. We identify a cavity configuration for which nonlinear lensing can simultaneously produce mode locking and correction of beam ellipticity at the output coupler.

  8. On the Role of Resonances in Nonradial Pulsators

    NASA Technical Reports Server (NTRS)

    Buchler, J. R.; Goupil, M. J.; Hansen, C. J.

    1997-01-01

    Resonances or near resonances are ubiquitous among the excited nonradial pulsation modes of variable stars and they must play an important role in determining their pulsational behavior. Here in a first step at nonlinear asteroseismology, we explore some of the consequences of resonances by means of the amplitude equation formalism. We show how parity and angular momentum constraints can be used to eliminate many of the possible nonlinear resonant couplings between modes (and multiplets of modes), and how the amplitude equations can thus be simplified. Even when we may not be able, nor wish, to make an ab initio computation of the values of the coupling coefficients, it is still possible to obtain constraints on the nature of the excited modes if a resonance between observed frequencies can be identified. Resonances can cause nonlinear frequency locking of modes. This means that the observed frequencies appear in exact resonance even though the linear frequencies are only approximately in resonance. The nonlinear frequency lock, when it occurs, it does so over a range of departures from linear resonance, and it is accompanied by constant pulsation amplitudes. The locked, nonlinear frequencies can differ noticeably from their nonresonant counterparts which are usually used in seismology. This is particularly true for multiplets of modes split by rotation. Beyond the regime of the frequency lock, amplitude and frequency modulations can appear in the pulsations. Far from the resonance condition one recovers the regime of steady pulsations with nonresonant frequencies for which the seismological studies, as they are presently carried out, are justified (provided furthermore, of course, that nonlinear frequency shifts are negligible). Success in identifying a resonance in an observed power spectrum depends on the quality of the data. While keeping this limitation in mind, ew discuss the possible existence of peculiar resonances the pulsations specific variable white dwarfs and delta Scuti stars.

  9. Saturation amplitude of the f-mode instability

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kastaun, Wolfgang; Willburger, Beatrix; Kokkotas, Kostas D.

    2010-11-15

    We investigate strong nonlinear damping effects which occur during high amplitude oscillations of neutron stars, and the gravitational waves they produce. For this, we use a general relativistic nonlinear hydrodynamics code in conjunction with a fixed spacetime (Cowling approximation) and a polytropic equation of state (EOS). Gravitational waves are estimated using the quadrupole formula. Our main interest are l=m=2 f modes subject to the CFS (Chandrasekhar, Friedman, Schutz) instability, but we also investigate axisymmetric and quasiradial modes. We study various models to determine the influence of rotation rate and EOS. We find that axisymmetric oscillations at high amplitudes are predominantlymore » damped by shock formation, while the nonaxisymmetric f modes are mainly damped by wave breaking and, for rapidly rotating models, coupling to nonaxisymmetric inertial modes. From the observed nonlinear damping, we derive upper limits for the saturation amplitude of CFS-unstable f modes. Finally, we estimate that the corresponding gravitational waves for an oscillation amplitude at the upper limit should be detectable with the advanced LIGO (Laser Interferometer Gravitational Wave Observatory) and VIRGO interferometers at distances above 10 Mpc. This strongly depends on the stellar model, in particular, on the mode frequency.« less

  10. Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach

    PubMed Central

    Xie, Weihong; Yu, Yang

    2017-01-01

    Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG) in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM) estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively “switch” from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly. PMID:29124062

  11. Beating Heart Motion Accurate Prediction Method Based on Interactive Multiple Model: An Information Fusion Approach.

    PubMed

    Liang, Fan; Xie, Weihong; Yu, Yang

    2017-01-01

    Robot-assisted motion compensated beating heart surgery has the advantage over the conventional Coronary Artery Bypass Graft (CABG) in terms of reduced trauma to the surrounding structures that leads to shortened recovery time. The severe nonlinear and diverse nature of irregular heart rhythm causes enormous difficulty for the robot to realize the clinic requirements, especially under arrhythmias. In this paper, we propose a fusion prediction framework based on Interactive Multiple Model (IMM) estimator, allowing each model to cover a distinguishing feature of the heart motion in underlying dynamics. We find that, at normal state, the nonlinearity of the heart motion with slow time-variant changing dominates the beating process. When an arrhythmia occurs, the irregularity mode, the fast uncertainties with random patterns become the leading factor of the heart motion. We deal with prediction problem in the case of arrhythmias by estimating the state with two behavior modes which can adaptively "switch" from one to the other. Also, we employed the signal quality index to adaptively determine the switch transition probability in the framework of IMM. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The test results indicate that the new proposed approach reduces prediction errors significantly.

  12. Validation of MHD Models using MST RFP Plasmas

    NASA Astrophysics Data System (ADS)

    Jacobson, C. M.; Chapman, B. E.; den Hartog, D. J.; McCollam, K. J.; Sarff, J. S.; Sovinec, C. R.

    2017-10-01

    Rigorous validation of computational models used in fusion energy sciences over a large parameter space and across multiple magnetic configurations can increase confidence in their ability to predict the performance of future devices. MST is a well diagnosed reversed-field pinch (RFP) capable of operation with plasma current ranging from 60 kA to 500 kA. The resulting Lundquist number S, a key parameter in resistive magnetohydrodynamics (MHD), ranges from 4 ×104 to 8 ×106 for standard RFP plasmas and provides substantial overlap with MHD RFP simulations. MST RFP plasmas are simulated using both DEBS, a nonlinear single-fluid visco-resistive MHD code, and NIMROD, a nonlinear extended MHD code, with S ranging from 104 to 105 for single-fluid runs, and the magnetic Prandtl number Pm = 1 . Validation metric comparisons are presented, focusing on how normalized magnetic fluctuations at the edge b scale with S. Preliminary results for the dominant n = 6 mode are b S - 0 . 20 +/- 0 . 02 for single-fluid NIMROD, b S - 0 . 25 +/- 0 . 05 for DEBS, and b S - 0 . 20 +/- 0 . 02 for experimental measurements, however there is a significant discrepancy in mode amplitudes. Preliminary two-fluid NIMROD results are also presented. Work supported by US DOE.

  13. Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

    DOE PAGES

    Mikkelsen, D. R.; Howard, N. T.; White, A. E.; ...

    2018-04-25

    Here, verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for k yρ smore » ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers.« less

  14. Verification of GENE and GYRO with L-mode and I-mode plasmas in Alcator C-Mod

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mikkelsen, D. R.; Howard, N. T.; White, A. E.

    Here, verification comparisons are carried out for L-mode and I-mode plasma conditions in Alcator C-Mod. We compare linear and nonlinear ion-scale calculations by the gyrokinetic codes GENE and GYRO to each other and to the experimental power balance analysis. The two gyrokinetic codes' linear growth rates and real frequencies are in good agreement throughout all the ion temperature gradient mode branches and most of the trapped electron mode branches of the kyρs spectra at r/a = 0.65, 0.7, and 0.8. The shapes of the toroidal mode spectra of heat fluxes in nonlinear simulations are very similar for k yρ smore » ≤ 0.5, but in most cases GENE has a relatively higher heat flux than GYRO at higher mode numbers.« less

  15. Influence of Stationary Crossflow Modulation on Secondary Instability

    NASA Technical Reports Server (NTRS)

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

    2016-01-01

    A likely scenario for swept wing transition on subsonic aircraft with natural laminar flow involves the breakdown of stationary crossflow vortices via high frequency secondary instability. A majority of the prior research on this secondary instability has focused on crossflow vortices with a single dominant spanwise wavelength. This paper investigates the effects of the spanwise modulation of stationary crossflow vortices at a specified wavelength by a subharmonic stationary mode. Secondary instability of the modulated crossflow pattern is studied using planar, partial-differential-equation based eigenvalue analysis. Computations reveal that weak modulation by the first subharmonic of the input stationary mode leads to mode splitting that is particularly obvious for Y-type secondary modes that are driven by the wall-normal shear of the basic state. Thus, for each Y mode corresponding to the fundamental wavelength of results in unmodulated train of crossflow vortices, the modulated flow supports a pair of secondary modes with somewhat different amplification rates. The mode splitting phenomenon suggests that a more complex stationary modulation such as that induced by natural surface roughness would yield a considerably richer spectrum of secondary instability modes. Even modest levels of subharmonic modulation are shown to have a strong effect on the overall amplification of secondary disturbances, particularly the Z-modes driven by the spanwise shear of the basic state. Preliminary computations related to the nonlinear breakdown of these secondary disturbances provide interesting insights into the process of crossflow transition in the presence of the first subharmonic of the dominant stationary vortex.

  16. On the nonlinear trapping nature of undamped, coherent structures in collisionless plasmas and its impact on stability

    NASA Astrophysics Data System (ADS)

    Schamel, Hans; Mandal, Debraj; Sharma, Devendra

    2017-03-01

    An outstanding notion for collisionless plasmas is the essential nonlinear character of their coherent structures, which in the stationary, weak amplitude limit are described by a continuum of cnoidal electron and ion hole modes governed by a multiparametric nonlinear dispersion relation. The well-known discrete structure of undamped linear plasma modes is seamlessly embedded in this nonlinear continuum as the microscopic texture of plasma begins to reveal itself in the high temperature collisionless plasma limit. This transforms the linear-threshold-based operating mechanism of plasma turbulence into a fundamental nonlinear, multifaceted one. Based on a comprehensive three-level description of increasing profundity, a proof of this novel dictum is presented, which makes use of the joint properties of such structures, their coherency and stationarity, and uses in succession a fluid, linear Vlasov and a full Vlasov description. It unifies discrete and continuum limits by resolving the inevitable resonant region and shows that coherent electrostatic equilibria are generally controlled by kinetic particle trapping and are hence fundamentally nonlinear. By forging a link between damped and growing wave solutions, these modes render plasma stability complex and difficult to evaluate due to the entangled pattern of the stability boundary in function and parameter space, respectively. A direct consequence is the existence of negative energy modes of arbitrarily small amplitudes in the subcritical region of the two-stream instability as well as the failure of linear Landau (Vlasov, van Kampen) theory, whenever resonant particles are involved, in addressing the onset of instability in a current-carrying plasma. Responsible for this subtle phase space behavior is hence the thresholdless omnipresence of the trapping nonlinearity originating from coherency. A high resolution, exact-mass-ratio, multispecies, and collisionless plasma simulation is employed to illustrate exemplarily how tiny seed fluctuations in phase-space can act as a triggering agent for a subcritical plasma excitation verifying an access to these modes in the noisy, collisionless plasma limit.

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

    NASA Technical Reports Server (NTRS)

    Balsa, Thomas F.; Gartside, James

    1995-01-01

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

  18. Wave-induced response of a floating two-dimensional body with a moonpool.

    PubMed

    Fredriksen, Arnt G; Kristiansen, Trygve; Faltinsen, Odd M

    2015-01-28

    Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier-Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

  19. Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment

    NASA Astrophysics Data System (ADS)

    Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

    2018-04-01

    Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

  20. Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment.

    PubMed

    Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

    2018-04-27

    Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

  1. Nonlinear MHD study on the influence of E×B flow in QH-mode plasma of DIII-D

    NASA Astrophysics Data System (ADS)

    Liu, Feng; Huijsmans, Guido; Loarte, Alberto; Garofalo, Andrea; Solomon, Wayne; Nkonga, Boniface; Hoelzl, Matthias

    2017-10-01

    In QH-mode experiments with zero-net NBI torque show that there remains a finite E×B rotation in the pedestal region implying that a minimum E×B flow or flow shear is required for the plasma to develop the Edge Harmonic Oscillation (EHO), which is a saturated KPM (kink-peeling mode) characteristic of the QH-mode. To understand the roles of E×B flow and its shear in the saturation of KPMs, non-linear MHD simulations of DIII-D QH-mode plasmas including toroidal mode numbers n = 0 to 10 with different E×B rotation speed have been performed. These simulation show that ExB rotation strongly stabilizes high-n modes but destabilizes low-n modes (particularly the n =2 mode) in the linear growth phase, which is consistent experimental observations and previous linear MHD modelling. US DOE under DE-FC02-04ER54698.

  2. Neuromodulation impact on nonlinear firing behavior of a reduced model motoneuron with the active dendrite

    PubMed Central

    Kim, Hojeong; Heckman, C. J.

    2014-01-01

    Neuromodulatory inputs from brainstem systems modulate the normal function of spinal motoneurons by altering the activation properties of persistent inward currents (PICs) in their dendrites. However, the effect of the PIC on firing outputs also depends on its location in the dendritic tree. To investigate the interaction between PIC neuromodulation and PIC location dependence, we used a two-compartment model that was biologically realistic in that it retains directional and frequency-dependent electrical coupling between the soma and the dendrites, as seen in multi-compartment models based on full anatomical reconstructions of motoneurons. Our two-compartment approach allowed us to systematically vary the coupling parameters between the soma and the dendrite to accurately reproduce the effect of location of the dendritic PIC on the generation of nonlinear (hysteretic) motoneuron firing patterns. Our results show that as a single parameter value for PIC activation was either increased or decreased by 20% from its default value, the solution space of the coupling parameter values for nonlinear firing outputs was drastically reduced by approximately 80%. As a result, the model tended to fire only in a linear mode at the majority of dendritic PIC sites. The same results were obtained when all parameters for the PIC activation simultaneously changed only by approximately ±10%. Our results suggest the democratization effect of neuromodulation: the neuromodulation by the brainstem systems may play a role in switching the motoneurons with PICs at different dendritic locations to a similar mode of firing by reducing the effect of the dendritic location of PICs on the firing behavior. PMID:25309410

  3. Estimation of splitting functions from Earth's normal mode spectra using the neighbourhood algorithm

    NASA Astrophysics Data System (ADS)

    Pachhai, Surya; Tkalčić, Hrvoje; Masters, Guy

    2016-01-01

    The inverse problem for Earth structure from normal mode data is strongly non-linear and can be inherently non-unique. Traditionally, the inversion is linearized by taking partial derivatives of the complex spectra with respect to the model parameters (i.e. structure coefficients), and solved in an iterative fashion. This method requires that the earthquake source model is known. However, the release of energy in large earthquakes used for the analysis of Earth's normal modes is not simple. A point source approximation is often inadequate, and a more complete account of energy release at the source is required. In addition, many earthquakes are required for the solution to be insensitive to the initial constraints and regularization. In contrast to an iterative approach, the autoregressive linear inversion technique conveniently avoids the need for earthquake source parameters, but it also requires a number of events to achieve full convergence when a single event does not excite all singlets well. To build on previous improvements, we develop a technique to estimate structure coefficients (and consequently, the splitting functions) using a derivative-free parameter search, known as neighbourhood algorithm (NA). We implement an efficient forward method derived using the autoregresssion of receiver strips, and this allows us to search over a multiplicity of structure coefficients in a relatively short time. After demonstrating feasibility of the use of NA in synthetic cases, we apply it to observations of the inner core sensitive mode 13S2. The splitting function of this mode is dominated by spherical harmonic degree 2 axisymmetric structure and is consistent with the results obtained from the autoregressive linear inversion. The sensitivity analysis of multiple events confirms the importance of the Bolivia, 1994 earthquake. When this event is used in the analysis, as little as two events are sufficient to constrain the splitting functions of 13S2 mode. Apart from not requiring the knowledge of earthquake source, the newly developed technique provides an approximate uncertainty measure of the structure coefficients and allows us to control the type of structure solved for, for example to establish if elastic structure is sufficient.

  4. A linear and nonlinear study of Mira

    NASA Astrophysics Data System (ADS)

    Cox, A. N.; Ostlie, D. A.

    1993-12-01

    Both linear and nonlinear calculations of the 331 day, long period variable star Mira have been undertaken to see what radial pulsation mode is naturally selected. Models are similar to those considered in the linear nonadiabatic stellar pulsation study of Ostlie and Cox (1986). Models are considered with masses near one solar mass, luminosities between 4000 and 5000 solar luminosities, and effective temperatures of approximately 3000 K. These models have fundamental mode periods that closely match the pulsation period of Mira. The equation of state for the stellar material is given by the Stellingwerf (1975ab) procedure, and the opacity is obtained from a fit by Cahn that matches the low temperature molecular absorption data for the poplulation I Ross-Aller 1 mixture calculated from the Los Alamos Astrophysical Opacity Library. For the linear study, the Cox, Brownlee, and Eilers (1966) approximation is used for the linear theory variation of the convection luminosity. For the nonlinear work, the method described by Ostlie (1990) and Cox (1990) is followed. Results showing internal details of the radial fundamental and first overtone modes behavior in linear theory are presented. Preliminary radial fundamental mode nonlinear calculations are discussed. The very tentative conclusion is that neither the fundamental or first overtone mode is excluded from being the actual observed one.

  5. Explanation of non-additive effects in mixtures of similar mode of action chemicals.

    PubMed

    Kamo, Masashi; Yokomizo, Hiroyuki

    2015-09-01

    Many models have been developed to predict the combined effect of drugs and chemicals. Most models are classified into two additive models: independent action (IA) and concentration addition (CA). It is generally considered if the modes of action of chemicals are similar then the combined effect obeys CA; however, many empirical studies report nonlinear effects deviating from the predictions by CA. Such deviations are termed synergism and antagonism. Synergism, which leads to a stronger toxicity, requires more careful management, and hence it is important to understand how and which combinations of chemicals lead to synergism. In this paper, three types of chemical reactions are mathematically modeled and the cause of the nonlinear effects among chemicals with similar modes of action was investigated. Our results show that combined effects obey CA only when the modes of action are exactly the same. Contrary to existing knowledge, combined effects are generally nonlinear even if the modes of action of the chemicals are similar. Our results further show that the nonlinear effects vanish out when the chemical concentrations are low, suggesting that the current management procedure of assuming CA is rarely inappropriate because environmental concentrations of chemicals are generally low. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr

    2015-08-15

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

  7. Interfacial characterization of flexible hybrid electronics

    NASA Astrophysics Data System (ADS)

    Najafian, Sara; Amirkhizi, Alireza V.; Stapleton, Scott

    2018-03-01

    Flexible Hybrid Electronics (FHEs) are the new generation of electronics combining flexible plastic film substrates with electronic devices. Besides the electrical features, design improvements of FHEs depend on the prediction of their mechanical and failure behavior. Debonding of electronic components from the flexible substrate is one of the most common and critical failures of these devices, therefore, the experimental determination of material and interface properties is of great importance in the prediction of failure mechanisms. Traditional interface characterization involves isolated shear and normal mode tests such as the double cantilever beam (DCB) and end notch flexure (ENF) tests. However, due to the thin, flexible nature of the materials and manufacturing restrictions, tests mirroring traditional interface characterization experiments may not always be possible. The ideal goal of this research is to design experiments such that each mode of fracture is isolated. However, due to the complex nonlinear nature of the response and small geometries of FHEs, design of the proper tests to characterize the interface properties can be significantly time and cost consuming. Hence numerical modeling has been implemented to design these novel characterization experiments. This research involves loading case and specimen geometry parametric studies using numerical modeling to design future experiments where either shear or normal fracture modes are dominant. These virtual experiments will provide a foundation for designing similar tests for many different types of flexible electronics and predicting the failure mechanism independent of the specific FHE materials.

  8. Modulational instability and discrete breathers in a nonlinear helicoidal lattice model

    NASA Astrophysics Data System (ADS)

    Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing

    2018-06-01

    We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.

  9. Effectively Single-Mode Self-Recovering Ultrafast Nonlinear Nanowire Surface Plasmons

    NASA Astrophysics Data System (ADS)

    Tuniz, Alessandro; Weidlich, Stefan; Schmidt, Markus A.

    2018-04-01

    We report on a regime for surface-plasmon propagation, which is robust to defects and effectively single mode, and we exploit it for accessing the ultrafast nonlinear response of gold on centimeter-long subwavelength-diameter cylindrical nanowires. The hybrid plasmonic-photonic platform is formed by a gold nanowire, monolithically integrated into the core of an optical fiber. We show that, despite the dual-waveguide nature of this structure, the long-range surface plasmon is the only effectively propagating mode in the near infrared, which self-recovers in the presence of gaps via a light-recapturing effect. This self-recovery overcomes detrimental effects of wire discontinuities and enables measurements of the ultrafast nonlinearity of gold, which we perform for a 28-fs pulse duration.

  10. Nonlinear helicons bearing multi-scale structures

    NASA Astrophysics Data System (ADS)

    Abdelhamid, Hamdi M.; Yoshida, Zensho

    2017-02-01

    The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here, we elucidate an intrinsic multi-scale property embodied by the combination of the dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing a wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution, which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

  11. Studying Climate Response to Forcing by the Nonlinear Dynamical Mode Decomposition

    NASA Astrophysics Data System (ADS)

    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 external factors, e.g. forecast their change in 21 century under different CO2 emission scenarios, are discussed. [1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510 [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. http://doi.org/10.1063/1.4968852

  12. Direct generation of 128-fs Gaussian pulses from a compensation-free fiber laser using dual mode-locking mechanisms

    NASA Astrophysics Data System (ADS)

    Peng, Junsong; Zhan, Li; Gu, Zhaochang; Qian, Kai; Luo, Shouyu; Shen, Qishun

    2012-03-01

    We have experimentally demonstrated the direct generation of 128-fs pulses in an all-anomalous-dispersion all-fiber mode-locked laser. The laser is free of dispersion compensation in the cavity based on standard single mode fiber (SMF). The time-bandwidth product is 0.536. The laser is achieved by using two mode-lockers, one is nonlinear polarization rotation (NPR), and the other is nonlinear amplifying loop mirror. The coexistence of dual mode-locking mechanisms can decrease the cavity length to 12-m, and also results in producing high-quality pulses with a Gaussian shape both on the pulse profile and spectrum, but without Kelly sidebands.

  13. Richtmyer-Meshkov evolution under steady shock conditions in the high-energy-density regime

    DOE PAGES

    Di Stefano, C. A.; Malamud, G.; Kuranz, C. C.; ...

    2015-03-17

    This work presents direct experimental evidence of long-predicted nonlinear aspects of the Richtmyer-Meshkov (RM) process, in which new modes first arise from the coupling of initially-present modes, and in which shorter-wavelength modes are eventually overtaken by longer-wavelength modes. This is accomplished using a technique we developed employing a long driving laser pulse to create a strong (Mach ~ 8) shock across a well-characterized material interface seeded by a two-mode sinusoidal perturbation. Furthermore, this technique further permits the shock to be sustained, without decay of the high-energy-density flow conditions, long enough for the system to evolve into the nonlinear phase.

  14. Quantum correlations across two octaves from combined up- and down-conversion

    NASA Astrophysics Data System (ADS)

    Li, Jingyan; Olsen, M. K.

    2018-04-01

    We propose and analyze a cascaded optical parametric system which involves three interacting modes across two octaves of frequency difference. Our system, combining degenerate optical parametric oscillation (OPO) with second harmonic generation (SHG), promises to be a useful source of squeezed and entangled light at three differing frequencies. We show how changes in damping rates and the ratio of the two concurrent nonlinearities affect the quantum correlations in the output fields. We analyze the threshold behavior, showing how the normal OPO threshold is changed by the addition of the SHG interactions. We also find that the inclusion of the OPO interaction removes the self-pulsing behavior found in normal SHG. Finally, we show how the Einstein-Podolsky-Rosen correlations can be controlled by the injection of a coherent seed field at the lower frequency.

  15. Nonlinear digital out-of-plane waveguide coupler based on nonlinear scattering of a single graphene layer

    NASA Astrophysics Data System (ADS)

    Asadi, Reza; Ouyang, Zhengbiao

    2018-03-01

    A new mechanism for out-of-plane coupling into a waveguide is presented and numerically studied based on nonlinear scattering of a single nano-scale Graphene layer inside the waveguide. In this mechanism, the refractive index nonlinearity of Graphene and nonhomogeneous light intensity distribution occurred due to the interference between the out-of-plane incident pump light and the waveguide mode provide a virtual grating inside the waveguide, coupling the out-of-plane pump light into the waveguide. It has been shown that the coupling efficiency has two distinct values with high contrast around a threshold pump intensity, providing suitable condition for digital optical applications. The structure operates at a resonance mode due to band edge effect, which enhances the nonlinearity and decreases the required threshold intensity.

  16. Robust model predictive control for constrained continuous-time nonlinear systems

    NASA Astrophysics Data System (ADS)

    Sun, Tairen; Pan, Yongping; Zhang, Jun; Yu, Haoyong

    2018-02-01

    In this paper, a robust model predictive control (MPC) is designed for a class of constrained continuous-time nonlinear systems with bounded additive disturbances. The robust MPC consists of a nonlinear feedback control and a continuous-time model-based dual-mode MPC. The nonlinear feedback control guarantees the actual trajectory being contained in a tube centred at the nominal trajectory. The dual-mode MPC is designed to ensure asymptotic convergence of the nominal trajectory to zero. This paper extends current results on discrete-time model-based tube MPC and linear system model-based tube MPC to continuous-time nonlinear model-based tube MPC. The feasibility and robustness of the proposed robust MPC have been demonstrated by theoretical analysis and applications to a cart-damper springer system and a one-link robot manipulator.

  17. Classical investigation of long-range coherence in biological systems

    NASA Astrophysics Data System (ADS)

    Preto, Jordane

    2016-12-01

    Almost five decades ago, H. Fröhlich [H. Fröhlich, "Long-range coherence and energy storage in biological systems," Int. J. Quantum Chem. 2(5), 641-649 (1968)] reported, on a theoretical basis, that the excitation of quantum modes of vibration in contact with a thermal reservoir may lead to steady states, where under high enough rate of energy supply, only specific low-frequency modes of vibration are strongly excited. This nonlinear phenomenon was predicted to occur in biomolecular systems, which are known to exhibit complex vibrational spectral properties, especially in the terahertz frequency domain. However, since the effects of terahertz or lower-frequency modes are mainly classical at physiological temperatures, there are serious doubts that Fröhlich's quantum description can be applied to predict such a coherent behavior in a biological environment, as suggested by the author. In addition, a quantum formalism makes the phenomenon hard to investigate using realistic molecular dynamics simulations (MD) as they are usually based on the classical principles. In the current paper, we provide a general classical Hamiltonian description of a nonlinear open system composed of many degrees of freedom (biomolecular structure) excited by an external energy source. It is shown that a coherent behaviour similar to Fröhlich's effect is to be expected in the classical case for a given range of parameter values. Thus, the supplied energy is not completely thermalized but stored in a highly ordered fashion. The connection between our Hamiltonian description, carried out in the space of normal modes, and a more standard treatment in the physical space is emphasized in order to facilitate the prediction of the effect from MD simulations. It is shown how such a coherent phenomenon may induce long-range resonance effects that could be of critical importance at the biomolecular level. The present work is motivated by recent experimental evidences of long-lived excited low-frequency modes in protein structures, which were reported as a consequence of the Fröhlich's effect.

  18. Modeling of magnetorheological fluid in quasi-static squeeze flow mode

    NASA Astrophysics Data System (ADS)

    Horak, Wojciech

    2018-06-01

    This work presents a new nonlinear model to describe MR fluid behavior in the squeeze flow mode. The basis for deriving the model were the principles of continuum mechanics and the theory of tensor transformation. The analyzed case concerned quasi-static squeeze with a constant area, between two parallel plates with non-slip boundary conditions. The developed model takes into account the rheological properties or MR fluids as a viscoplastic material for which yield stress increases due to compression. The model also takes into account the formation of normal force in the MR fluid as a result of the magnetic field impact. Moreover, a new parameter has been introduced which characterizes the behavior of MR fluid subjected to compression. The proposed model has been experimentally validated and the obtained results suggest that the assumptions made in the model development are reasonable, as good model compatibility with the experiments was obtained.

  19. Contribution to the development of low frequency terahertz coherent Raman micro-spectroscopy and microscopy

    NASA Astrophysics Data System (ADS)

    Ujj, Laszlo

    2018-06-01

    We report the construction and characterization of a coherent Raman tabletop system utilizing a novel astigmatic optical focusing geometry, a broadband nanosecond optical parametric oscillator and volumetric Bragg filters assisting 3CBCRS measuring system for the first time. In order to illustrate the versatility of the measurements and reveal the molecular information obtainable, two well-characterized chemicals were selected. Polarization sensitive epi-detected 3CBCRS spectra of liquid CCl4 and calcite crystal were recorded and analyzed. An unexpected polarization dependence of the signals of the lowest frequency modes of CCl4 was observed. The 1122 third order susceptibility component was phase flipped. The non-resonant susceptibility normalized 1122 component was found to be larger than the 1111 component for the lowest vibrational modes. This anomalous comportment was attributable to the anisotropy Raman tensor invariant in the third order nonlinear susceptibility tensor.

  20. Internal friction and mode relaxation in a simple chain model.

    PubMed

    Fugmann, S; Sokolov, I M

    2009-12-21

    We consider the equilibrium relaxation properties of the end-to-end distance and of the principal components in a one-dimensional polymer chain model with nonlinear interaction between the beads. While for the single-well potentials these properties are similar to the ones of a Rouse chain, for the double-well interaction potentials, modeling internal friction, they differ vastly from the ones of the harmonic chain at intermediate times and intermediate temperatures. This minimal description within a one-dimensional model mimics the relaxation properties found in much more complex polymer systems. Thus, the relaxation time of the end-to-end distance may grow by orders of magnitude at intermediate temperatures. The principal components (whose directions are shown to coincide with the normal modes of the harmonic chain, whatever interaction potential is assumed) not only display larger relaxation times but also subdiffusive scaling.

  1. Nonlinear electron-phonon coupling in doped manganites

    DOE PAGES

    Esposito, Vincent; Fechner, M.; Mankowsky, R.; ...

    2017-06-15

    Here, we employ time-resolved resonant x-ray diffraction to study the melting of charge order and the associated insulator-to-metal transition in the doped manganite Pr 0.5Ca 0.5MnO 3 after resonant excitation of a high-frequency infrared-active lattice mode. We find that the charge order reduces promptly and highly nonlinearly as function of excitation fluence. Density-functional theory calculations suggest that direct anharmonic coupling between the excited lattice mode and the electronic structure drives these dynamics, highlighting a new avenue of nonlinear phonon control.

  2. Nonlinear Electron-Phonon Coupling in Doped Manganites.

    PubMed

    Esposito, V; Fechner, M; Mankowsky, R; Lemke, H; Chollet, M; Glownia, J M; Nakamura, M; Kawasaki, M; Tokura, Y; Staub, U; Beaud, P; Först, M

    2017-06-16

    We employ time-resolved resonant x-ray diffraction to study the melting of charge order and the associated insulator-to-metal transition in the doped manganite Pr_{0.5}Ca_{0.5}MnO_{3} after resonant excitation of a high-frequency infrared-active lattice mode. We find that the charge order reduces promptly and highly nonlinearly as function of excitation fluence. Density-functional theory calculations suggest that direct anharmonic coupling between the excited lattice mode and the electronic structure drives these dynamics, highlighting a new avenue of nonlinear phonon control.

  3. Second-harmonic generation using tailored whispering gallery modes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dumeige, Yannick; Feron, Patrice

    It has been shown that whispering gallery modes can be used to obtain a combination of modal and geometrical quasi-phase-matching in second-harmonic generation. This could be achieved in isotropic, nonferroelectric, strongly dispersive and highly nonlinear materials such as III-V semiconductors. Unfortunately the poor overlap between the second-harmonic field and second order nonlinear polarization limits the conversion efficiency. In this paper we show that by engineering the refractive index it is possible to increase field overlap and to enhance effective second order nonlinear polarization of semiconductor microdisks.

  4. Nonlinear dynamic analysis of a rotor-bearing-seal system under two loading conditions

    NASA Astrophysics Data System (ADS)

    Ma, Hui; Li, Hui; Niu, Heqiang; Song, Rongze; Wen, Bangchun

    2013-11-01

    The operating speed of the rotating machinery often exceeds the second or even higher order critical speeds to pursue higher efficiency. Thus, how to restrain the higher order mode instability caused by the nonlinear oil-film force and seal force at high speed as far as possible has become more and more important. In this study, a lumped mass model of a rotor-bearing-seal system considering the gyroscopic effect is established. The graphite self-lubricating bearing and the sliding bearing are simulated by a spring-damping model and a nonlinear oil-film force model based on the assumption of short bearings, respectively. The seal is simulated by Muszynska nonlinear seal force model. Effects of the seal force and oil-film force on the first and second mode instabilities are investigated under two loading conditions which are determined by API Standard 617 (Axial and Centrifugal Compressors and Expander-compressors for Petroleum, Chemical and Gas Industry Services, Seventh Edition). The research focuses on the effects of exciting force forms and their magnitudes on the first and second mode whips in a rotor-bearing-seal system by using the spectrum cascades, vibration waveforms, orbits and Poincaré maps. The first and second mode instability laws are compared by including and excluding the seal effect in a rotor system with single-diameter shaft and two same discs. Meanwhile, the instability laws are also verified in a rotor system with multi-diameter shaft and two different discs. The results show that the second loading condition (out-of-phase unbalances of two discs) and the nonlinear seal force can mainly restrain the first mode instability and have slight effects on the second mode instability. This study may contribute to a further understanding about the higher order mode instability of such a rotor system with fluid-induced forces from the oil-film bearings and seals.

  5. Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

    NASA Astrophysics Data System (ADS)

    Midya, Bikashkali; Konotop, Vladimir V.

    2017-07-01

    We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e., the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn, the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications, the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.

  6. Self-action of propagating and standing Lamb waves in the plates exhibiting hysteretic nonlinearity: Nonlinear zero-group velocity modes.

    PubMed

    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 S 1 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.

  7. Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

    PubMed

    Heise, M; Hoffmann, Ch; Abshagen, J; Pinter, A; Pfister, G; Lücke, M

    2008-02-15

    We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

  8. Mixing of ultrasonic Lamb waves in thin plates with quadratic nonlinearity.

    PubMed

    Li, Feilong; Zhao, Youxuan; Cao, Peng; Hu, Ning

    2018-07-01

    This paper investigates the propagation of Lamb waves in thin plates with quadratic nonlinearity by one-way mixing method using numerical simulations. It is shown that an A 0 -mode wave can be generated by a pair of S 0 and A 0 mode waves only when mixing condition is satisfied, and mixing wave signals are capable of locating the damage zone. Additionally, it is manifested that the acoustic nonlinear parameter increases linearly with quadratic nonlinearity but monotonously with the size of mixing zone. Furthermore, because of frequency deviation, the waveform of the mixing wave changes significantly from a regular diamond shape to toneburst trains. Copyright © 2018 Elsevier B.V. All rights reserved.

  9. Linear and nonlinear interactions of an electron beam with oblique whistler and electrostatic waves in the magnetosphere

    NASA Astrophysics Data System (ADS)

    Zhang, Y. L.; Matsumoto, H.; Omura, Y.

    1993-12-01

    Both linear and nonlinear interactions between oblique whistler, electrostatic, quasi-upper hybrid mode waves and an electron beam are studied by linear analyses and electromagnetic particle simulations. In addition to a background cold plasma, we assumed a hot electron beam drifting along a static magnetic field. Growth rates of the oblique whistler, oblique electrostatic, and quasi-upper hybrid instabilities were first calculated. We found that there are four kinds of unstable mode waves for parallel and oblique propagations. They are the electromagnetic whistler mode wave (WW1), the electrostatic whistler mode wave (WW2), the electrostatic mode wave (ESW), and the quasi-upper hybrid mode wave (UHW). A possible mechanism is proposed to explain the satellite observations of whistler mode chorus and accompanied electrostatic waves, whose amplitudes are sometimes modulated at the chorus frequency.

  10. New Instability Mode in A Driven Granular Gas: Athermal and Thermal Convection

    NASA Astrophysics Data System (ADS)

    Shukla, Priyanka; Alam, Meheboob

    2017-11-01

    For a thermally-driven granular gas confined between two plates under gravity, we report a new instability mode which is found to be active at very small values of the heat-loss parameter. We show that the origin of this new mode is tied to the ``thermal'' mode of the well-studied Rayleigh-Benard convection. This is dubbed purely elastic instability since it survives even for perfectly elastic collisions (en = 1). The distinction of this new instability mode from its dissipative/athermal counterpart is clarified for the first time. Furthermore, a weakly nonlinear analysis using Stuart-Landau equation has been carried out for both instability modes, and the underlying bifurcation scenario (supercritical/subcritical) from each mode is elucidated. The resulting linear and nonlinear patterns with respect to inelasticity and gravity are compared.

  11. Investigation of self-phase modulation based optical regeneration in single mode As2Se3 chalcogenide glass fiber.

    PubMed

    Fu, L; Rochette, M; Ta'eed, V; Moss, D; Eggleton, B

    2005-09-19

    We investigate the feasibility of all-optical regeneration based on self-phase modulation in single mode As2Se3 chalcogenide fiber. By combining the chalcogenide fiber with a bandpass filter, we achieve a near step-like power transfer function with no pulse distortion. The device is shown to operate with 5.8 ps duration pulses, thus demonstrating the feasibility of this device operating with high bit-rate data signals. These results are achieved with pulse peak powers <10 W in a fully passive device, including only 2.8 m of chalcogenide fiber. We obtain an excellent agreement between theory and experiment and show that both the high nonlinearity of the chalcogenide glass along with its high normal dispersion near 1550 nm enables a significant device length reduction in comparison with silica-based devices, without compromise on the performance. We find that even for only a few meters of fiber, the large normal dispersion of the chalcogenide glass inhibits spectral oscillations that would appear with self-phase modulation alone. We measure the two photon absorption attenuation coefficient and find that it advantageously affects the device transfer function.

  12. Density-Gradient-Driven trapped-electron-modes in improved-confinement RFP plasmas

    NASA Astrophysics Data System (ADS)

    Duff, James; Sarff, John; Ding, Weixing; Brower, David; Parke, Eli; Chapman, Brett; Terry, Paul; Pueschel, M. J.; Williams, Zach

    2017-10-01

    Short wavelength density fluctuations in improved-confinement MST plasmas exhibit multiple features characteristic of the trapped-electron-mode (TEM). Core transport in the RFP is normally governed by magnetic stochasticity stemming from long wavelength tearing modes that arise from current profile peaking, which are suppressed via inductive control for this work. The improved confinement is associated with an increase in the pressure gradient that can destabilize drift waves. The measured density fluctuations have f 50 kHz, kϕρs < 0.14 , and propagate in the electron drift direction. Their spectral emergence coincides with a sharp decrease in global tearing mode associated fluctuations, their amplitude increases with local density gradient, and they exhibit a density-gradient threshold at R /Ln 15 . The GENE code, modified for the RFP, predicts the onset of density-gradient-driven TEM for these strong-gradient plasma conditions. While nonlinear analysis shows a large Dimits shift associated with predicted strong zonal flows, the inclusion of residual magnetic fluctuations, comparable to experimental magnetic fluctuations, causes a collapse of the zonal flows and an increase in the predicted transport to a level close to the experimentally measured heat flux. Work supported by US DOE.

  13. Waveguide structures in anisotropic nonlinear crystals

    NASA Astrophysics Data System (ADS)

    Li, Da; Hong, Pengda; Meissner, Helmuth E.

    2017-02-01

    We report on the design and manufacturing parameters of waveguiding structures of anisotropic nonlinear crystals that are employed for harmonic conversions, using Adhesive-Free Bonding (AFB®). This technology enables a full range of predetermined refractive index differences that are essential for the design of single mode or low-mode propagation with high efficiency in anisotropic nonlinear crystals which in turn results in compact frequency conversion systems. Examples of nonlinear optical waveguides include periodically bonded walk-off corrected nonlinear optical waveguides and periodically poled waveguide components, such as lithium triborate (LBO), beta barium borate (β-BBO), lithium niobate (LN), potassium titanyl phosphate (KTP), zinc germanium phosphide (ZGP) and silver selenogallate (AGSE). Simulation of planar LN waveguide shows that when the electric field vector E lies in the k-c plane, the power flow is directed precisely along the propagation direction, demonstrating waveguiding effect in the planar waveguide. Employment of anisotropic nonlinear optical waveguides, for example in combination with AFB® crystalline fiber waveguides (CFW), provides access to the design of a number of novel high power and high efficiency light sources spanning the range of wavelengths from deep ultraviolet (as short as 200 nm) to mid-infrared (as long as about 18 μm). To our knowledge, the technique is the only generally applicable one because most often there are no compatible cladding crystals available to nonlinear optical cores, especially not with an engineer-able refractive index difference and large mode area.

  14. Sliding mode control of magnetic suspensions for precision pointing and tracking applications

    NASA Technical Reports Server (NTRS)

    Misovec, Kathleen M.; Flynn, Frederick J.; Johnson, Bruce G.; Hedrick, J. Karl

    1991-01-01

    A recently developed nonlinear control method, sliding mode control, is examined as a means of advancing the achievable performance of space-based precision pointing and tracking systems that use nonlinear magnetic actuators. Analytic results indicate that sliding mode control improves performance compared to linear control approaches. In order to realize these performance improvements, precise knowledge of the plant is required. Additionally, the interaction of an estimating scheme and the sliding mode controller has not been fully examined in the literature. Estimation schemes were designed for use with this sliding mode controller that do not seriously degrade system performance. The authors designed and built a laboratory testbed to determine the feasibility of utilizing sliding mode control in these types of applications. Using this testbed, experimental verification of the authors' analyses is ongoing.

  15. Three-dimensional vibration analysis of a uniform beam with offset inertial masses at the ends

    NASA Technical Reports Server (NTRS)

    Robertson, D. K.

    1985-01-01

    Analysis of a flexible beam with displaced end-located inertial masses is presented. The resulting three-dimensional mode shape is shown to consist of two one-plane bending modes and one torsional mode. These three components of the mode shapes are shown to be linear combinations of trigonometric and hyperbolic sine and cosine functions. Boundary conditions are derived to obtain nonlinear algebraic equations through kinematic coupling of the general solutions of the three governing partial differential equations. A method of solution which takes these boundary conditions into account is also presented. A computer program has been written to obtain unique solutions to the resulting nonlinear algebraic equations. This program, which calculates natural frequencies and three-dimensional mode shapes for any number of modes, is presented and discussed.

  16. Sliding mode control: an approach to regulate nonlinear chemical processes

    PubMed

    Camacho; Smith

    2000-01-01

    A new approach for the design of sliding mode controllers based on a first-order-plus-deadtime model of the process, is developed. This approach results in a fixed structure controller with a set of tuning equations as a function of the characteristic parameters of the model. The controller performance is judged by simulations on two nonlinear chemical processes.

  17. Acoustic fatigue life prediction for nonlinear structures with multiple resonant modes

    NASA Technical Reports Server (NTRS)

    Miles, R. N.

    1992-01-01

    This report documents an effort to develop practical and accurate methods for estimating the fatigue lives of complex aerospace structures subjected to intense random excitations. The emphasis of the current program is to construct analytical schemes for performing fatigue life estimates for structures that exhibit nonlinear vibration behavior and that have numerous resonant modes contributing to the response.

  18. Dynamics of shaping ultrashort optical dissipative solitary pulses in the actively mode-locked semiconductor laser with an external long-haul single-mode fiber cavity

    NASA Astrophysics Data System (ADS)

    Shcherbakov, Alexandre S.; Moreno Zarate, Pedro

    2010-02-01

    We describe the conditions of shaping regular trains of optical dissipative solitary pulses, excited by multi-pulse sequences of periodic modulating signals, in the actively mode-locked semiconductor laser heterostructure with an external long-haul single-mode silicon fiber exhibiting square-law dispersion, cubic Kerr nonlinearity, and linear optical losses. The presented model for the analysis includes three principal contributions associated with the modulated gain, optical losses, as well as linear and nonlinear phase shifts. In fact, the trains of optical dissipative solitary pulses appear within simultaneous presenting and a balance of mutually compensating interactions between the second-order dispersion and cubic-law Kerr nonlinearity as well as between active medium gain and linear optical losses in the combined cavity. Within such a model, a contribution of the nonlinear Ginzburg-Landau operator to shaping the parameters of optical dissipative solitary pulses is described via exploiting an approximate variational procedure involving the technique of trial functions. Finally, the results of the illustrating proof-of-principle experiments are briefly presented and discussed in terms of optical dissipative solitary pulses.

  19. Comparison between measured and predicted turbulence frequency spectra in ITG and TEM regimes

    NASA Astrophysics Data System (ADS)

    Citrin, J.; Arnichand, H.; Bernardo, J.; Bourdelle, C.; Garbet, X.; Jenko, F.; Hacquin, S.; Pueschel, M. J.; Sabot, R.

    2017-06-01

    The observation of distinct peaks in tokamak core reflectometry measurements—named quasi-coherent-modes (QCMs)—are identified as a signature of trapped-electron-mode (TEM) turbulence (Arnichand et al 2016 Plasma Phys. Control. Fusion 58 014037). This phenomenon is investigated with detailed linear and nonlinear gyrokinetic simulations using the Gene code. A Tore-Supra density scan is studied, which traverses through a linear (LOC) to saturated (SOC) ohmic confinement transition. The LOC and SOC phases are both simulated separately. In the LOC phase, where QCMs are observed, TEMs are robustly predicted unstable in linear studies. In the later SOC phase, where QCMs are no longer observed, ion-temperature-gradient (ITG) modes are identified. In nonlinear simulations, in the ITG (SOC) phase, a broadband spectrum is seen. In the TEM (LOC) phase, a clear emergence of a peak at the TEM frequencies is seen. This is due to reduced nonlinear frequency broadening of the underlying linear modes in the TEM regime compared with the ITG regime. A synthetic diagnostic of the nonlinearly simulated frequency spectra reproduces the features observed in the reflectometry measurements. These results support the identification of core QCMs as an experimental marker for TEM turbulence.

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

    PubMed

    Cui, Liping; Knox, Wayne H

    2010-01-01

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

  1. Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport

    DOE PAGES

    Hegna, Chris C.; Terry, Paul W.; Faber, Ben J.

    2018-02-01

    A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3Dmore » geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.« less

  2. Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hegna, Chris C.; Terry, Paul W.; Faber, Ben J.

    A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3Dmore » geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.« less

  3. Particle simulations of mode conversion between slow mode and fast mode in lower hybrid range of frequencies

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jia, Guozhang; Xiang, Nong; Huang, Yueheng

    2016-01-15

    The propagation and mode conversion of lower hybrid waves in an inhomogeneous plasma are investigated by using the nonlinear δf algorithm in a two-dimensional particle-in-cell simulation code based on the gyrokinetic electron and fully kinetic ion (GeFi) scheme [Lin et al., Plasma Phys. Controlled Fusion 47, 657 (2005)]. The characteristics of the simulated waves, such as wavelength, frequency, phase, and group velocities, agree well with the linear theoretical analysis. It is shown that a significant reflection component emerges in the conversion process between the slow mode and the fast mode when the scale length of the density variation is comparablemore » to the local wavelength. The dependences of the reflection coefficient on the scale length of the density variation are compared with the results based on the linear full wave model for cold plasmas. It is indicated that the mode conversion for the waves with a frequency of 2.45 GHz (ω ∼ 3ω{sub LH}, where ω{sub LH} represents the lower hybrid resonance) and within Tokamak relevant amplitudes can be well described in the linear scheme. As the frequency decreases, the modification due to the nonlinear term becomes important. For the low-frequency waves (ω ∼ 1.3ω{sub LH}), the generations of the high harmonic modes and sidebands through nonlinear mode-mode coupling provide new power channels and thus could reduce the reflection significantly.« less

  4. Observing (non)linear lattice dynamics in graphite by ultrafast Kikuchi diffraction

    PubMed Central

    Liang, Wenxi; Vanacore, Giovanni M.; Zewail, Ahmed H.

    2014-01-01

    In materials, the nature of the strain–stress relationship, which is fundamental to their properties, is determined by both the linear and nonlinear elastic responses. Whereas the linear response can be measured by various techniques, the nonlinear behavior is nontrivial to probe and to reveal its nature. Here, we report the methodology of time-resolved Kikuchi diffraction for mapping the (non)linear elastic response of nanoscale graphite following an ultrafast, impulsive strain excitation. It is found that the longitudinal wave propagating along the c-axis exhibits echoes with a frequency of 9.1 GHz, which indicates the reflections of strain between the two surfaces of the material with a speed of ∼4 km/s. Because Kikuchi diffraction enables the probing of strain in the transverse direction, we also observed a higher-frequency mode at 75.5 GHz, which has a relatively long lifetime, on the order of milliseconds. The fluence dependence and the polarization properties of this nonlinear mode are entirely different from those of the linear, longitudinal mode, and here we suggest a localized breather motion in the a-b plane as the origin of the nonlinear shear dynamics. The approach presented in this contribution has the potential for a wide range of applications because most crystalline materials exhibit Kikuchi diffraction. PMID:24706785

  5. Theoretical Studies of Alfven Waves and Energetic Particle Physics in Fusion Plasmas

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chen, Liu

    This report summarizes major theoretical findings in the linear as well as nonlinear physics of Alfvén waves and energetic particles in magnetically confined fusion plasmas. On the linear physics, a variational formulation, based on the separation of singular and regular spatial scales, for drift-Alfvén instabilities excited by energetic particles is established. This variational formulation is then applied to derive the general fishbone-like dispersion relations corresponding to the various Alfvén eigenmodes and energetic-particle modes. It is further employed to explore in depth the low-frequency Alfvén eigenmodes and demonstrate the non-perturbative nature of the energetic particles. On the nonlinear physics, new novelmore » findings are obtained on both the nonlinear wave-wave interactions and nonlinear wave-energetic particle interactions. It is demonstrated that both the energetic particles and the fine radial mode structures could qualitatively affect the nonlinear evolution of Alfvén eigenmodes. Meanwhile, a theoretical approach based on the Dyson equation is developed to treat self-consistently the nonlinear interactions between Alfvén waves and energetic particles, and is then applied to explain simulation results of energetic-particle modes. Relevant list of journal publications on the above findings is also included.« less

  6. Modeling of dispersion and nonlinear characteristics of tapered photonic crystal fibers for applications in nonlinear optics

    NASA Astrophysics Data System (ADS)

    Pakarzadeh, H.; Rezaei, S. M.

    2016-01-01

    In this article, we investigate for the first time the dispersion and the nonlinear characteristics of the tapered photonic crystal fibers (PCFs) as a function of length z, via solving the eigenvalue equation of the guided mode using the finite-difference frequency-domain method. Since the structural parameters such as the air-hole diameter and the pitch of the microstructured cladding change along the tapered PCFs, dispersion and nonlinear properties change with the length as well. Therefore, it is important to know the exact behavior of such fiber parameters along z which is necessary for nonlinear optics applications. We simulate the z dependency of the zero-dispersion wavelength, dispersion slope, effective mode area, nonlinear parameter, and the confinement loss along the tapered PCFs and propose useful relations for describing dispersion and nonlinear parameters. The results of this article, which are in a very good agreement with the available experimental data, are important for simulating pulse propagation as well as investigating nonlinear effects such as supercontinuum generation and parametric amplification in tapered PCFs.

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yan, R.; Aluie, H.; Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14627

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

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

    PubMed

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

    2017-07-01

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

  9. Coherent nonlinear coupling between a long-wavelength mode and small-scale turbulence in the TEXT tokamak

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tsui, H.Y.W.; Rypdal, K.; Ritz, C.P.

    1993-04-26

    Bispectral analysis of Langmuir probe data indicates that coherent nonlinear coupling, in addition to the noncoherent turbulent interactions, exists in the edge plasma of the tokamak TEXT. Not all the modes involved reside within the spectral region of the usual broadband turbulence. At a major resonant surface the small-scale turbulent activity interacts [ital coherently] with a localized long-wavelength mode; a signature of regular or coherent structure. By the observed coupling to the transport related turbulence, the long-wavelength mode can influence plasma confinement indirectly. These observations signify the influence of low-order resonant surfaces on the edge turbulence in tokamaks.

  10. Toroidal gyro-Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.; Kerbel, G. D.; Milovich, J.

    1994-07-01

    The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyrokinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro-Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel three-dimensional (3-D) nonlinear ballooning mode representation. The representation is a Fourier transform of a field line following basis (ky',kx',z') with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky' = 0, kx' ≠ 0) ``radial modes'' in stabilizing the transport from the finite-n ITG ballooning modes. Detailing the parametric dependence of toroidal ITG turbulence is a key result.

  11. Fully 3D modeling of tokamak vertical displacement events with realistic parameters

    NASA Astrophysics Data System (ADS)

    Pfefferle, David; Ferraro, Nathaniel; Jardin, Stephen; Bhattacharjee, Amitava

    2016-10-01

    In this work, we model the complex multi-domain and highly non-linear physics of Vertical Displacement Events (VDEs), one of the most damaging off-normal events in tokamaks, with the implicit 3D extended MHD code M3D-C1. The code has recently acquired the capability to include finite thickness conducting structures within the computational domain. By exploiting the possibility of running a linear 3D calculation on top of a non-linear 2D simulation, we monitor the non-axisymmetric stability and assess the eigen-structure of kink modes as the simulation proceeds. Once a stability boundary is crossed, a fully 3D non-linear calculation is launched for the remainder of the simulation, starting from an earlier time of the 2D run. This procedure, along with adaptive zoning, greatly increases the efficiency of the calculation, and allows to perform VDE simulations with realistic parameters and high resolution. Simulations are being validated with NSTX data where both axisymmetric (toroidally averaged) and non-axisymmetric induced and conductive (halo) currents have been measured. This work is supported by US DOE Grant DE-AC02-09CH11466.

  12. Marshall N. Rosenbluth Outstanding Doctoral Thesis Award Talk: Simultaneous Measurement of Electron Temperature and Density Fluctuations in the Core of DIII-D Plasmas

    NASA Astrophysics Data System (ADS)

    White, A. E.

    2009-11-01

    Multi-field fluctuation measurements provide opportunities for rigorous comparison between experiment and nonlinear gyrokinetic turbulence simulations. A unique set of diagnostics on DIII-D allows for simultaneous study of local, long-wavelength (0 < kθρs< 0.5) electron temperature and density fluctuations in the core plasma (0.4 < ρ< 0.8). Previous experiments in L-mode indicate that normalized electron temperature fluctuation levels (40 < f < 400,kHz) increase with radius from ˜0.4% at ρ= 0.5 to ˜2% at ρ=0.8, similar to simultaneously measured density fluctuations. Electron cyclotron heating (ECH) is used to increase Te, which increases electron temperature fluctuation levels and electron heat transport in the experiments. In contrast, long wavelength density fluctuation levels change very little. The different responses are consistent with increased TEM drive relative to ITG-mode drive. A new capability at DIII-D is the measurement of phase angle between electron temperature and density fluctuations using coupled correlation electron cyclotron emission radiometer and reflectometer diagnostics. Linear and nonlinear GYRO runs have been used to design validation experiments that focus on measurements of the phase angle. GYRO shows that if Te and ∇Te increase 50% in a beam-heated L-mode plasma (ρ=0.5), then the phase angle between electron temperature and density fluctuations decreases 30%-50% and electron temperature fluctuation levels increase a factor of two more than density fluctuations. Comparisons between these predictions and experimental results will be presented.

  13. Critical Layers and Protoplanetary Disk Turbulence

    NASA Astrophysics Data System (ADS)

    Umurhan, Orkan M.; Shariff, Karim; Cuzzi, Jeffrey N.

    2016-10-01

    A linear analysis of the zombie vortex instability (ZVI) is performed in a stratified shearing sheet setting for three model barotropic shear flows. The linear analysis is done by utilizing a Green’s function formulation to resolve the critical layers of the associated normal-mode problem. The instability is the result of a resonant interaction between a Rossby wave and a gravity wave that we refer to as Z-modes. The associated critical layer is the location where the Doppler-shifted frequency of a distant Rossby wave equals the local Brunt-Väisälä frequency. The minimum required Rossby number for instability, {\\mathtt{Ro}}=0.2, is confirmed for parameter values reported in the literature. It is also found that the shear layer supports the instability in the limit where stratification vanishes. The ZVI is examined in a jet model, finding that the instability can occur for {\\mathtt{Ro}}=0.05. Nonlinear vorticity forcing due to unstable Z-modes is shown to result in the creation of a jet flow at the critical layer emerging as the result of the competition between the vertical lifting of perturbation radial vorticity and the radial transport of perturbation vertical vorticity. We find that the picture of this instability leading to a form of nonlinearly driven self-replicating pattern of creation and destruction is warranted: a parent jet spawns a growing child jet at associated critical layers. A mature child jet creates a next generation of child jets at associated critical layers of the former while simultaneously contributing to its own destruction via the Rossby wave instability.

  14. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Samanta, C.; Yasasvi Gangavarapu, P. R.; Naik, A. K.

    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 MoS{sub 2} 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 essentialmore » for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS{sub 2} 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.« less

  15. Edge localized mode rotation and the nonlinear dynamics of filaments

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Morales, J. A.; Bécoulet, M.; Garbet, X.

    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,more » 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.« less

  16. Finite-time adaptive sliding mode force control for electro-hydraulic load simulator based on improved GMS friction model

    NASA Astrophysics Data System (ADS)

    Kang, Shuo; Yan, Hao; Dong, Lijing; Li, Changchun

    2018-03-01

    This paper addresses the force tracking problem of electro-hydraulic load simulator under the influence of nonlinear friction and uncertain disturbance. A nonlinear system model combined with the improved generalized Maxwell-slip (GMS) friction model is firstly derived to describe the characteristics of load simulator system more accurately. Then, by using particle swarm optimization (PSO) algorithm ​combined with the system hysteresis characteristic analysis, the GMS friction parameters are identified. To compensate for nonlinear friction and uncertain disturbance, a finite-time adaptive sliding mode control method is proposed based on the accurate system model. This controller has the ability to ensure that the system state moves along the nonlinear sliding surface to steady state in a short time as well as good dynamic properties under the influence of parametric uncertainties and disturbance, which further improves the force loading accuracy and rapidity. At the end of this work, simulation and experimental results are employed to demonstrate the effectiveness of the proposed sliding mode control strategy.

  17. NIMROD: A computational laboratory for studying nonlinear fusion magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Sovinec, C. R.; Gianakon, T. A.; Held, E. D.; Kruger, S. E.; Schnack, D. D.

    2003-05-01

    Nonlinear numerical studies of macroscopic modes in a variety of magnetic fusion experiments are made possible by the flexible high-order accurate spatial representation and semi-implicit time advance in the NIMROD simulation code [A. H. Glasser et al., Plasma Phys. Controlled Fusion 41, A747 (1999)]. Simulation of a resistive magnetohydrodynamics mode in a shaped toroidal tokamak equilibrium demonstrates computation with disparate time scales, simulations of discharge 87009 in the DIII-D tokamak [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] confirm an analytic scaling for the temporal evolution of an ideal mode subject to plasma-β increasing beyond marginality, and a spherical torus simulation demonstrates nonlinear free-boundary capabilities. A comparison of numerical results on magnetic relaxation finds the n=1 mode and flux amplification in spheromaks to be very closely related to the m=1 dynamo modes and magnetic reversal in reversed-field pinch configurations. Advances in local and nonlocal closure relations developed for modeling kinetic effects in fluid simulation are also described.

  18. Nonlinear Stability and Structure of Compressible Reacting Mixing Layers

    NASA Technical Reports Server (NTRS)

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

    2000-01-01

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

  19. Stimulated Brillouin scattering in ultra-long distributed feedback Bragg gratings in standard optical fiber.

    PubMed

    Loranger, Sébastien; Lambin-Iezzi, Victor; Wahbeh, Mamoun; Kashyap, Raman

    2016-04-15

    Distributed feedback (DFB) fiber Bragg gratings (FBG) are widely used as narrow-band filters and single-mode cavities for lasers. Recently, a nonlinear generation has been shown in 10-20 cm DFB gratings in a highly nonlinear fiber. First, we show in this Letter a novel fabrication technique of ultra-long DFBs in a standard fiber (SMF-28). Second, we demonstrate nonlinear generation in such gratings. A particular inscription technique was used to fabricate all-in-phase ultra-long FBG and to implement reproducible phase shift to form a DFB mode. We demonstrate stimulated Brillouin scattering (SBS) emission from this DFB mode and characterize the resulting laser. It seems that such a SBS based DFB laser stabilizes a pump's jittering and reduces its linewidth.

  20. Nonlinear absorption properties of ZnO and Al doped ZnO thin films under continuous and pulsed modes of operations

    NASA Astrophysics Data System (ADS)

    Sandeep, K. M.; Bhat, Shreesha; Dharmaprakash, S. M.

    2018-06-01

    In the present investigation, we present the variations in nonlinear optical (NLO) properties of undoped and Al doped ZnO (AZO) films under two different off-resonant regimes using continuous and pulsed mode lasers. Z-scan open aperture experiment is performed to quantify nonlinear absorption constant and imaginary component of third order susceptibility. Reverse saturable absorption (RSA) and saturable absorption (SA) behaviors are noticed in both undoped and AZO films under pulsed mode and continuous wavelength (CW) regime respectively. The RSA and SA behavior observed in the films are attributed to two photon absorption (TPA) and thermal lensing properties respectively. The thermal lensing is assisted by the thermo-optic effects within the films due to the continuous illumination of the laser.

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

    PubMed

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

    2006-01-01

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

  2. Fourier imaging of non-linear structure formation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk

    We perform a Fourier space decomposition of the dynamics of non-linear cosmological structure formation in ΛCDM models. From N -body simulations involving only cold dark matter we calculate 3-dimensional non-linear density, velocity divergence and vorticity Fourier realizations, and use these to calculate the fully non-linear mode coupling integrals in the corresponding fluid equations. Our approach allows for a reconstruction of the amount of mode coupling between any two wavenumbers as a function of redshift. With our Fourier decomposition method we identify the transfer of power from larger to smaller scales, the stable clustering regime, the scale where vorticity becomes important,more » and the suppression of the non-linear divergence power spectrum as compared to linear theory. Our results can be used to improve and calibrate semi-analytical structure formation models.« less

  3. Tailoring of the free spectral range and geometrical cavity dispersion of a microsphere by a coating layer.

    PubMed

    Ristić, Davor; Mazzola, Maurizio; Chiappini, Andrea; Rasoloniaina, Alphonse; Féron, Patrice; Ramponi, Roberta; Righini, Giancarlo C; Cibiel, Gilles; Ivanda, Mile; Ferrari, Maurizio

    2014-09-01

    The modal dispersion of a whispering gallery mode (WGM) resonator is a very important parameter for use in all nonlinear optics applications. In order to tailor the WGM modal dispersion of a microsphere, we have coated a silica microsphere with a high-refractive-index coating in order to study its effect on the WGM modal dispersion. We used Er(3+) ions as a probe for a modal dispersion assessment. We found that, by varying the coating thickness, the geometrical cavity dispersion can be used to shift overall modal dispersion in a very wide range in both the normal and anomalous dispersion regime.

  4. Time-resolved measurements of statistics for a Nd:YAG laser.

    PubMed

    Hubschmid, W; Bombach, R; Gerber, T

    1994-08-20

    Time-resolved measurements of the fluctuating intensity of a multimode frequency-doubled Nd:YAG laser have been performed. For various operating conditions the enhancement factors in nonlinear optical processes that use a fluctuating instead of a single-mode laser have been determined up to the sixth order. In the case of reduced flash-lamp excitation and a switched-off laser amplifier, the intensity fluctuations agree with the normalized Gaussian model for the fluctuations of the fundamental frequency, whereas strong deviations are found under usual operating conditions. The frequencydoubled light has in the latter case enhancement factors not so far from values of Gaussian statistics.

  5. Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bierwage, Andreas; Shinohara, Kouji

    2016-04-15

    The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectramore » of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfvén modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-dimensional phase locking process. In the n = 1 case, a new chirping mechanism is found, which involves multiple dimensions, namely, wave-particle trapping in the radial direction and phase mixing across velocity coordinates.« less

  6. A seven-month solar cycle observed with the Langmuir probe on Pioneer Venus Orbiter

    NASA Technical Reports Server (NTRS)

    Hoegy, W. R.; Wolff, C. L.

    1989-01-01

    Data collected by the Langmuir probe aboard the Pioneer Venus orbiter (PVO) over the years 1979 though 1987 were normalized to remove the long-period 11-year solar maximum to minimum trend and were analyzed for periodicity. Results yield evidence for the existence of an approximately 7-month solar cycle, which was also observed from SME Lyman alpha and 2800-MHz radio flux measurements carried out from an earth-based platform. This coincidence suggests that the cycle is an intrinsic periodicity in the solar output. The cycle has a frequency independent of the orbital frequency of the PVO and is distinct from a 'rotating beacon' cycle whose period depends on the orbital motion of the PVO about the sun. The second most dominant cycle discovered was a 5-month period. Results of an oscillation model of solar periodicity indicate that the 7-month and 5-month cycles are caused by long-lived flux enhancements from nonlinear interactions of global oscillation modes in the sun's convective envelope (r modes) and radiative interior (g modes).

  7. Simulation of multi-pulse coaxial helicity injection in the Sustained Spheromak Physics Experiment

    NASA Astrophysics Data System (ADS)

    O'Bryan, J. B.; Romero-Talamás, C. A.; Woodruff, S.

    2018-03-01

    Nonlinear, numerical computation with the NIMROD code is used to explore magnetic self-organization during multi-pulse coaxial helicity injection in the Sustained Spheromak Physics eXperiment. We describe multiple distinct phases of spheromak evolution, starting from vacuum magnetic fields and the formation of the initial magnetic flux bubble through multiple refluxing pulses and the eventual onset of the column mode instability. Experimental and computational magnetic diagnostics agree on the onset of the column mode instability, which first occurs during the second refluxing pulse of the simulated discharge. Our computations also reproduce the injector voltage traces, despite only specifying the injector current and not explicitly modeling the external capacitor bank circuit. The computations demonstrate that global magnetic evolution is fairly robust to different transport models and, therefore, that a single fluid-temperature model is sufficient for a broader, qualitative assessment of spheromak performance. Although discharges with similar traces of normalized injector current produce similar global spheromak evolution, details of the current distribution during the column mode instability impact the relative degree of poloidal flux amplification and magnetic helicity content.

  8. The influence of and the identification of nonlinearity in flexible structures

    NASA Technical Reports Server (NTRS)

    Zavodney, Lawrence D.

    1988-01-01

    Several models were built at NASA Langley and used to demonstrate the following nonlinear behavior: internal resonance in a free response, principal parametric resonance and subcritical instability in a cantilever beam-lumped mass structure, combination resonance in a parametrically excited flexible beam, autoparametric interaction in a two-degree-of-freedom system, instability of the linear solution, saturation of the excited mode, subharmonic bifurcation, and chaotic responses. A video tape documenting these phenomena was made. An attempt to identify a simple structure consisting of two light-weight beams and two lumped masses using the Eigensystem Realization Algorithm showed the inherent difficulty of using a linear based theory to identify a particular nonlinearity. Preliminary results show the technique requires novel interpretation, and hence may not be useful for structural modes that are coupled by a guadratic nonlinearity. A literature survey was also completed on recent work in parametrically excited nonlinear system. In summary, nonlinear systems may possess unique behaviors that require nonlinear identification techniques based on an understanding of how nonlinearity affects the dynamic response of structures. In this was, the unique behaviors of nonlinear systems may be properly identified. Moreover, more accutate quantifiable estimates can be made once the qualitative model has been determined.

  9. Interaction between mantle and crustal detachments: A nonlinear system controlling lithospheric extension

    NASA Astrophysics Data System (ADS)

    Rosenbaum, Gideon; Regenauer-Lieb, Klaus; Weinberg, Roberto F.

    2010-11-01

    We use numerical modeling to investigate the development of crustal and mantle detachments during lithospheric extension. Our models simulate a wide range of extensional systems with varying values of crustal thickness and heat flow, showing how strain localization in the mantle interacts with localization in the upper crust and controls the evolution of extensional systems. Model results reveal a richness of structures and deformation styles as a response to a self-organized mechanism that minimizes the internal stored energy of the system by localizing deformation. Crustal detachments, here referred as low-angle normal decoupling horizons, are well developed during extension of overthickened (60 km) continental crust, even when the initial heat flow is relatively low (50 mW m-2). In contrast, localized mantle deformation is most pronounced when the extended lithosphere has a normal crustal thickness (30-40 km) and an intermediate heat flow (60-70 mW m-2). Results show a nonlinear response to subtle changes in crustal thickness or heat flow, characterized by abrupt and sometimes unexpected switches in extension modes (e.g., from diffuse extensional deformation to effective lithospheric-scale rupturing) or from mantle- to crust-dominated strain localization. We interpret this nonlinearity to result from the interference of doming wavelengths in the presence of multiple necking instabilities. Disharmonic crust and mantle doming wavelengths results in efficient communication between shear zones at different lithospheric levels, leading to rupturing of the whole lithosphere. In contrast, harmonic crust and mantle doming inhibits interaction of shear zones across the lithosphere and results in a prolonged history of extension prior to continental breakup.

  10. Nonlinear ELM simulations based on a nonideal peeling–ballooning model using the BOUT++ code

    DOE PAGES

    Xu, X. Q.; Dudson, B. D.; Snyder, P. B.; ...

    2011-09-23

    A minimum set of equations based on the peeling–ballooning (P–B) model with nonideal physics effects (diamagnetic drift, E × B drift, resistivity and anomalous electron viscosity) is found to simulate pedestal collapse when using the BOUT++ simulation code, developed in part from the original fluid edge code BOUT. Linear simulations of P–B modes find good agreement in growth rate and mode structure with ELITE calculations. The influence of the E × B drift, diamagnetic drift, resistivity, anomalous electron viscosity, ion viscosity and parallel thermal diffusivity on P–B modes is being studied; we find that (1) the diamagnetic drift and Emore » × B drift stabilize the P–B mode in a manner consistent with theoretical expectations; (2) resistivity destabilizes the P–B mode, leading to resistive P–B mode; (3) anomalous electron and parallel ion viscosities destabilize the P–B mode, leading to a viscous P–B mode; (4) perpendicular ion viscosity and parallel thermal diffusivity stabilize the P–B mode. With addition of the anomalous electron viscosity under the assumption that the anomalous kinematic electron viscosity is comparable to the anomalous electron perpendicular thermal diffusivity, or the Prandtl number is close to unity, it is found from nonlinear simulations using a realistic high Lundquist number that the pedestal collapse is limited to the edge region and the ELM size is about 5–10% of the pedestal stored energy. Furthermore, this is consistent with many observations of large ELMs. The estimated island size is consistent with the size of fast pedestal pressure collapse. In the stable α-zones of ideal P–B modes, nonlinear simulations of viscous ballooning modes or current-diffusive ballooning mode (CDBM) for ITER H-mode scenarios are presented.« less

  11. Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements.

    PubMed

    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.

  12. Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

    PubMed Central

    Olivier, Michel; Gagnon, Marc-Daniel; Habel, Joé

    2016-01-01

    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. PMID:26967924

  13. Fault-tolerant nonlinear adaptive flight control using sliding mode online learning.

    PubMed

    Krüger, Thomas; Schnetter, Philipp; Placzek, Robin; Vörsmann, Peter

    2012-08-01

    An expanded nonlinear model inversion flight control strategy using sliding mode online learning for neural networks is presented. The proposed control strategy is implemented for a small unmanned aircraft system (UAS). This class of aircraft is very susceptible towards nonlinearities like atmospheric turbulence, model uncertainties and of course system failures. Therefore, these systems mark a sensible testbed to evaluate fault-tolerant, adaptive flight control strategies. Within this work the concept of feedback linearization is combined with feed forward neural networks to compensate for inversion errors and other nonlinear effects. Backpropagation-based adaption laws of the network weights are used for online training. Within these adaption laws the standard gradient descent backpropagation algorithm is augmented with the concept of sliding mode control (SMC). Implemented as a learning algorithm, this nonlinear control strategy treats the neural network as a controlled system and allows a stable, dynamic calculation of the learning rates. While considering the system's stability, this robust online learning method therefore offers a higher speed of convergence, especially in the presence of external disturbances. The SMC-based flight controller is tested and compared with the standard gradient descent backpropagation algorithm in the presence of system failures. Copyright © 2012 Elsevier Ltd. All rights reserved.

  14. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Liu, Rumeng; Wang, Lifeng, E-mail: walfe@nuaa.edu.cn

    The nonlinear thermal vibration behavior of a single-walled carbon nanotube (SWCNT) is investigated by molecular dynamics simulation and a nonlinear, nonplanar beam model. Whirling motion with energy transfer between flexural motions is found in the free vibration of the SWCNT excited by the thermal motion of atoms where the geometric nonlinearity is significant. A nonlinear, nonplanar beam model considering the coupling in two vertical vibrational directions is presented to explain the whirling motion of the SWCNT. Energy in different vibrational modes is not equal even over a time scale of tens of nanoseconds, which is much larger than the periodmore » of fundamental natural vibration of the SWCNT at equilibrium state. The energy of different modes becomes equal when the time scale increases to the microsecond range.« less

  15. Nonlinear optics and crystalline whispering gallery mode resonators

    NASA Technical Reports Server (NTRS)

    Matsko, Andrey B.; Savchenkov, Anatoliy A.; Ilchenko, Vladimir S.; Maleki, Lute

    2004-01-01

    We report on our recent results concerning fabrication of high-Q whispering gallery mode (WGM) crystalline resonators, and discuss some possible applications of lithium niobate WGM resonators in nonlinear optics and photonics. In particular, we demonstrate experimentally a tunable third-order optical filter fabricated from the three metalized resonators; and report observation of parametric frequency dobuling in a WGM resonator made of periodically poled lithium niobate (PPLN).

  16. Role of orbital filling on nonlinear ionic Raman scattering in perovskite titanates

    NASA Astrophysics Data System (ADS)

    Gu, Mingqiang; Rondinelli, James M.

    2017-01-01

    The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the d0 (CaTiO3) and d1 (LaTiO3) titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the Ag or B1 g mode amplitudes coupled to the Au or the B3 u mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth (˜100 meV ) and band gap (˜50 meV). By comparing the coupling coefficients of undoped CaTiO3 and LaTiO3 to those for electron-doped (CaTiO3) and hole-doped (LaTiO3) titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the d manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.

  17. Head-on collision of the second mode internal solitary waves

    NASA Astrophysics Data System (ADS)

    Terletska, Kateryna; Maderich, Vladimir; Jung, Kyung Tae

    2017-04-01

    Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internal waves on the oceanic shelf. Large amplitude internal solitary waves (ISW) of second mode containing trapped cores associated with closed streamlines can also transport plankton and nutrients. An interaction of ISWs with trapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-on collision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3D numerical model based on the Navier-Stokes equations for a continuously stratified fluid. Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneous deep layers can be identified: (i) the weakly nonlinear waves; (ii) the stable strongly nonlinear waves with trapped cores; and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Four interaction regimes for symmetric collision were separated from simulation results using this classification: (A) an almost elastic interaction of the weakly nonlinear waves; (B) a non-elastic interaction of waves with trapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h; (C) an almost elastic interaction of stable strongly nonlinear waves with trapped cores; (D) non-elastic interaction of the unstable strongly nonlinear waves. The unexpected result of simulation was that relative loss of energy due to the collision was maximal for regime B. New regime appeared when ISW of different amplitudes belonged to class (ii) collide. In result of interaction the exchange of mass between ISW occurred: the trapped core of smaller wave was entrained by core of larger ISW without mixing forming a new ISW of larger amplitude whereas in smaller ISW core of smaller wave totally substituted by fluid from larger wave. Overall, the wave characteristics induced by head-on collision agree well with the results of several available laboratory experiments. References [1] V. Maderich, K. T. Jung, K. Terletska, I. Brovchenko, T. Talipova, "Incomplete similarity of internal solitary waves with trapped core," Fluid Dynamics Research 47, 035511 (2015).

  18. On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, P. W.; Hall, P.

    1988-01-01

    Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub 0. At values of the radius above a sub 0 all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

  19. On the interaction of Tollmien-Schlichting waves in axisymmetric supersonic flows

    NASA Technical Reports Server (NTRS)

    Duck, P. W.; Hall, P.

    1989-01-01

    Two-dimensional lower branch Tollmien-Schlichting waves described by triple-deck theory are always stable for planar supersonic flows. The possible occurrence of axisymmetric unstable modes in the supersonic flow around an axisymmetric body is investigated. In particular flows around bodies with typical radii comparable with the thickness of the upper deck are considered. It is shown that such unstable modes exist below a critical nondimensional radius of the body a sub O. At values of the radius above a sub O all the modes are stable while if unstable modes exist they are found to occur in pairs. The interaction of these modes in the nonlinear regime is investigated using a weakly nonlinear approach and it is found that, dependent on the frequencies of the imposed Tollmien-Schlichting waves, either of the modes can be set up.

  20. Optical properties of solid-core photonic crystal fibers filled with nonlinear absorbers.

    PubMed

    Butler, James J; Bowcock, Alec S; Sueoka, Stacey R; Montgomery, Steven R; Flom, Steven R; Friebele, E Joseph; Wright, Barbara M; Peele, John R; Pong, Richard G S; Shirk, James S; Hu, Jonathan; Menyuk, Curtis R; Taunay, T F

    2013-09-09

    A theoretical and experimental investigation of the transmission of solid-core photonic crystal fibers (PCFs) filled with nonlinear absorbers shows a sharp change in the threshold for optical limiting and in leakage loss as the refractive index of the material in the holes approaches that of the glass matrix. Theoretical calculations of the mode profiles and leakage loss of the PCF are in agreement with experimental results and indicate that the change in limiting response is due to the interaction of the evanescent field of the guided mode with the nonlinear absorbers in the holes.

  1. Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

    NASA Astrophysics Data System (ADS)

    Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

    2017-12-01

    The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

  2. Guided wave methods and apparatus for nonlinear frequency generation

    DOEpatents

    Durfee, III, Charles G.; Rundquist, Andrew; Kapteyn, Henry C.; Murnane, Margaret M.

    2000-01-01

    Methods and apparatus are disclosed for the nonlinear generation of sum and difference frequencies of electromagnetic radiation propagating in a nonlinear material. A waveguide having a waveguide cavity contains the nonlinear material. Phase matching of the nonlinear generation is obtained by adjusting a waveguide propagation constant, the refractive index of the nonlinear material, or the waveguide mode in which the radiation propagates. Phase matching can be achieved even in isotropic nonlinear materials. A short-wavelength radiation source uses phase-matched nonlinear generation in a waveguide to produce high harmonics of a pulsed laser.

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

    NASA Astrophysics Data System (ADS)

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

    2017-12-01

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

  4. Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands

    NASA Astrophysics Data System (ADS)

    Todo, Y.; Berk, H. L.; Breizman, B. N.

    2012-09-01

    This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ⩾ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping.

  5. Impact of a large density gradient on linear and nonlinear edge-localized mode simulations

    DOE PAGES

    Xi, P. W.; Xu, X. Q.; Xia, T. Y.; ...

    2013-09-27

    Here, the impact of a large density gradient on edge-localized modes (ELMs) is studied linearly and nonlinearly by employing both two-fluid and gyro-fluid simulations. In two-fluid simulations, the ion diamagnetic stabilization on high-n modes disappears when the large density gradient is taken into account. But gyro-fluid simulations show that the finite Larmor radius (FLR) effect can effectively stabilize high-n modes, so the ion diamagnetic effect alone is not sufficient to represent the FLR stabilizing effect. We further demonstrate that additional gyroviscous terms must be kept in the two-fluid model to recover the linear results from the gyro-fluid model. Nonlinear simulations show that the density variation significantly weakens the E × B shearing at the top of the pedestal and thus leads to more energy loss during ELMs. The turbulence spectrum after an ELM crash is measured and has the relation ofmore » $$P(k_{z})\\propto k_{z}^{-3.3}$$ .« less

  6. Clutch pressure estimation for a power-split hybrid transmission using nonlinear robust observer

    NASA Astrophysics Data System (ADS)

    Zhou, Bin; Zhang, Jianwu; Gao, Ji; Yu, Haisheng; Liu, Dong

    2018-06-01

    For a power-split hybrid transmission, using the brake clutch to realize the transition from electric drive mode to hybrid drive mode is an available strategy. Since the pressure information of the brake clutch is essential for the mode transition control, this research designs a nonlinear robust reduced-order observer to estimate the brake clutch pressure. Model uncertainties or disturbances are considered as additional inputs, thus the observer is designed in order that the error dynamics is input-to-state stable. The nonlinear characteristics of the system are expressed as the lookup tables in the observer. Moreover, the gain matrix of the observer is solved by two optimization procedures under the constraints of the linear matrix inequalities. The proposed observer is validated by offline simulation and online test, the results have shown that the observer achieves significant performance during the mode transition, as the estimation error is within a reasonable range, more importantly, it is asymptotically stable.

  7. Field analysis of the Cerenkov doubling of infrared coherent radiation utilizing an organic crystal core bounded by a glass capillary

    NASA Astrophysics Data System (ADS)

    Hayata, K.; Yanagawa, K.; Koshiba, M.

    1990-12-01

    A mode field analysis is presented of the second-harmonic electromagnetic wave that radiates from a nonlinear core bounded by a dielectric cladding. With this analysis the ultimate performance of the organic crystal-cored single-mode optical fiber waveguide as a guided-wave frequency doubler is evaluated through the solution of nonlinear parametric equations derived from Maxwell's equations under some assumptions. As a phase-matching scheme, a Cerenkov approach is considered because of advantages in actual device applications, in which the phase matching is achievable between the fundamental guided LP01 mode and the second-harmonic radiation (leaky) mode. Calculated results for organic cores made of benzil, 4-(N,N-dimethyl-amino)-3-acetamidonitrobenzen, 2-methyl-4-nitroaniline, and 4'-nitrobenzilidene-3-acetoamino-4-metxianiline provide useful data for designing an efficient fiber-optic wavelength converter utilizing nonlinear parametric processes. A detailed comparison is made between results for infinite and finite cladding thicknesses.

  8. Molecular structure of hybrid imino-chalcone in the solid state: X-ray diffraction, spectroscopy study and third-order nonlinear optical properties

    NASA Astrophysics Data System (ADS)

    Custodio, J. M. F.; Santos, F. G.; Vaz, W. F.; Cunha, C. E. P.; Silveira, R. G.; Anjos, M. M.; Campos, C. E. M.; Oliveira, G. R.; Martins, F. T.; da Silva, C. C.; Valverde, C.; Baseia, B.; Napolitano, H. B.

    2018-04-01

    A comprehensive structural study of the compound (2E)-1-((E)-4-(4-methoxybenzylideneamino)phenyl)-3-(4-methoxyphenyl)prop-2-en-1-one was carried out in this work. Single crystal X-ray diffraction (SCXRD), X-ray powder diffraction (XRPD), NMR, Raman and Infrared spectroscopies, and DFT calculations were performed for characterization of this iminochalcone hybrid. Intermolecular interactions were described by Hirshfeld surface analysis derived from crystal structure. Reactivity and intramolecular charge transfer were investigated using the frontier molecular orbitals and molecular electrostatic potential. In addition, we have calculated the Nonlinear Optical Properties at the CAM-B3LYP/6-311+g(d) level of theory in the presence of different solvents (gas-phase, acetone, chloroform, dichloromethane, dimethyl sulfoxide, ethanol, methanol, and water), being found meaningful NLO parameters for our compound. At last, there is a good agreement between calculated and experimental IR spectrum, allowing the assignment of some of normal vibrational modes of the iminochalcone hybrid.

  9. Hierarchical nonlinear dynamics of human attention.

    PubMed

    Rabinovich, Mikhail I; Tristan, Irma; Varona, Pablo

    2015-08-01

    Attention is the process of focusing mental resources on a specific cognitive/behavioral task. Such brain dynamics involves different partially overlapping brain functional networks whose interconnections change in time according to the performance stage, and can be stimulus-driven or induced by an intrinsically generated goal. The corresponding activity can be described by different families of spatiotemporal discrete patterns or sequential dynamic modes. Since mental resources are finite, attention modalities compete with each other at all levels of the hierarchy, from perception to decision making and behavior. Cognitive activity is a dynamical process and attention possesses some universal dynamical characteristics. Thus, it is time to apply nonlinear dynamical theory for the description and prediction of hierarchical attentional tasks. Such theory has to include the analyses of attentional control stability, the time cost of attention switching, the finite capacity of informational resources in the brain, and the normal and pathological bifurcations of attention sequential dynamics. In this paper we have integrated today's knowledge, models and results in these directions. Copyright © 2015 Elsevier Ltd. All rights reserved.

  10. Nonlinear Dynamic Modeling and Controls Development for Supersonic Propulsion System Research

    NASA Technical Reports Server (NTRS)

    Connolly, Joseph W.; Kopasakis, George; Paxson, Daniel E.; Stuber, Eric; Woolwine, Kyle

    2012-01-01

    This paper covers the propulsion system component modeling and controls development of an integrated nonlinear dynamic simulation for an inlet and engine that can be used for an overall vehicle (APSE) model. The focus here is on developing a methodology for the propulsion model integration, which allows for controls design that prevents inlet instabilities and minimizes the thrust oscillation experienced by the vehicle. Limiting thrust oscillations will be critical to avoid exciting vehicle aeroelastic modes. Model development includes both inlet normal shock position control and engine rotor speed control for a potential supersonic commercial transport. A loop shaping control design process is used that has previously been developed for the engine and verified on linear models, while a simpler approach is used for the inlet control design. Verification of the modeling approach is conducted by simulating a two-dimensional bifurcated inlet and a representative J-85 jet engine previously used in a NASA supersonics project. Preliminary results are presented for the current supersonics project concept variable cycle turbofan engine design.

  11. Inviscid dynamics of a wet foam drop with monodisperse bubble size distribution

    NASA Astrophysics Data System (ADS)

    McDaniel, J. Gregory; Akhatov, Iskander; Holt, R. Glynn

    2002-06-01

    Motivated by recent experiments involving the acoustic levitation of foam drops, we develop a model for nonlinear oscillations of a spherical drop composed of monodisperse aqueous foam with void fraction below 0.1. The model conceptually divides a foam drop into many cells, each cell consisting of a spherical volume of liquid with a bubble at its center. By treating the liquid as incompressible and inviscid, a nonlinear equation is obtained for bubble motion due to a pressure applied at the outer radius of the liquid sphere. Upon linearizing this equation and connecting the cells at their outer radii, a wave equation is obtained with a dispersion relation for the sound waves in a bubbly liquid. For the spherical drop, this equation is solved by a normal mode expansion that yields the natural frequencies as functions of standard foam parameters. Numerical examples illustrate how the analysis may be used to extract foam parameters, such as void fraction and bubble radius, from the experimentally measured natural frequencies of a foam drop.

  12. Supercontinuum generation in quadratic nonlinear waveguides without quasi-phase matching.

    PubMed

    Guo, Hairun; Zhou, Binbin; Steinert, Michael; Setzpfandt, Frank; Pertsch, Thomas; Chung, Hung-ping; Chen, Yen-Hung; Bache, Morten

    2015-02-15

    Supercontinuum generation (SCG) is most efficient when the solitons can be excited directly at the pump laser wavelength. Quadratic nonlinear waveguides may induce an effective negative Kerr nonlinearity, so temporal solitons can be directly generated in the normal (positive) dispersion regime overlapping with common ultrafast laser wavelengths. There is no need for waveguide dispersion engineering. Here, we experimentally demonstrate SCG in standard lithium niobate (LN) waveguides without quasi-phase matching (QPM), pumped with femtosecond pulses in the normal dispersion regime. The observed large bandwidths (even octave spanning), together with other experimental data, indicate that negative nonlinearity solitons are indeed excited, which is backed up by numerical simulations. The QPM-free design reduces production complexity, extends the maximum waveguide length, and limits undesired spectral resonances. Finally, nonlinear crystals can be used where QPM is inefficient or impossible, which is important for mid-IR SCG. QPM-free waveguides in mid-IR nonlinear crystals can support negative nonlinearity solitons, as these waveguides have a normal dispersion at the emission wavelengths of mid-IR ultrafast lasers.

  13. Nonlinear acoustic spectroscopy of cracked flaws and disbonds: Fundamentals, techniques, and applications

    NASA Astrophysics Data System (ADS)

    Maev, R. Gr.; Solodov, I. Yu.

    2000-05-01

    Classical nonlinear acoustics of solids operates with distributed material nonlinearity related to unharmonicity of molecular interaction forces. Weakening of molecular bonds in a defect area or intermittent lack of elastic coupling between the faces of a vibrating crack or unbond ("clapping") results in anomalously high local contact acoustic nonlinearity (CAN). CAN properties and spectral features are different from those of the classical analog and important to develop new acoustic NDE techniques. Three approaches to nonlinear NDE methodology have been experimentally verified: low-frequency (hundreds of Hz) vibration technique, intermediate-frequency (hundreds of kHz) standing wave and high-frequency (tens of MHz) propagation modes. Low-frequency nonlinear contact vibrations revealed multiple sub- and super-harmonics generation featuring non-monotonous (sinx/x type) spectra. Parametric instability observed in resonator with a nonlinear contact leads to the output spectrum splitting up into successive sub-harmonics as the wave amplitude increases. High-frequency experiments demonstrated abnormal increases in the third harmonic amplitude: 3 or 4 order enhancement of the 3-ω nonlinear parameter was measured for the nonlinear contact. The CAN spectral features in both acoustic and vibration modes were used for nonlinear NDE of simulated and realistic flaws in glass, metal welds, etc. The sensitivities of the techniques are compared and their practical applicability assessed.

  14. Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

    PubMed

    Jeong, Bongwon; Cho, Hanna; Keum, Hohyun; Kim, Seok; Michael McFarland, D; Bergman, Lawrence A; King, William P; Vakakis, Alexander F

    2014-11-21

    Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

  15. Limbic hyperconnectivity in the vegetative state.

    PubMed

    Di Perri, Carol; Bastianello, Stefano; Bartsch, Andreas J; Pistarini, Caterina; Maggioni, Giorgio; Magrassi, Lorenzo; Imberti, Roberto; Pichiecchio, Anna; Vitali, Paolo; Laureys, Steven; Di Salle, Francesco

    2013-10-15

    To investigate functional connectivity between the default mode network (DMN) and other networks in disorders of consciousness. We analyzed MRI data from 11 patients in a vegetative state and 7 patients in a minimally conscious state along with age- and sex-matched healthy control subjects. MRI data analysis included nonlinear spatial normalization to compensate for disease-related anatomical distortions. We studied brain connectivity data from resting-state MRI temporal series, combining noninferential (independent component analysis) and inferential (seed-based general linear model) methods. In DMN hypoconnectivity conditions, a patient's DMN functional connectivity shifts and paradoxically increases in limbic structures, including the orbitofrontal cortex, insula, hypothalamus, and the ventral tegmental area. Concurrently with DMN hypoconnectivity, we report limbic hyperconnectivity in patients in vegetative and minimally conscious states. This hyperconnectivity may reflect the persistent engagement of residual neural activity in self-reinforcing neural loops, which, in turn, could disrupt normal patterns of connectivity.

  16. Precluding nonlinear ISI in direct detection long-haul fiber optic systems

    NASA Technical Reports Server (NTRS)

    Swenson, Norman L.; Shoop, Barry L.; Cioffi, John M.

    1991-01-01

    Long-distance, high-rate fiber optic systems employing directly modulated 1.55-micron single-mode lasers and conventional single-mode fiber suffer severe intersymbol interference (ISI) with a large nonlinear component. A method of reducing the nonlinearity of the ISI, thereby making linear equalization more viable, is investigated. It is shown that the degree of nonlinearity is highly dependent on the choice of laser bias current, and that in some cases the ISI nonlinearity can be significantly reduced by biasing the laser substantially above threshold. Simulation results predict that an increase in signal-to-nonlinear-distortion ratio as high as 25 dB can be achieved for synchronously spaced samples at an optimal sampling phase by increasing the bias current from 1.2 times threshold to 3.5 times threshold. The high SDR indicates that a linear tapped delay line equalizer could be used to mitigate ISI. Furthermore, the shape of the pulse response suggests that partial response precoding and digital feedback equalization would be particularly effective for this channel.

  17. Modelling of NSTX hot vertical displacement events using M 3 D -C 1

    NASA Astrophysics Data System (ADS)

    Pfefferlé, D.; Ferraro, N.; Jardin, S. C.; Krebs, I.; Bhattacharjee, A.

    2018-05-01

    The main results of an intense vertical displacement event (VDE) modelling activity using the implicit 3D extended MHD code M3D-C1 are presented. A pair of nonlinear 3D simulations are performed using realistic transport coefficients based on the reconstruction of a so-called NSTX frozen VDE where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase is solved assuming axisymmetry until the plasma contacts the first wall, at which point the intricate evolution of the plasma, decaying to large extent in force-balance with induced halo/wall currents, is carefully resolved via 3D nonlinear simulations. The faster 2D nonlinear runs allow to assess the sensitivity of the simulations to parameter changes. In the limit of perfectly conducting wall, the expected linear relation between vertical growth rate and wall resistivity is recovered. For intermediate wall resistivities, the halo region contributes to slowing the plasma down, and the characteristic VDE time depends on the choice of halo temperature. The evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed in detail. The 3D simulations highlight a rich structure of toroidal modes, penetrating inwards from edge to core and cascading from high-n to low-n mode numbers. The break-up of flux-surfaces results in a progressive stochastisation of field-lines precipitating the thermalisation of the plasma with the wall. The plasma current then decays rapidly, inducing large currents in the halo region and the wall. Analysis of normal currents flowing in and out of the divertor plate reveals rich time-varying patterns.

  18. Off-axis fishbone-like instability and excitation of resistive wall modes in JT-60U and DIII-D

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Okabayashi, M.; Solomon, W. M.; Budny, R. V.

    2011-05-15

    An energetic-particle (EP)-driven ''off-axis-fishbone-like mode (OFM)'' often triggers a resistive wall mode (RWM) in JT-60U and DIII-D devices, preventing long-duration high-{beta}{sub N} discharges. In these experiments, the EPs are energetic ions (70-85 keV) injected by neutral beams to produce high-pressure plasmas. EP-driven bursting events reduce the EP density and the plasma rotation simultaneously. These changes are significant in high-{beta}{sub N} low-rotation plasmas, where the RWM stability is predicted to be strongly influenced by the EP precession drift resonance and by the plasma rotation near the q=2 surface (kinetic effects). Analysis of these effects on stability with a self-consistent perturbation tomore » the mode structure using the MARS-K code showed that the impact of EP losses and rotation drop is sufficient to destabilize the RWM in low-rotation plasmas, when the plasma rotation normalized by Alfven frequency is only a few tenths of a percent near the q=2 surface. The OFM characteristics are very similar in JT-60U and DIII-D, including nonlinear mode evolution. The modes grow initially like a classical fishbone, and then the mode structure becomes strongly distorted. The dynamic response of the OFM to an applied n=1 external field indicates that the mode retains its external kink character. These comparative studies suggest that an energetic particle-driven 'off-axis-fishbone-like mode' is a new EP-driven branch of the external kink mode in wall-stabilized plasmas, analogous to the relationship of the classical fishbone branch to the internal kink mode.« less

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

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yan, R.; Betti, R.; Sanz, J.

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

  20. Special class of nonlinear damping models in flexible space structures

    NASA Technical Reports Server (NTRS)

    Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

    1991-01-01

    A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

  1. Impact of E × B shear flow on low-n MHD instabilities.

    PubMed

    Chen, J G; Xu, X Q; Ma, C H; Xi, P W; Kong, D F; Lei, Y A

    2017-05-01

    Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al. , Phys. Plasmas 23 , 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E  ×  B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E  ×  B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the E r shear. Adopting the much more general shape of E  ×  B shear ([Formula: see text]) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

  2. Impact of E × B shear flow on low-n MHD instabilities

    NASA Astrophysics Data System (ADS)

    Chen, J. G.; Xu, X. Q.; Ma, C. H.; Xi, P. W.; Kong, D. F.; Lei, Y. A.

    2017-05-01

    Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear ( ω E = E r / R B θ ) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

  3. Impact of E × B shear flow on low-n MHD instabilities

    PubMed Central

    Chen, J. G.; Ma, C. H.; Xi, P. W.; Lei, Y. A.

    2017-01-01

    Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear (ωE=Er/RBθ) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode. PMID:28579732

  4. Time-frequency analysis : mathematical analysis of the empirical mode decomposition.

    DOT National Transportation Integrated Search

    2009-01-01

    Invented over 10 years ago, empirical mode : decomposition (EMD) provides a nonlinear : time-frequency analysis with the ability to successfully : analyze nonstationary signals. Mathematical : Analysis of the Empirical Mode Decomposition : is a...

  5. Rogue wave modes for a derivative nonlinear Schrödinger model.

    PubMed

    Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin

    2014-03-01

    Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described.

  6. Nonlinear simulations of beam-driven Compressional Alfv´en Eigenmodes in NSTX

    DOE PAGES

    Belova, Elena V.; Gorelenkov, N. N.; Crocker, N. A.; ...

    2017-03-10

    We present results for the 3D nonlinear simulations of neutral-beam-driven compressional Alfv´en eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX). Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n = 4 - 9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfv´en wave (KAW) that occurs on the high-field side at the Alfv´en resonance location. We frequently observe high-frequency Alfv´en eigenmodes in beam-heated NSTX plasmas, and have been linkedmore » to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. Furthermore, a set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.« less

  7. Nonlinear simulations of beam-driven Compressional Alfv´en Eigenmodes in NSTX

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Belova, Elena V.; Gorelenkov, N. N.; Crocker, N. A.

    We present results for the 3D nonlinear simulations of neutral-beam-driven compressional Alfv´en eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX). Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n = 4 - 9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfv´en wave (KAW) that occurs on the high-field side at the Alfv´en resonance location. We frequently observe high-frequency Alfv´en eigenmodes in beam-heated NSTX plasmas, and have been linkedmore » to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. Furthermore, a set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.« less

  8. Study of solar wind spectra by nonlinear waves interaction

    NASA Astrophysics Data System (ADS)

    Dwivedi, Navin; Sharma, Rampal; Narita, Yasuhito

    2014-05-01

    The nature of small-scale turbulent fluctuations in the solar wind (SW) turbulence is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations predict the evidence of the dominance of kinetic Alfvén waves (KAW) at sub-ion scales with frequency below than ion cyclotron frequency, while other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode is more relevant. In the present work, nonlinear interaction of kinetic Alfvén wave with whistler wave is considered as one of the possible cause responsible for the solar wind turbulence. A set of coupled dimensionless equations are derived for the intermediate beta plasmas and the nonlinear interaction between these two wave modes has been studied. As a consequence of ponderomotive nonlinearity, the pump KAW becomes filamented when its power exceeds the threshold for the filamentation instability. Whistler is considered to be weak and thus doesn't have enough intensity to initiate its own localization. It gets localized while propagating through the density channel created by KAW localization. In addition, spectral scales of power spectra of KAW and whistler are also calculated. The steeper spectra are found with scaling greater than -5/3. This type of nonlinear interaction between different wave modes and steeper spectra is one of the reasons for the solar wind turbulence and particles acceleration. This work is partially supported by DST (India) and FP7/STORM (313038)

  9. Experimental observation of multi-scale interactions among kink /tearing modes and high-frequency fluctuations in the HL-2A core NBI plasmas

    NASA Astrophysics Data System (ADS)

    Chen, W.; Jiang, M.; Xu, Y.; Shi, P. W.; Yu, L. M.; Ding, X. T.; Shi, Z. B.; Ji, X. Q.; Yu, D. L.; Li, Y. G.; Yang, Z. C.; Zhong, W. L.; Qiu, Z. Y.; Li, J. Q.; Dong, J. Q.; Yang, Q. W.; Liu, Yi.; Yan, L. W.; Xu, M.; Duan, X. R.

    2017-11-01

    Multi-scale interactions have been observed recently in the HL-2A core NBI plasmas, including the synchronous coupling between m/n=1/1 kink mode and m/n=2/1 tearing mode, nonlinear couplings of TAE/BAE and m/n=2/1 TM near q=2 surface, AITG/KBM/BAE and m/n=1/1 kink mode near q=1 surface, and between m/n=1/1 kink mode and high-frequency turbulence. Experimental results suggest that several couplings can exist simultaneously, Alfvenic fluctuations have an important contribution to the high-frequency turbulence spectra, and the couplings reveal the electromagnetic character. Multi-scale interactions via the nonlinear modulation process maybe enhance plasma transport and trigger sawtooth-crash onset.

  10. Coupling of damped and growing modes in unstable shear flow

    DOE PAGES

    Fraser, A. E.; Terry, P. W.; Zweibel, E. G.; ...

    2017-06-14

    Analysis of the saturation of the Kelvin-Helmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewise-continuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injection-scale sink of the fluctuation energy similar to what has been found for gyroradius-scale drift-wave turbulence. Quantitative evaluation of the contribution of the stable mode to the energy balance at the onset of saturation shows that nonlinear energy transfer to the stable mode is as significant as energy transfer to smallmore » scales in balancing energy injected into the spectrum by the instability. The effect of the stable mode on momentum transport is quantified by expressing the Reynolds stress in terms of stable and unstable mode amplitudes at saturation, from which it is found that the stable mode can produce a sizable reduction in the momentum flux.« less

  11. Coupling of damped and growing modes in unstable shear flow

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Fraser, A. E.; Terry, P. W.; Zweibel, E. G.

    Analysis of the saturation of the Kelvin-Helmholtz instability is undertaken to determine the extent to which the conjugate linearly stable mode plays a role. For a piecewise-continuous mean flow profile with constant shear in a fixed layer, it is shown that the stable mode is nonlinearly excited, providing an injection-scale sink of the fluctuation energy similar to what has been found for gyroradius-scale drift-wave turbulence. Quantitative evaluation of the contribution of the stable mode to the energy balance at the onset of saturation shows that nonlinear energy transfer to the stable mode is as significant as energy transfer to smallmore » scales in balancing energy injected into the spectrum by the instability. The effect of the stable mode on momentum transport is quantified by expressing the Reynolds stress in terms of stable and unstable mode amplitudes at saturation, from which it is found that the stable mode can produce a sizable reduction in the momentum flux.« less

  12. Independent-Cluster Parametrizations of Wave Functions in Model Field Theories III. The Coupled-Cluster Phase Spaces and Their Geometrical Structure

    NASA Astrophysics Data System (ADS)

    Arponen, J. S.; Bishop, R. F.

    1993-11-01

    In this third paper of a series we study the structure of the phase spaces of the independent-cluster methods. These phase spaces are classical symplectic manifolds which provide faithful descriptions of the quantum mechanical pure states of an arbitrary system. They are "superspaces" in the sense that the full physical many-body or field-theoretic system is described by a point of the space, in contrast to "ordinary" spaces for which the state of the physical system is described rather by the whole space itself. We focus attention on the normal and extended coupled-cluster methods (NCCM and ECCM). Both methods provide parametrizations of the Hilbert space which take into account in increasing degrees of completeness the connectivity properties of the associated perturbative diagram structure. This corresponds to an increasing incorporation of locality into the description of the quantum system. As a result the degree of nonlinearity increases in the dynamical equations that govern the temporal evolution and determine the equilibrium state. Because of the nonlinearity, the structure of the manifold becomes geometrically complicated. We analyse the neighbourhood of the ground state of the one-mode anharmonic bosonic field theory and derive the nonlinear expansion beyond the linear response regime. The expansion is given in terms of normal-mode amplitudes, which provide the best local coordinate system close to the ground state. We generalize the treatment to other nonequilibrium states by considering the similarly defined normal coordinates around the corresponding phase space point. It is pointed out that the coupled-cluster method (CCM) maps display such features as (an)holonomy, or geometric phase. For example, a physical state may be represented by a number of different points on the CCM manifold. For this reason the whole phase spaces in the NCCM or ECCM cannot be covered by a single chart. To account for this non-Euclidean nature we introduce a suitable pseudo-Riemannian metric structure which is compatible with an important subset of all canonical transformations. It is then shown that the phase space of the configuration-interaction method is flat, namely the complex Euclidean space; that the NCCM manifold has zero curvature even though its Reimann tensor does not vanish; and that the ECCM manifold is intrinsically curved. It is pointed out that with the present metrization many of the dimensions of the ECCM phase space are effectively compactified and that the overall topological structure of the space is related to the distribution of the zeros of the Bargmann wave function.

  13. Wave-Kinetic Simulations of the Nonlinear Generation of Electromagnetic VLF Waves through Velocity Ring Instabilities

    NASA Astrophysics Data System (ADS)

    Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.

    2014-12-01

    Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].

  14. A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

    NASA Technical Reports Server (NTRS)

    Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.

    1991-01-01

    A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

  15. Handheld nonlinear microscope system comprising a 2 MHz repetition rate, mode-locked Yb-fiber laser for in vivo biomedical imaging

    PubMed Central

    Krolopp, Ádám; Csákányi, Attila; Haluszka, Dóra; Csáti, Dániel; Vass, Lajos; Kolonics, Attila; Wikonkál, Norbert; Szipőcs, Róbert

    2016-01-01

    A novel, Yb-fiber laser based, handheld 2PEF/SHG microscope imaging system is introduced. It is suitable for in vivo imaging of murine skin at an average power level as low as 5 mW at 200 kHz sampling rate. Amplified and compressed laser pulses having a spectral bandwidth of 8 to 12 nm at around 1030 nm excite the biological samples at a ~1.89 MHz repetition rate, which explains how the high quality two-photon excitation fluorescence (2PEF) and second harmonic generation (SHG) images are obtained at the average power level of a laser pointer. The scanning, imaging and detection head, which comprises a conventional microscope objective for beam focusing, has a physical length of ~180 mm owing to the custom designed imaging telescope system between the laser scanner mirrors and the entrance aperture of the microscope objective. Operation of the all-fiber, all-normal dispersion Yb-fiber ring laser oscillator is electronically controlled by a two-channel polarization controller for Q-switching free mode-locked operation. The whole nonlinear microscope imaging system has the main advantages of the low price of the fs laser applied, fiber optics flexibility, a relatively small, light-weight scanning and detection head, and a very low risk of thermal or photochemical damage of the skin samples. PMID:27699118

  16. Handheld nonlinear microscope system comprising a 2 MHz repetition rate, mode-locked Yb-fiber laser for in vivo biomedical imaging.

    PubMed

    Krolopp, Ádám; Csákányi, Attila; Haluszka, Dóra; Csáti, Dániel; Vass, Lajos; Kolonics, Attila; Wikonkál, Norbert; Szipőcs, Róbert

    2016-09-01

    A novel, Yb-fiber laser based, handheld 2PEF/SHG microscope imaging system is introduced. It is suitable for in vivo imaging of murine skin at an average power level as low as 5 mW at 200 kHz sampling rate. Amplified and compressed laser pulses having a spectral bandwidth of 8 to 12 nm at around 1030 nm excite the biological samples at a ~1.89 MHz repetition rate, which explains how the high quality two-photon excitation fluorescence (2PEF) and second harmonic generation (SHG) images are obtained at the average power level of a laser pointer. The scanning, imaging and detection head, which comprises a conventional microscope objective for beam focusing, has a physical length of ~180 mm owing to the custom designed imaging telescope system between the laser scanner mirrors and the entrance aperture of the microscope objective. Operation of the all-fiber, all-normal dispersion Yb-fiber ring laser oscillator is electronically controlled by a two-channel polarization controller for Q-switching free mode-locked operation. The whole nonlinear microscope imaging system has the main advantages of the low price of the fs laser applied, fiber optics flexibility, a relatively small, light-weight scanning and detection head, and a very low risk of thermal or photochemical damage of the skin samples.

  17. SU-F-T-263: Dosimetric Characteristics of the Cine Acquisition Mode of An A-Si EPID

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bawazeer, O; Deb, P; Sarasanandarajah, S

    2016-06-15

    Purpose: To investigate the dosimetric characteristics of Varian a-Si-500 electronic portal imaging device (EPID) operated in cine mode particularly considering linearity with delivered dose, dose rate, field size, phantom thickness, MLC speed and common IMRT fields. Methods: The EPID that attached to a Varian Clinac 21iX linear accelerator, was irradiated with 6 and 18 MV using 600 MU/min. Image acquisition is controlled by the IAS3 software, Trigger delay was 6 ms, BeamOnDelay and FrameStartDelay were zero. Different frame rates were utilized. Cine mode response was calculated using MATLAB as summation of mean pixel values in a region of interest ofmore » the acquired images. The performance of cine mode was compared to integrated mode and dose measurements in water using CC13 ionization chamber. Results: Figure1 illustrates that cine mode has nonlinear response for small MU, when delivering 10 MU was about 0.5 and 0.64 for 6 and 18 MV respectively. This is because the missing acquired images that were calculated around four images missing in each delivery. With the increase MU the response became linear and comparable with integrated mode and ionization chamber within 2%. Figure 2 shows that cine mode has comparable response with integrated mode and ionization chamber within 2% with changing dose rate for 10 MU delivered. This indicates that the dose rate change has no effect on nonlinearity of cine mode response. Except nonlinearity, cine mode is well matched to integrated mode response within 2% for field size, phantom thickness, MLC speed dependences. Conclusion: Cine mode has similar dosimetric characteristics to integrated mode with open and IMRT fields, and the main limitation with cine mode is missing images. Therefore, the calibration of EPID images with this mode should be run with large MU, and when IMRT verification field has low MU, the correction for missing images are required.« less

  18. Classifying depression patients and normal subjects using machine learning techniques and nonlinear features from EEG signal.

    PubMed

    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.

  19. Methods for discrete solitons in nonlinear lattices.

    PubMed

    Ablowitz, Mark J; Musslimani, Ziad H; Biondini, Gino

    2002-02-01

    A method to find discrete solitons in nonlinear lattices is introduced. Using nonlinear optical waveguide arrays as a prototype application, both stationary and traveling-wave solitons are investigated. In the limit of small wave velocity, a fully discrete perturbative analysis yields formulas for the mode shapes and velocity.

  20. Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope

    PubMed Central

    Nitzan, Sarah H.; Zega, Valentina; Li, Mo; Ahn, Chae H.; Corigliano, Alberto; Kenny, Thomas W.; Horsley, David A.

    2015-01-01

    Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes. PMID:25762243

  1. Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

    PubMed

    Nitzan, Sarah H; Zega, Valentina; Li, Mo; Ahn, Chae H; Corigliano, Alberto; Kenny, Thomas W; Horsley, David A

    2015-03-12

    Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

  2. Simulation of Vortex Structure in Supersonic Free Shear Layer Using Pse Method

    NASA Astrophysics Data System (ADS)

    Guo, Xin; Wang, Qiang

    The method of parabolized stability equations (PSE) are applied in the analysis of nonlinear stability and the simulation of flow structure in supersonic free shear layer. High accuracy numerical techniques including self-similar basic flow, high order differential method, appropriate transformation and decomposition of nonlinear terms are adopted and developed to solve the PSE effectively for free shear layer. The spatial evolving unstable waves which dominate the flow structure are investigated through nonlinear coupling spatial marching methods. The nonlinear interactions between harmonic waves are further analyzed and instantaneous flow field are obtained by adding the harmonic waves into basic flow. Relevant data agree well with that of DNS. The results demonstrate that T-S wave does not keeping growing exponential as the linear evolution, the energy transfer to high order harmonic modes and finally all harmonic modes get saturation due to the nonlinear interaction; Mean flow distortion is produced by the nonlinear interaction between the harmonic and its conjugate harmonic, makes great change to the average flow and increases the thickness of shear layer; PSE methods can well capture the large scale nonlinear flow structure in the supersonic free shear layer such as vortex roll-up, vortex pairing and nonlinear saturation.

  3. Nonlinear Metasurface for Simultaneous Control of Spin and Orbital Angular Momentum in Second Harmonic Generation.

    PubMed

    Li, Guixin; Wu, Lin; Li, King F; Chen, Shumei; Schlickriede, Christian; Xu, Zhengji; Huang, Siya; Li, Wendi; Liu, Yanjun; Pun, Edwin Y B; Zentgraf, Thomas; Cheah, Kok W; Luo, Yu; Zhang, Shuang

    2017-12-13

    The spin and orbital angular momentum (SAM and OAM) of light is providing a new gateway toward high capacity and robust optical communications. While the generation of light with angular momentum is well studied in linear optics, its further integration into nonlinear optical devices will open new avenues for increasing the capacity of optical communications through additional information channels at new frequencies. However, it has been challenging to manipulate the both SAM and OAM of nonlinear signals in harmonic generation processes with conventional nonlinear materials. Here, we report the generation of spin-controlled OAM of light in harmonic generations by using ultrathin photonic metasurfaces. The spin manipulation of OAM mode of harmonic waves is experimentally verified by using second harmonic generation (SHG) from gold meta-atom with 3-fold rotational symmetry. By introducing nonlinear phase singularity into the metasurface devices, we successfully generate and measure the topological charges of spin-controlled OAM mode of SHG through an on-chip metasurface interferometer. The nonlinear photonic metasurface proposed in this work not only opens new avenues for manipulating the OAM of nonlinear optical signals but also benefits the understanding of the nonlinear spin-orbit interaction of light in nanoscale devices.

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

    NASA Astrophysics Data System (ADS)

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

    2018-04-01

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

  5. Quantitative Analysis of Temperature Dependence of Raman shift of monolayer WS2

    NASA Astrophysics Data System (ADS)

    Huang, Xiaoting; Gao, Yang; Yang, Tianqi; Ren, Wencai; Cheng, Hui-Ming; Lai, Tianshu

    2016-08-01

    We report the temperature-dependent evolution of Raman spectra of monolayer WS2 directly CVD-grown on a gold foil and then transferred onto quartz substrates over a wide temperature range from 84 to 543 K. The nonlinear temperature dependence of Raman shifts for both and A1g modes has been observed. The first-order temperature coefficients of Raman shifts are obtained to be -0.0093 (cm-1/K) and -0.0122 (cm-1/K) for and A1g peaks, respectively. A physical model, including thermal expansion and three- and four-phonon anharmonic effects, is used quantitatively to analyze the observed nonlinear temperature dependence. Thermal expansion coefficient (TEC) of monolayer WS2 is extracted from the experimental data for the first time. It is found that thermal expansion coefficient of out-plane mode is larger than one of in-plane mode, and TECs of and A1g modes are temperature-dependent weakly and strongly, respectively. It is also found that the nonlinear temperature dependence of Raman shift of mode mainly originates from the anharmonic effect of three-phonon process, whereas one of A1g mode is mainly contributed by thermal expansion effect in high temperature region, revealing that thermal expansion effect cannot be ignored.

  6. Validation of nonlinear gyrokinetic simulations of L- and I-mode plasmas on Alcator C-Mod

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Creely, A. J.; Howard, N. T.; Rodriguez-Fernandez, P.

    New validation of global, nonlinear, ion-scale gyrokinetic simulations (GYRO) is carried out for L- and I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and temperature fluctuations. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [White PoP 2015], suggesting that multi-scale (cross-scale coupling) effects [Howard PoP 2016] may be less important in I-mode than in L-mode. New results presented here, however, show that global, nonlinear, ion-scale GYRO simulations are able to match the experimental ion heat flux, but underpredict electron heat flux (at most radii),more » electron temperature fluctuations, and perturbative thermal diffusivity in both L- and I-mode. Linear addition of electron heat flux from electron scale runs does not resolve this discrepancy. These results indicate that single-scale simulations do not sufficiently describe the I-mode core transport, and that multi-scale (coupled electron- and ion-scale) transport models are needed. In conclusion a preliminary investigation with multi-scale TGLF, however, was unable to resolve the discrepancy between ion-scale GYRO and experimental electron heat fluxes and perturbative diffusivity, motivating further work with multi-scale GYRO simulations and a more comprehensive study with multi-scale TGLF.« less

  7. Validation of nonlinear gyrokinetic simulations of L- and I-mode plasmas on Alcator C-Mod

    DOE PAGES

    Creely, A. J.; Howard, N. T.; Rodriguez-Fernandez, P.; ...

    2017-03-02

    New validation of global, nonlinear, ion-scale gyrokinetic simulations (GYRO) is carried out for L- and I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and temperature fluctuations. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [White PoP 2015], suggesting that multi-scale (cross-scale coupling) effects [Howard PoP 2016] may be less important in I-mode than in L-mode. New results presented here, however, show that global, nonlinear, ion-scale GYRO simulations are able to match the experimental ion heat flux, but underpredict electron heat flux (at most radii),more » electron temperature fluctuations, and perturbative thermal diffusivity in both L- and I-mode. Linear addition of electron heat flux from electron scale runs does not resolve this discrepancy. These results indicate that single-scale simulations do not sufficiently describe the I-mode core transport, and that multi-scale (coupled electron- and ion-scale) transport models are needed. In conclusion a preliminary investigation with multi-scale TGLF, however, was unable to resolve the discrepancy between ion-scale GYRO and experimental electron heat fluxes and perturbative diffusivity, motivating further work with multi-scale GYRO simulations and a more comprehensive study with multi-scale TGLF.« less

  8. Wide-range radiation dose monitor

    DOEpatents

    Kopp, Manfred K.

    1986-01-01

    A radiation dose-rate monitor is provided which operates in a conventional linear mode for radiation in the 0 to 0.5 R/h range and utilizes a nonlinear mode of operation for sensing radiation from 0.5 R/h to over 500 R/h. The nonlinear mode is achieved by a feedback circuit which adjusts the high voltage bias of the proportional counter, and hence its gas gain, in accordance with the amount of radiation being monitored. This allows compression of readout onto a single scale over the range of 0 to greater than 500 R/h without scale switching operations.

  9. Wide-range radiation dose monitor

    DOEpatents

    Kopp, M.K.

    1984-09-20

    A radiation dose-rate monitor is provided which operates in a conventional linear mode for radiation in the 0 to 0.5 R/h range and utilizes a nonlinear mode of operation for sensing radiation from 0.5 R/h to over 500 R/h. The nonlinear mode is achieved by a feedback circuit which adjusts the high voltage bias of the proportional counter, and hence its gas gain, in accordance with the amount of radiation being monitored. This allows compression of readout onto a single scale over the range of 0 to greater than 500 R/h without scale switching operations.

  10. Multimode nonlinear optical imaging of the dermis in ex vivo human skin based on the combination of multichannel mode and Lambda mode.

    PubMed

    Zhuo, Shuangmu; Chen, Jianxin; Luo, Tianshu; Zou, Dingsong

    2006-08-21

    A Multimode nonlinear optical imaging technique based on the combination of multichannel mode and Lambda mode is developed to investigate human dermis. Our findings show that this technique not only improves the image contrast of the structural proteins of extracellular matrix (ECM) but also provides an image-guided spectral analysis method to identify both cellular and ECM intrinsic components including collagen, elastin, NAD(P)H and flavin. By the combined use of multichannel mode and Lambda mode in tandem, the obtained in-depth two photon-excited fluorescence (TPEF) and second-harmonic generation (SHG) imaging and TPEF/SHG signals depth-dependence decay can offer a sensitive tool for obtaining quantitative tissue structural and biochemical information. These results suggest that the technique has the potential to provide more accurate information for determining tissue physiological and pathological states.

  11. The nonlinear interaction of convection modes in a box of a saturated porous medium

    NASA Astrophysics Data System (ADS)

    Florio, Brendan J.; Bassom, Andrew P.; Fowkes, Neville; Judd, Kevin; Stemler, Thomas

    2015-05-01

    A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.

  12. Fuzzy fractional order sliding mode controller for nonlinear systems

    NASA Astrophysics Data System (ADS)

    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.

  13. A nonlinear investigation of the stationary modes of instability of the three-dimensional compressible boundary layer due to a rotating disc

    NASA Technical Reports Server (NTRS)

    Seddougui, Sharon O.

    1989-01-01

    The effects of compressibility on a stationary mode of instability of the 3-D boundary layer due to a rotating disc are investigated. The aim is to determine whether this mode will be important in the finite amplitude destabilization of the boundary layer. This stationary mode is characterized by the effective velocity profile having zero shear stress at the wall. Triple-deck solutions are presented for an adiabatic wall and an isothermal wall. It is found that this stationary mode is only possible over a finite range of Mach numbers. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of these modes as functions of the local Mach number. The effects of nonlinearity are investigated allowing the finite amplitude growth of a disturbance close to the neutral location to be described.

  14. Mirror Instability: Quasi-linear Effects

    NASA Astrophysics Data System (ADS)

    Hellinger, P.; Travnicek, P. M.; Passot, T.; Sulem, P.; Kuznetsov, E. A.

    2008-12-01

    Nonlinear properties of the mirror instability are investigated by direct integration of the quasi-linear diffusion equation [Shapiro and Shevchenko, 1964] near threshold. The simulation results are compared to the results of standard hybrid simulations [Califano et al., 2008] and discussed in the context of the nonlinear dynamical model by Kuznetsov et al. [2007]. References: Califano, F., P. Hellinger, E. Kuznetsov, T. Passot, P. L. Sulem, and P. M. Travnicek (2008), Nonlinear mirror mode dynamics: Simulations and modeling, J. Geophys. Res., 113, A08219, doi:10.1029/2007JA012898. Kuznetsov, E., T. Passot and P. L. Sulem (2007), Dynamical model for nonlinear mirror modes near threshold, Phys. Rev. Lett., 98, 235003 . Shapiro, V. D., and V. I. Shevchenko (1964), Quasilinear theory of instability of a plasma with an anisotropic ion velocity distribution, Sov. JETP, 18, 1109.

  15. The response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric resonance

    NASA Astrophysics Data System (ADS)

    Nayfeh, A. H.

    1983-09-01

    An analysis is presented of the response of multidegree-of-freedom systems with quadratic non-linearities to a harmonic parametric excitation in the presence of an internal resonance of the combination type ω3 ≈ ω2 + ω1, where the ωn are the linear natural frequencies of the systems. In the case of a fundamental resonance of the third mode (i.e., Ω ≈ω 3, where Ω is the frequency of the excitation), one can identify two critical values ζ 1 and ζ 2, where ζ 2 ⩾ ζ 1, of the amplitude F of the excitation. The value F = ζ2 corresponds to the transition from stable to unstable solutions. When F < ζ1, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but the non-linearity limits the motion to a finite amplitude steady state. The amplitude of the third mode, which is directly excited, is independent of F, whereas the amplitudes of the first and second modes, which are indirectly excited through the internal resonance, are functions of F. When ζ1 ⩽ F ⩽ ζ2, the motion decays or achieves a finite amplitude steady state depending on the initial conditions according to the non-linear theory, whereas it decays to zero according to the linear theory. This is an example of subcritical instability. In the case of a fundamental resonance of either the first or second mode, the trivial response is the only possible steady state. When F ⩽ ζ2, the motion decays to zero according to both linear and non-linear theories. When F > ζ2, the motion grows exponentially with time according to the linear theory but it is aperiodic according to the non-linear theory. Experiments are being planned to check these theoretical results.

  16. Practical guidelines to select and scale earthquake records for nonlinear response history analysis of structures

    USGS Publications Warehouse

    Kalkan, Erol; Chopra, Anil K.

    2010-01-01

    Earthquake engineering practice is increasingly using nonlinear response history analysis (RHA) to demonstrate performance of structures. This rigorous method of analysis requires selection and scaling of ground motions appropriate to design hazard levels. Presented herein is a modal-pushover-based scaling (MPS) method to scale ground motions for use in nonlinear RHA of buildings and bridges. In the MPS method, the ground motions are scaled to match (to a specified tolerance) a target value of the inelastic deformation of the first-'mode' inelastic single-degree-of-freedom (SDF) system whose properties are determined by first-'mode' pushover analysis. Appropriate for first-?mode? dominated structures, this approach is extended for structures with significant contributions of higher modes by considering elastic deformation of second-'mode' SDF system in selecting a subset of the scaled ground motions. Based on results presented for two bridges, covering single- and multi-span 'ordinary standard' bridge types, and six buildings, covering low-, mid-, and tall building types in California, the accuracy and efficiency of the MPS procedure are established and its superiority over the ASCE/SEI 7-05 scaling procedure is demonstrated.

  17. Toroidal turbulence simulations with gyro-Landau fluid models in a nonlinear ballooning mode representation

    NASA Astrophysics Data System (ADS)

    Waltz, R. E.; Kerbel, G. D.

    1994-05-01

    The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyro-kinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro-Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel 3D nonlinear ballooning mode representation. The representation is a Fourier transform of the Cowley et al. [Phys. Fluids B 3, 2767 (1991)] field line following twisted eddy basis (kx',ky',z') with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky'=0, kx'≠0) ``radial modes'' in stabilizing the transport from the finite-n ITG ballooning modes.

  18. Plasmonic modes in nanowire dimers: A study based on the hydrodynamic Drude model including nonlocal and nonlinear effects

    NASA Astrophysics Data System (ADS)

    Moeferdt, Matthias; Kiel, Thomas; Sproll, Tobias; Intravaia, Francesco; Busch, Kurt

    2018-02-01

    A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a discontinuous Galerkin time-domain approach, and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, second-harmonic-generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interpret the physical mechanisms that lead to corresponding field distributions, the associated linear quasielectrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes in both the linear and nonlinear regimes. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nanoantenna systems.

  19. Spatial solitons and stability in the one-dimensional and the two-dimensional generalized nonlinear Schrödinger equation with fourth-order diffraction and parity-time-symmetric potentials

    NASA Astrophysics Data System (ADS)

    Tiofack, C. G. L.; Ndzana, F., II; Mohamadou, A.; Kofane, T. C.

    2018-03-01

    We investigate the existence and stability of solitons in parity-time (PT )-symmetric optical media characterized by a generic complex hyperbolic refractive index distribution and fourth-order diffraction (FOD). For the linear case, we demonstrate numerically that the FOD parameter can alter the PT -breaking points. For nonlinear cases, the exact analytical expressions of the localized modes are obtained both in one- and two-dimensional nonlinear Schrödinger equations with self-focusing and self-defocusing Kerr nonlinearity. The effect of FOD on the stability structure of these localized modes is discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. Examples of stable and unstable solutions are given. The transverse power flow density associated with these localized modes is also discussed. It is found that the relative strength of the FOD coefficient can utterly change the direction of the power flow, which may be used to control the energy exchange among gain or loss regions.

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

    NASA Astrophysics Data System (ADS)

    Abbott, Stephen; Germaschewski, Kai

    2014-10-01

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

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