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.

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.

Nonlinear cross-field coupling on the route to broadband turbulence

NASA Astrophysics Data System (ADS)

Brandt, Christian; Thakur, Saikat C.; Cui, Lang; Gosselin, Jordan J.; Negrete, Jose, Jr.; Holland, Chris; Tynan, George R.

2013-10-01

In the linear magnetized plasma device CSDX (Controlled Shear De-correlation eXperiment) drift interchange modes are studied coexisting on top of a weak turbulence driven azimuthally symmetric, radially sheared plasma flow. In helicon discharges (helicon antenna diameter 15 cm) with increasing magnetic field (B <= 0 . 24 T) the system can be driven to fully developed broadband turbulence. Fast imaging using a refractive telescope setup is applied to study the dynamics in the azimuthal-radial cross-section. The image data is supported by Langmuir probe measurements. In the present study we examine the development of nonlinear transfer as the fully developed turbulence emerges. Nonlinear cross-field coupling between eigenmodes at different radial positions is investigated using Fourier decomposition of azimuthal eigenmodes. The coupling strength between waves at different radial positions is inferred to radial profiles and cross-field transport between adjacent magnetic flux surfaces. Nonlinear effects like synchronization, phase slippages, phase pulling and periodic pulling are observed. The effects of mode coupling and the stability of modes is compared to the dynamics of a coupled chain of Kuramoto oscillators.

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.

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.

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.

Approximate analytical solutions of a pair of coupled anharmonic oscillators

NASA Astrophysics Data System (ADS)

Alam, Nasir; Mandal, Swapan; Öhberg, Patrik

2015-02-01

The Hamiltonian and the corresponding equations of motion involving the field operators of two quartic anharmonic oscillators indirectly coupled via a linear oscillator are constructed. The approximate analytical solutions of the coupled differential equations involving the non-commuting field operators are solved up to the second order in the anharmonic coupling. In the absence of nonlinearity these solutions are used to calculate the second order variances and hence the squeezing in pure and in mixed modes. The higher order quadrature squeezing and the amplitude squared squeezing of various field modes are also investigated where the squeezing in pure and in mixed modes are found to be suppressed. Moreover, the absence of a nonlinearity prohibits the higher order quadrature and higher ordered amplitude squeezing of the input coherent states. It is established that the mere coupling of two oscillators through a third one is unable to produce any squeezing effects of input coherent light, but the presence of a nonlinear interaction may provide squeezed states and other nonclassical phenomena.

Nonclassical properties of coherent light in a pair of coupled anharmonic oscillators

NASA Astrophysics Data System (ADS)

Alam, Nasir; Mandal, Swapan

2016-01-01

The Hamiltonian and hence the equations of motion involving the field operators of two anharmonic oscillators coupled through a linear one is framed. It is found that these equations of motion involving the non-commuting field operators are nonlinear and are coupled to each other and hence pose a great problem for getting the solutions. In order to investigate the dynamics and hence the nonclassical properties of the radiation fields, we obtain approximate analytical solutions of these coupled nonlinear differential equations involving the non-commuting field operators up to the second orders in anharmonic and coupling constants. These solutions are found useful for investigating the squeezing of pure and mixed modes, amplitude squared squeezing, principal squeezing, and the photon antibunching of the input coherent radiation field. With the suitable choice of the parameters (photon number in various field modes, anharmonic, and coupling constants, etc.), we calculate the second order variances of field quadratures of various modes and hence the squeezing, amplitude squared, and mixed mode squeezing of the input coherent light. In the absence of anharmonicities, it is found that these nonlinear nonclassical phenomena (squeezing of pure and mixed modes, amplitude squared squeezing and photon antibunching) are completely absent. The percentage of squeezing, mixed mode squeezing, amplitude squared squeezing increase with the increase of photon number and the dimensionless interaction time. The collapse and revival phenomena in squeezing, mixed mode squeezing and amplitude squared squeezing are exhibited. With the increase of the interaction time, the monotonic increasing nature of the squeezing effects reveal the presence of unwanted secular terms. It is established that the mere coupling of two oscillators through a third one does not produces the squeezing effects of input coherent light. However, the pure nonclassical phenomena of antibunching of photons in vacuum field modes are obtained through the mere coupling and hence the transfers of photons from the remaining coupled mode.

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.

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.

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.

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

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

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

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.

Non-linear Frequency Shifts, Mode Couplings, and Decay Instability of Plasma Waves

NASA Astrophysics Data System (ADS)

Affolter, Mathew; Anderegg, F.; Driscoll, C. F.; Valentini, F.

2015-11-01

We present experiments and theory for non-linear plasma wave decay to longer wavelengths, in both the oscillatory coupling and exponential decay regimes. The experiments are conducted on non-neutral plasmas in cylindrical Penning-Malmberg traps, θ-symmetric standing plasma waves have near acoustic dispersion ω (kz) ~kz - αkz2 , discretized by kz =mz (π /Lp) . Large amplitude waves exhibit non-linear frequency shifts δf / f ~A2 and Fourier harmonic content, both of which are increased as the plasma dispersion is reduced. Non-linear coupling rates are measured between large amplitude mz = 2 waves and small amplitude mz = 1 waves, which have a small detuning Δω = 2ω1 -ω2 . At small excitation amplitudes, this detuning causes the mz = 1 mode amplitude to ``bounce'' at rate Δω , with amplitude excursions ΔA1 ~ δn2 /n0 consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, where the non-linear coupling exceeds the dispersion, phase-locked exponential growth of the mz = 1 mode is observed, in qualitative agreement with simple 3-wave instability theory. However, significant variations are observed experimentally, and N-wave theory gives stunningly divergent predictions that depend sensitively on the dispersion-moderated harmonic content. Measurements on higher temperature Langmuir waves and the unusual ``EAW'' (KEEN) waves are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates. Department of Energy Grants DE-SC0002451and DE-SC0008693.

Saturation of the lower-hybrid-drift instability by mode coupling

NASA Technical Reports Server (NTRS)

Drake, J. F.; Guzdar, P. N.; Huba, J. D.

1983-01-01

A nonlinear mode-coupling theory of the lower-hybrid-drift instability is presented. It is found that the instability saturates by transferring energy from the growing, long wavelength modes to the damped, short wavelength modes. The saturation energy, mean square of the potential fluctuations, and diffusion coefficient are calculated self-consistently.

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.

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.

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

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 [

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.

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.

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.

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.

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.

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

Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

NASA Astrophysics Data System (ADS)

Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.

2018-05-01

Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.

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.

Rogue-wave pattern transition induced by relative frequency.

PubMed

Zhao, Li-Chen; Xin, Guo-Guo; Yang, Zhan-Ying

2014-08-01

We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.

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'

Direct observation of coherent energy transfer in nonlinear micromechanical oscillators.

PubMed

Chen, Changyao; Zanette, Damián H; Czaplewski, David A; Shaw, Steven; López, Daniel

2017-05-26

Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. The fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.

Spinor Field Nonlinearity and Space-Time Geometry

NASA Astrophysics Data System (ADS)

Saha, Bijan

2018-03-01

Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time, though the isotropy of space-time can be attained for a large proportionality constant. As far as evolution is concerned, depending on the sign of coupling constant the model allows both accelerated and oscillatory mode of expansion. A negative coupling constant leads to an oscillatory mode of expansion, whereas a positive coupling constant generates expanding Universe with late time acceleration. Both deceleration parameter and EoS parameter in this case vary with time and are in agreement with modern concept of space-time evolution. In case of a Bianchi type-I space-time the non-diagonal components lead to three different possibilities. In case of a full BI space-time we find that the spinor field nonlinearity and the massive term vanish, hence the spinor field Lagrangian becomes massless and linear. In two other cases the space-time evolves into either LRSBI or FRW Universe. If we consider a locally rotationally symmetric BI( LRSBI) model, neither the mass term nor the spinor field nonlinearity vanishes. In this case depending on the sign of coupling constant we have either late time accelerated mode of expansion or oscillatory mode of evolution. In this case for an expanding Universe we have asymptotical isotropization. Finally, in case of a FRW model neither the mass term nor the spinor field nonlinearity vanishes. Like in LRSBI case we have either late time acceleration or cyclic mode of evolution. These findings allow us to conclude that the spinor field is very sensitive to the gravitational one.

Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions

NASA Astrophysics Data System (ADS)

BoŻek, Piotr

2018-03-01

The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.

Raman-Suppressing Coupling for Optical Parametric Oscillator

NASA Technical Reports Server (NTRS)

Savchenkov, Anatoliy; Maleki, Lute; Matsko, Andrey; Rubiola, Enrico

2007-01-01

A Raman-scattering-suppressing input/ output coupling scheme has been devised for a whispering-gallery-mode optical resonator that is used as a four-wave-mixing device to effect an all-optical parametric oscillator. Raman scattering is undesired in such a device because (1) it is a nonlinear process that competes with the desired nonlinear four-wave conversion process involved in optical parametric oscillation and (2) as such, it reduces the power of the desired oscillation and contributes to output noise. The essence of the present input/output coupling scheme is to reduce output loading of the desired resonator modes while increasing output loading of the undesired ones.

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.

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.

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.

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

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

Chaotic neoclassical separatrix dissipation in parametric drift-wave decay.

PubMed

Kabantsev, A A; Tsidulko, Yu A; Driscoll, C F

2014-02-07

Experiments and theory characterize a parametric decay instability between plasma drift waves when the nonlinear coupling is modified by an electrostatic barrier. Novel mode coupling terms representing enhanced dissipation and mode phase shifts are caused by chaotic separatrix crossings on the wave-ruffled separatrix. Experimental determination of these coupling terms is in broad agreement with new chaotic neoclassical transport analyses.

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

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.

Driven superconducting quantum circuits

NASA Astrophysics Data System (ADS)

Nakamura, Yasunobu

2014-03-01

Driven nonlinear quantum systems show rich phenomena in various fields of physics. Among them, superconducting quantum circuits have very attractive features such as well-controlled quantum states with design flexibility, strong nonlinearity of Josephson junctions, strong coupling to electromagnetic driving fields, little internal dissipation, and tailored coupling to the electromagnetic environment. We have investigated properties and functionalities of driven superconducting quantum circuits. A transmon qubit coupled to a transmission line shows nearly perfect spatial mode matching between the incident and scattered microwave field in the 1D mode. Dressed states under a driving field are studied there and also in a semi-infinite 1D mode terminated by a resonator containing a flux qubit. An effective Λ-type three-level system is realized under an appropriate driving condition. It allows ``impedance-matched'' perfect absorption of incident probe photons and down conversion into another frequency mode. Finally, the weak signal from the qubit is read out using a Josephson parametric amplifier/oscillator which is another nonlinear circuit driven by a strong pump field. This work was partly supported by the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST), Project for Developing Innovation Systems of MEXT, MEXT KAKENHI ``Quantum Cybernetics,'' and the NICT Commissioned Research.

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.

Simulating the effect of non-linear mode coupling in cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Kiessling, A.; Taylor, A. N.; Heavens, A. F.

2011-09-01

Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment and to optimize the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimization it is usually assumed that the power-spectrum covariance matrix is diagonal in Fourier space. However, in the low-redshift Universe, non-linear mode coupling will tend to correlate small-scale power, moving information from lower to higher order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naïve Gaussian Fisher matrix forecasts with a maximum likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2D and tomographic shear analysis of a Euclid-like survey. In both cases, we find that the 68 per cent confidence area of the Ωm-σ8 plane increases by a factor of 5. However, the marginal errors increase by just 20-40 per cent. We propose a new method to model the effects of non-linear shear-power mode coupling in the Fisher matrix by approximating the shear-power distribution as a multivariate Gaussian with a covariance matrix derived from the mock weak lensing survey. We find that this approximation can reproduce the 68 per cent confidence regions of the full maximum likelihood analysis in the Ωm-σ8 plane to high accuracy for both 2D and tomographic weak lensing surveys. Finally, we perform a multiparameter analysis of Ωm, σ8, h, ns, w0 and wa to compare the Gaussian and non-linear mode-coupled Fisher matrix contours. The 6D volume of the 1σ error contours for the non-linear Fisher analysis is a factor of 3 larger than for the Gaussian case, and the shape of the 68 per cent confidence volume is modified. We propose that future Fisher matrix estimates of cosmological parameter accuracies should include mode-coupling effects.

Regression of non-linear coupling of noise in LIGO detectors

NASA Astrophysics Data System (ADS)

Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.

2018-03-01

In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.

Enhancement of Optical Nonlinearities in Composite Media and Structures via Local Fields and Electromagnetic Coupling Effects

NASA Technical Reports Server (NTRS)

Smith, David D.

2002-01-01

This talk will review the linear and nonlinear optical properties of metal nanoparticles and dielectric microparticles, with an emphasis on local field effects, and whispering gallery modes (WGMs), as well as the conjunction of these two effects for enhanced Raman. In particular, enhanced optical properties that result from electromagnetic coupling effects will be discussed in the context of Mie scattering from concentric spheres and bispheres. Predictions of mode splitting and photonic bandgaps in micro-spheres will be presented and will be shown to be analogous to effects that occur in coupled resonator optical waveguides (CROW). Slow and fast light in SCISSOR / CROW configurations will also be discussed.

Perturbation solutions of combustion instability problems

NASA Technical Reports Server (NTRS)

Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

1979-01-01

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Nonlinear quantum Langevin equations for bosonic modes in solid-state systems

NASA Astrophysics Data System (ADS)

Manninen, Juuso; Agasti, Souvik; Massel, Francesco

2017-12-01

Based on the experimental evidence that impurities contribute to the dissipation properties of solid-state open quantum systems, we provide here a description in terms of nonlinear quantum Langevin equations of the role played by two-level systems in the dynamics of a bosonic degree of freedom. Our starting point is represented by the description of the system-environment coupling in terms of coupling to two separate reservoirs, modeling the interaction with external bosonic modes and two-level systems, respectively. Furthermore, we show how this model represents a specific example of a class of open quantum systems that can be described by nonlinear quantum Langevin equations. Our analysis offers a potential explanation of the parametric effects recently observed in circuit-QED cavity optomechanics experiments.

Direct observation of coherent energy transfer in nonlinear micromechanical oscillators

DOE PAGES

Chen, Changyao; Zanette, Damian H.; Czaplewski, David A.; ...

2017-05-26

Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. Themore » fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.« less

Direct observation of coherent energy transfer in nonlinear micromechanical oscillators

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

Chen, Changyao; Zanette, Damian H.; Czaplewski, David A.

Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. In an oscillatory system, it leads to the decay of the oscillation amplitude. In situations where stable oscillations are required, the energy dissipated by the vibrations is usually compensated by replenishment from external energy sources. Consequently, if the external energy supply is removed, the amplitude of oscillations start to decay immediately, since there is no means to restitute the energy dissipated. Here, we demonstrate a novel dissipation engineering strategy that can support stable oscillations without supplying external energy to compensate losses. Themore » fundamental intrinsic mechanism of resonant mode coupling is used to redistribute and store mechanical energy among vibrational modes and coherently transfer it back to the principal mode when the external excitation is off. To experimentally demonstrate this phenomenon, we exploit the nonlinear dynamic response of microelectromechanical oscillators to couple two different vibrational modes through an internal resonance.« less

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

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

Exact docking flight controller for autonomous aerial refueling with back-stepping based high order sliding mode

NASA Astrophysics Data System (ADS)

Su, Zikang; Wang, Honglun; Li, Na; Yu, Yue; Wu, Jianfa

2018-02-01

Autonomous aerial refueling (AAR) exact docking control has always been an intractable problem due to the strong nonlinearity, the tight coupling of the 6 DOF aircraft model and the complex disturbances of the multiple environment flows. In this paper, the strongly coupled nonlinear 6 DOF model of the receiver aircraft which considers the multiple flow disturbances is established in the affine nonlinear form to facilitate the nonlinear controller design. The items reflecting the influence of the unknown flow disturbances in the receiver dynamics are taken as the components of the "lumped disturbances" together with the items which have no linear correlation with the virtual control variables. These unmeasurable lumped disturbances are estimated and compensated by a specially designed high order sliding mode observer (HOSMO) with excellent estimation property. With the compensation of the estimated lumped disturbances, a back-stepping high order sliding mode based exact docking flight controller is proposed for AAR in the presence of multiple flow disturbances. Extensive simulation results demonstrate the feasibility and superiority of the proposed docking controller.

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

Marek, Petr; Filip, Radim; Ogawa, Hisashi; Sakaguchi, Atsushi; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

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.

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

A Sliding Mode Controller Using Nonlinear Sliding Surface Improved With Fuzzy Logic: Application to the Coupled Tanks System

NASA Astrophysics Data System (ADS)

Boubakir, A.; Boudjema, F.; Boubakir, C.

2008-06-01

This paper proposes an approach of hybrid control that is based on the concept of combining fuzzy logic and the methodology of sliding mode control (SMC). In the present works, a first-order nonlinear sliding surface is presented, on which the developed control law is based. Mathematical proof for the stability and convergence of the system is presented. In order to reduce the chattering in sliding mode control, a fixed boundary layer around the switch surface is used. Within the boundary layer, since the fuzzy logic control is applied, the chattering phenomenon, which is inherent in a sliding mode control, is avoided by smoothing the switch signal. Outside the boundary, the sliding mode control is applied to driving the system states into the boundary layer. Experimental studies carried out on a coupled Tanks system indicate that the proposed fuzzy sliding mode control (FSMC) is a good candidate for control applications.

Aeroelastic oscillations of a cantilever with structural nonlinearities: theory and numerical simulation.

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

Robinson, Brandon; Rocha da Costa, Leandro Jose; Poirel, Dominique

Our study details the derivation of the nonlinear equations of motion for the axial, biaxial bending and torsional vibrations of an aeroelastic cantilever undergoing rigid body (pitch) rotation at the base. The primary attenstion is focussed on the geometric nonlinearities of the system, whereby the aeroelastic load is modeled by the theory of linear quasisteady aerodynamics. This modelling effort is intended to mimic the wind-tunnel experimental setup at the Royal Military College of Canada. While the derivation closely follows the work of Hodges and Dowell [1] for rotor blades, this aeroelastic system contains new inertial terms which stem from themore » fundamentally different kinematics than those exhibited by helicopter or wind turbine blades. Using the Hamilton’s principle, a set of coupled nonlinear partial differential equations (PDEs) and an ordinary differential equation (ODE) are derived which describes the coupled axial-bending-bending-torsion-pitch motion of the aeroelastic cantilever with the pitch rotation. The finite dimensional approximation of the coupled system of PDEs are obtained using the Galerkin projection, leading to a coupled system of ODEs. Subsequently, these nonlinear ODEs are solved numerically using the built-in MATLAB implicit ODE solver and the associated numerical results are compared with those obtained using Houbolt’s method. It is demonstrated that the system undergoes coalescence flutter, leading to a limit cycle oscillation (LCO) due to coupling between the rigid body pitching mode and teh flexible mode arising from the flapwise bending motion.« less

Diffraction-induced instability of coupled dark solitary waves.

PubMed

Assanto, Gaetano; MacNeil, J Michael L; Smyth, Noel F

2015-04-15

We report on a novel instability arising from the propagation of coupled dark solitary beams governed by coupled defocusing nonlinear Schrödinger equations. Considering dark notches on backgrounds with different wavelengths, hence different diffraction coefficients, we find that the vector dark soliton solution is unstable to radiation modes. Using perturbation theory and numerical integration, we demonstrate that the component undergoing stronger diffraction radiates away, leaving a single dark soliton in the other mode/wavelength.

Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators

DOE PAGES

Zhang, Steven S. -L.; Iacocca, Ezio; Heinonen, Olle

2017-07-27

Recent experiments on spin-torque oscillators have revealed interactions between multiple magneto-dynamic modes, including mode coexistence, mode hopping, and temperature-driven crossover between modes. The initial multimode theory indicates that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magneto-dynamic modes in a nanocontact spin-torque oscillator. Here, expressions for both linear and nonlinear coupling terms are obtained, whichmore » allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space and demonstrate in the phase portraits how the manifolds of periodic orbits and fixed points vary with an external magnetic field as well as with the temperature.« less

Tunable Mode Coupling in Nanocontact Spin-Torque Oscillators

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

Zhang, Steven S. -L.; Iacocca, Ezio; Heinonen, Olle

Recent experiments on spin-torque oscillators have revealed interactions between multiple magneto-dynamic modes, including mode coexistence, mode hopping, and temperature-driven crossover between modes. The initial multimode theory indicates that a linear coupling between several dominant modes, arising from the interaction of the subdynamic system with a magnon bath, plays an essential role in the generation of various multimode behaviors, such as mode hopping and mode coexistence. In this work, we derive a set of rate equations to describe the dynamics of coupled magneto-dynamic modes in a nanocontact spin-torque oscillator. Here, expressions for both linear and nonlinear coupling terms are obtained, whichmore » allow us to analyze the dependence of the coupled dynamic behaviors of modes on external experimental conditions as well as intrinsic magnetic properties. For a minimal two-mode system, we further map the energy and phase difference of the two modes onto a two-dimensional phase space and demonstrate in the phase portraits how the manifolds of periodic orbits and fixed points vary with an external magnetic field as well as with the temperature.« less

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.

Quasinormal modes of scale dependent black holes in (1 +2 )-dimensional Einstein-power-Maxwell theory

NASA Astrophysics Data System (ADS)

Rincón, Ángel; Panotopoulos, Grigoris

2018-01-01

We study for the first time the stability against scalar perturbations, and we compute the spectrum of quasinormal modes of three-dimensional charged black holes in Einstein-power-Maxwell nonlinear electrodynamics assuming running couplings. Adopting the sixth order Wentzel-Kramers-Brillouin (WKB) approximation we investigate how the running of the couplings change the spectrum of the classical theory. Our results show that all modes corresponding to nonvanishing angular momentum are unstable both in the classical theory and with the running of the couplings, while the fundamental mode can be stable or unstable depending on the running parameter and the electric charge.

Efficient excitation of nonlinear phonons via chirped pulses: Induced structural phase transitions

NASA Astrophysics Data System (ADS)

Itin, A. P.; Katsnelson, M. I.

2018-05-01

Nonlinear phononics play important role in strong laser-solid interactions. We discuss a dynamical protocol for efficient phonon excitation, considering recent inspiring proposals: inducing ferroelectricity in paraelectric perovskites, and inducing structural deformations in cuprates [Subedi et al., Phys. Rev. B 89, 220301(R) (2014), 10.1103/PhysRevB.89.220301; Phys. Rev. B 95, 134113 (2017), 10.1103/PhysRevB.95.134113]. High-frequency phonon modes are driven by midinfrared pulses, and coupled to lower-frequency modes those indirect excitations cause structural deformations. We study in more detail the case of KTaO3 without strain, where it was not possible to excite the needed low-frequency phonon mode by resonant driving of the higher frequency one. Behavior of the system is explained using a reduced model of coupled driven nonlinear oscillators. We find a dynamical mechanism which prevents effective excitation at resonance driving. To induce ferroelectricity, we employ driving with sweeping frequency, realizing so-called capture into resonance. The method can be applied to many other related systems.

Dynamics of coupled mode solitons in bursting neural networks

NASA Astrophysics Data System (ADS)

Nfor, N. Oma; Ghomsi, P. Guemkam; Moukam Kakmeni, F. M.

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Dynamics of coupled mode solitons in bursting neural networks.

PubMed

Nfor, N Oma; Ghomsi, P Guemkam; Moukam Kakmeni, F M

2018-02-01

Using an electrically coupled chain of Hindmarsh-Rose neural models, we analytically derived the nonlinearly coupled complex Ginzburg-Landau equations. This is realized by superimposing the lower and upper cutoff modes of wave propagation and by employing the multiple scale expansions in the semidiscrete approximation. We explore the modified Hirota method to analytically obtain the bright-bright pulse soliton solutions of our nonlinearly coupled equations. With these bright solitons as initial conditions of our numerical scheme, and knowing that electrical signals are the basis of information transfer in the nervous system, it is found that prior to collisions at the boundaries of the network, neural information is purely conveyed by bisolitons at lower cutoff mode. After collision, the bisolitons are completely annihilated and neural information is now relayed by the upper cutoff mode via the propagation of plane waves. It is also shown that the linear gain of the system is inextricably linked to the complex physiological mechanisms of ion mobility, since the speeds and spatial profiles of the coupled nerve impulses vary with the gain. A linear stability analysis performed on the coupled system mainly confirms the instability of plane waves in the neural network, with a glaring example of the transition of weak plane waves into a dark soliton and then static kinks. Numerical simulations have confirmed the annihilation phenomenon subsequent to collision in neural systems. They equally showed that the symmetry breaking of the pulse solution of the system leaves in the network static internal modes, sometime referred to as Goldstone modes.

Yield stress in amorphous solids: A mode-coupling-theory analysis

NASA Astrophysics Data System (ADS)

Ikeda, Atsushi; Berthier, Ludovic

2013-11-01

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly nonlinear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyze several classes of disordered solids, using simple models of hard-sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard-sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the caging dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and nonlinear rheology of amorphous materials.

Acoustic mode coupling induced by shallow water nonlinear internal waves: sensitivity to environmental conditions and space-time scales of internal waves.

PubMed

Colosi, John A

2008-09-01

While many results have been intuited from numerical simulation studies, the precise connections between shallow-water acoustic variability and the space-time scales of nonlinear internal waves (NLIWs) as well as the background environmental conditions have not been clearly established analytically. Two-dimensional coupled mode propagation through NLIWs is examined using a perturbation series solution in which each order n is associated with nth-order multiple scattering. Importantly, the perturbation solution gives resonance conditions that pick out specific NLIW scales that cause coupling, and seabed attenuation is demonstrated to broaden these resonances, fundamentally changing the coupling behavior at low frequency. Sound-speed inhomogeneities caused by internal solitary waves (ISWs) are primarily considered and the dependence of mode coupling on ISW amplitude, range width, depth structure, location relative to the source, and packet characteristics are delineated as a function of acoustic frequency. In addition, it is seen that significant energy transfer to modes with initially low or zero energy involves at least a second order scattering process. Under moderate scattering conditions, comparisons of first order, single scattering theoretical predictions to direct numerical simulation demonstrate the accuracy of the approach for acoustic frequencies upto 400 Hz and for single as well as multiple ISW wave packets.

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.

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.

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

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

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.

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1977-01-01

It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.

Directional nonlinear guided wave mixing: Case study of counter-propagating shear horizontal waves

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2018-04-01

While much nonlinear ultrasonics research has been conducted on higher harmonic generation, wave mixing provides the potential for sensitive measurements of incipient damage unencumbered by instrumentation nonlinearity. Studies of nonlinear ultrasonic wave mixing, both collinear and noncollinear, for bulk waves have shown the robust capability of wave mixing for early damage detection. One merit of bulk wave mixing lies in their non-dispersive nature, but guided waves enable inspection of otherwise inaccessible material and a variety of mixing options. Co-directional guided wave mixing was studied previously, but arbitrary direction guided wave mixing has not been addressed until recently. Wave vector analysis is applied to study variable mixing angles to find wave mode triplets (two primary waves and a secondary wave) resulting in the phase matching condition. As a case study, counter-propagating Shear Horizontal (SH) guided wave mixing is analyzed. SH wave interactions generate a secondary Lamb wave mode that is readily receivable. Reception of the secondary Lamb wave mode is compared for an angle beam transducer, an air coupled transducer, and a laser Doppler vibrometer (LDV). Results from the angle beam and air coupled transducers are quite consistent, while the LDV measurement is plagued by variability issues.

Few-Photon Nonlinearity with an Atomic Ensemble in an Optical Cavity

NASA Astrophysics Data System (ADS)

Tanji, Haruka

2011-12-01

This thesis investigates the effect of the cavity vacuum field on the dispersive properties of an atomic ensemble in a strongly coupled high-finesse cavity. In particular, we demonstrate vacuum-induced transparency (VIT). The light absorption by the ensemble is suppressed by up to 40% in the presence of a cavity vacuum field. The sharp transparency peak is accompanied by the reduction in the group velocity of a light pulse, measured to be as low as 1800 m/s. This observation is a large step towards the realization of photon number-state filters, recently proposed by Nikoghosyan et al. Furthermore, we demonstrate few-photon optical nonlinearity, where the transparency is increased from 40% to 80% with ˜12 photons in the cavity mode. The result may be viewed as all-optical switching, where the transmission of photons in one mode may be controlled by 12 photons in another. These studies point to the possibility of nonlinear interaction between photons in different free-space modes, a scheme that circumvents cavity-coupling losses that plague cavity-based quantum information processing. Potential applications include advanced quantum devices such as photonic quantum gates, photon-number resolving detectors, and single-photon transistors. In the efforts leading up to these results, we investigate the collective enhancement of atomic coupling to a single mode of a low-finesse cavity. With the strong collective coupling, we obtain exquisite control of quantum states in the atom-photon coupled system. In this system, we demonstrate a heralded single-photon source with 84% conditional efficiency, a quantum bus for deterministic entanglement of two remote ensembles, and heralded polarization-state quantum memory with fidelity above 90%.

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

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

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.

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.

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.

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.

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.

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.

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.

Coupling Ideality of Integrated Planar High-Q Microresonators

NASA Astrophysics Data System (ADS)

Pfeiffer, Martin H. P.; Liu, Junqiu; Geiselmann, Michael; Kippenberg, Tobias J.

2017-02-01

Chip-scale optical microresonators with integrated planar optical waveguides are useful building blocks for linear, nonlinear, and quantum-optical photonic devices alike. Loss reduction through improving fabrication processes results in several integrated microresonator platforms attaining quality (Q ) factors of several millions. Beyond the improvement of the quality factor, the ability to operate the microresonator with high coupling ideality in the overcoupled regime is of central importance. In this regime, the dominant source of loss constitutes the coupling to a single desired output channel, which is particularly important not only for quantum-optical applications such as the generation of squeezed light and correlated photon pairs but also for linear and nonlinear photonics. However, to date, the coupling ideality in integrated photonic microresonators is not well understood, in particular, design-dependent losses and their impact on the regime of high ideality. Here we investigate design-dependent parasitic losses described by the coupling ideality of the commonly employed microresonator design consisting of a microring-resonator waveguide side coupled to a straight bus waveguide, a system which is not properly described by the conventional input-output theory of open systems due to the presence of higher-order modes. By systematic characterization of multimode high-Q silicon nitride microresonator devices, we show that this design can suffer from low coupling ideality. By performing 3D simulations, we identify the coupling to higher-order bus waveguide modes as the dominant origin of parasitic losses which lead to the low coupling ideality. Using suitably designed bus waveguides, parasitic losses are mitigated with a nearly unity ideality and strong overcoupling (i.e., a ratio of external coupling to internal resonator loss rate >9 ) are demonstrated. Moreover, we find that different resonator modes can exchange power through the coupler, which, therefore, constitutes a mechanism that induces modal coupling, a phenomenon known to distort resonator dispersion properties. Our results demonstrate the potential for significant performance improvements of integrated planar microresonators for applications in quantum optics and nonlinear photonics achievable by optimized coupler designs.

Vibronic coupling simulations for linear and nonlinear optical processes: Theory

NASA Astrophysics Data System (ADS)

Silverstein, Daniel W.; Jensen, Lasse

2012-02-01

A comprehensive vibronic coupling model based on the time-dependent wavepacket approach is derived to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering. This approach is particularly well suited for combination with first-principles calculations. Expressions for the Franck-Condon terms, and non-Condon effects via the Herzberg-Teller coupling approach in the independent-mode displaced harmonic oscillator model are presented. The significance of each contribution to the different spectral types is discussed briefly.

Coherent two-dimensional terahertz-terahertz-Raman spectroscopy.

PubMed

Finneran, Ian A; Welsch, Ralph; Allodi, Marco A; Miller, Thomas F; Blake, Geoffrey A

2016-06-21

We present 2D terahertz-terahertz-Raman (2D TTR) spectroscopy, the first technique, to our knowledge, to interrogate a liquid with multiple pulses of terahertz (THz) light. This hybrid approach isolates nonlinear signatures in isotropic media, and is sensitive to the coupling and anharmonicity of thermally activated THz modes that play a central role in liquid-phase chemistry. Specifically, by varying the timing between two intense THz pulses, we control the orientational alignment of molecules in a liquid, and nonlinearly excite vibrational coherences. A comparison of experimental and simulated 2D TTR spectra of bromoform (CHBr3), carbon tetrachloride (CCl4), and dibromodichloromethane (CBr2Cl2) shows previously unobserved off-diagonal anharmonic coupling between thermally populated vibrational modes.

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.

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.

A simulation of atomic force microscope microcantilever in the tapping mode utilizing couple stress theory.

PubMed

Abbasi, Mohammad

2018-04-01

The nonlinear vibration behavior of a Tapping mode atomic force microscopy (TM-AFM) microcantilever under acoustic excitation force has been modeled and investigated. In dynamic AFM, the tip-surface interactions are strongly nonlinear, rapidly changing and hysteretic. First, the governing differential equation of motion and boundary conditions for dynamic analysis are obtained using the modified couple stress theory. Afterwards, closed-form expressions for nonlinear frequency and effective nonlinear damping ratio are derived utilizing perturbation method. The effect of tip connection position on the vibration behavior of the microcantilever are also analyzed. The results show that nonlinear frequency is size dependent. According to the results, an increase in the equilibrium separation between the tip and the sample surface reduces the overall effect of van der Waals forces on the nonlinear frequency, but its effect on the effective nonlinear damping ratio is negligible. The results also indicate that both the change in the distance between tip and cantilever free end and the reduction of tip radius have significant effects on the accuracy and sensitivity of the TM-AFM in the measurement of surface forces. The hysteretic behavior has been observed in the near resonance frequency response due to softening and hardening of the forced vibration response. Copyright © 2018 Elsevier Ltd. All rights reserved.

Theory and modeling of atmospheric turbulence, part 1

NASA Technical Reports Server (NTRS)

1984-01-01

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

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.

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.

Mode competition and hopping in optomechanical nano-oscillators

NASA Astrophysics Data System (ADS)

Zhang, Xingwang; Lin, Tong; Tian, Feng; Du, Han; Zou, Yongchao; Chau, Fook Siong; Zhou, Guangya

2018-04-01

We investigate the inter-mode nonlinear interaction in the multi-mode optomechanical nano-oscillator which consists of coupled silicon nanocantilevers, where the integrated photonic crystal nanocavities provide the coupling between the optical and mechanical modes. Due to the self-saturation and cross-saturation of the mechanical gain, the inter-mode competition is observed, which leads to the bistable operation of the optomechanical nano-oscillator: only one of the mechanical modes can oscillate at any one time, and the oscillation of one mode extremely suppresses that of the other with a side mode suppression ratio (SMSR) up to 40 dB. In the meantime, mode hopping, i.e., the optomechanical oscillation switches from one mode to the other, is also observed and found to be able to be provoked by excitation laser fluctuations.

Gyrokinetic simulation of ITG modes in a three-mode coupling model

NASA Astrophysics Data System (ADS)

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

2004-11-01

A three-mode coupling model of ITG modes with adiabatic electrons is studied both analytically and numerically in 2-dimensional slab geometry using the gyrokinetic formalism. It can be shown analytically that the (quasilinear) saturation amplitude of the waves in the system should be enhanced by the inclusion of the parallel velocity nonlinearity in the governing gyrokinetic equation. The effect of this (frequently neglected) nonlinearity on the steady-state transport properties of the plasma is studied numerically using standard gyrokinetic particle simulation techniques. The balance [1] between various steady-state transport properties of the model (particle and heat flux, entropy production, and collisional dissipation) is examined. Effects resulting from the inclusion of nonadiabatic electrons in the model are also considered numerically, making use of the gyrokinetic split-weight scheme [2] in the simulations. [1] W. W. Lee and W. M. Tang, Phys. Fluids 31, 612 (1988). [2] I. Manuilskiy and W. W. Lee, Phys. Plasmas 7, 1381 (2000).

Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments.

PubMed

Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M

2010-12-01

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

Phase-locking of magnetic islands diagnosed by ECE-imaging

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

Tobias, Benjamin; Grierson, Brian A.; Muscatello, Christopher M.

2014-08-13

Millimeter-wave imaging diagnostics identify phase-locking and the satisfaction of 3-wave coupling selection criteria amongst multiple magnetic island chains by providing a localized, internal measurement of the 2D power spectral density, S(ω, k pol). In high-confinement tokamak discharges, these interactions impact both plasma rotation and tearing stability. Here, nonlinear coupling amongst neoclassical tearing modes (NTMs) of different n-number, with islands not satisfying the poloidal mode number selection criterion {m, m ', m - m ' }, contributes to a reduction in core rotation and flow shear in the vicinity of the modes.

Quantum entanglement and position-momentum entropic squeezing of a moving Lambda-type three-level atom interacting with a single-mode quantized field with intensity-dependent coupling

NASA Astrophysics Data System (ADS)

Faghihi, M. J.; Tavassoly, M. K.

2013-07-01

In this paper, we study the interaction between a moving Λ-type three-level atom and a single-mode cavity field in the presence of intensity-dependent atom-field coupling. After obtaining the state vector of the entire system explicitly, we study the nonclassical features of the system such as quantum entanglement, position-momentum entropic squeezing, quadrature squeezing and sub-Poissonian statistics. According to the obtained numerical results we illustrate that the squeezed period, the duration of entropy squeezing and the maximal squeezing can be controlled by choosing the appropriate nonlinearity function together with entering the atomic motion effect by the suitable selection of the field-mode structure parameter. Also, the atomic motion, as well as the nonlinearity function, leads to the oscillatory behaviour of the degree of entanglement between the atom and field.

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.

Sensing nitrous oxide with QCL-coupled silicon-on-sapphire ring resonators.

PubMed

Smith, Clinton J; Shankar, Raji; Laderer, Matthew; Frish, Michael B; Loncar, Marko; Allen, Mark G

2015-03-09

We report the initial evaluation of a mid-infrared QCL-coupled silicon-on-sapphire ring resonator gas sensor. The device probes the N(2)O 2241.79 cm(-1) optical transition (R23 line) in the ν(3) vibrational band. N(2)O concentration is deduced using a non-linear least squares fit, based on coupled-mode theory, of the change in ring resonator Q due to gas absorption losses in the evanescent portion of the waveguide optical mode. These early experiments demonstrated response to 5000 ppmv N(2)O.

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.

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.

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

Dependence of neoclassical toroidal viscosity on the poloidal spectrum of applied nonaxisymmetric fields

DOE PAGES

Logan, Nikolas C.; Park, Jong -Kyu; Paz-Soldan, Carloa; ...

2016-02-05

This paper presents a single mode model that accurately predicts the coupling of applied nonaxisymmetric fields to the plasma response that induces neoclassical toroidal viscosity (NTV) torque in DIII-D H-mode plasmas. The torque is measured and modeled to have a sinusoidal dependence on the relative phase of multiple nonaxisymmetric field sources, including a minimum in which large amounts of nonaxisymmetric drive is decoupled from the NTV torque. This corresponds to the coupling and decoupling of the applied field to a NTV-driving mode spectrum. Modeling using the perturbed equilibrium nonambipolar transport (PENT) code confirms an effective single mode coupling between themore » applied field and the resultant torque, despite its inherent nonlinearity. Lastly, the coupling to the NTV mode is shown to have a similar dependence on the relative phasing as that of the IPEC dominant mode, providing a physical basis for the efficacy of this linear metric in predicting error field correction optima in NTV dominated regimes.« less

Dependence of neoclassical toroidal viscosity on the poloidal spectrum of applied nonaxisymmetric fields

NASA Astrophysics Data System (ADS)

Logan, N. C.; Park, J.-K.; Paz-Soldan, C.; Lanctot, M. J.; Smith, S. P.; Burrell, K. H.

2016-03-01

This paper presents a single mode model that accurately predicts the coupling of applied nonaxisymmetric fields to the plasma response that induces neoclassical toroidal viscosity (NTV) torque in DIII-D H-mode plasmas. The torque is measured and modeled to have a sinusoidal dependence on the relative phase of multiple nonaxisymmetric field sources, including a minimum in which large amounts of nonaxisymmetric drive is decoupled from the NTV torque. This corresponds to the coupling and decoupling of the applied field to a NTV-driving mode spectrum. Modeling using the perturbed equilibrium nonambipolar transport (PENT) code confirms an effective single mode coupling between the applied field and the resultant torque, despite its inherent nonlinearity. The coupling to the NTV mode is shown to have a similar dependence on the relative phasing as that of the IPEC dominant mode, providing a physical basis for the efficacy of this linear metric in predicting error field correction optima in NTV dominated regimes.

Formalism of photons in a nonlinear microring resonator

NASA Astrophysics Data System (ADS)

Tran, Quang Loc; Yupapin, Preecha

2018-03-01

In this paper, using short Gaussian pulses input from a monochromatic light source, we simulate the photon distribution and analyse the output gate's signals of PANDA nonlinear ring resonator. The present analysis is restricted to directional couplers characterized by two parameters, the power coupling coefficient κ and power coupling loss γ. Add/drop filters are also employed and investigated for the suitable to implement in the practical communication system. The experiment was conducted by using the combination of Lumerical FDTD Solutions and Lumerical MODE Solutions software.

The coupled nonlinear dynamics of a lift system

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

Crespo, Rafael Sánchez, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Kaczmarczyk, Stefan, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk; Picton, Phil, E-mail: rafael.sanchezcrespo@northampton.ac.uk, E-mail: stefan.kaczmarczyk@northampton.ac.uk, E-mail: phil.picton@northampton.ac.uk, E-mail: huijuan.su@northampton.ac.uk

2014-12-10

Coupled lateral and longitudinal vibrations of suspension and compensating ropes in a high-rise lift system are often induced by the building motions due to wind or seismic excitations. When the frequencies of the building become near the natural frequencies of the ropes, large resonance motions of the system may result. This leads to adverse coupled dynamic phenomena involving nonplanar motions of the ropes, impact loads between the ropes and the shaft walls, as well as vertical vibrations of the car, counterweight and compensating sheave. Such an adverse dynamic behaviour of the system endangers the safety of the installation. This papermore » presents two mathematical models describing the nonlinear responses of a suspension/ compensating rope system coupled with the elevator car / compensating sheave motions. The models accommodate the nonlinear couplings between the lateral and longitudinal modes, with and without longitudinal inertia of the ropes. The partial differential nonlinear equations of motion are derived using Hamilton Principle. Then, the Galerkin method is used to discretise the equations of motion and to develop a nonlinear ordinary differential equation model. Approximate numerical solutions are determined and the behaviour of the system is analysed.« less

Supermodes in Coupled Multi-Core Waveguide Structures

DTIC Science & Technology

2016-04-01

and therefore can be treated as linear polarization (LP) modes. In essence, the LP modes are scalar approximations of the vector mode fields and contain...field, including the discovery of optical discrete solitons , Bragg and vector solitons in fibers, nonlinear surface waves, and the discovery of self...increased for an isolated core, it can guide high-order modes. For optical fibers with low re- fractive index contrast, the vector modes are weakly guided

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.

Spurious cross-frequency amplitude-amplitude coupling in nonstationary, nonlinear signals

NASA Astrophysics Data System (ADS)

Yeh, Chien-Hung; Lo, Men-Tzung; Hu, Kun

2016-07-01

Recent studies of brain activities show that cross-frequency coupling (CFC) plays an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies - cross-frequency amplitude-amplitude coupling (AAC). In this short communication, we describe how nonstationary, nonlinear oscillatory signals may produce spurious cross-frequency AAC. Utilizing the empirical mode decomposition, we also propose a new method for assessment of AAC that can potentially reduce the effects of nonlinearity and nonstationarity and, thus, help to avoid the detection of artificial AACs. We compare the performances of this new method and the traditional Fourier-based AAC method. We also discuss the strategies to identify potential spurious AACs.

Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks

PubMed Central

Mangussi, Franco

2016-01-01

In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829

Spin-wave resonance frequency in ferromagnetic thin film with interlayer exchange coupling and surface anisotropy

NASA Astrophysics Data System (ADS)

Zhang, Shuhui; Rong, Jianhong; Wang, Huan; Wang, Dong; Zhang, Lei

2018-01-01

We have investigated the dependence of spin-wave resonance(SWR) frequency on the surface anisotropy, the interlayer exchange coupling, the ferromagnetic layer thickness, the mode number and the external magnetic field in a ferromagnetic superlattice film by means of the linear spin-wave approximation and Green's function technique. The SWR frequency of the ferromagnetic thin film is shifted to higher values corresponding to those of above factors, respectively. It is found that the linear behavior of SWR frequency curves of all modes in the system is observed as the external magnetic field is increasing, however, SWR frequency curves are nonlinear with the lower and the higher modes for different surface anisotropy and interlayer exchange coupling in the system. In addition, the SWR frequency of the lowest (highest) mode is shifted to higher (lower) values when the film thickness is thinner. The interlayer exchange coupling is more important for the energetically higher modes than for the energetically lower modes. The surface anisotropy has a little effect on the SWR frequency of the highest mode, when the surface anisotropy field is further increased.

Enhanced photon-phonon cross-Kerr nonlinearity with two-photon driving.

PubMed

Yin, Tai-Shuang; Lü, Xin-You; Wan, Liang-Liang; Bin, Shang-Wu; Wu, Ying

2018-05-01

We propose a scheme to significantly enhance the cross-Kerr (CK) nonlinearity between photons and phonons in a quadratically coupled optomechanical system (OMS) with two-photon driving. This CK nonlinear enhancement originates from the parametric-driving-induced squeezing and the underlying nonlinear optomechanical interaction. Moreover, the noise of the squeezed mode can be suppressed completely by introducing a squeezed vacuum reservoir. As a result of this dramatic nonlinear enhancement and the suppressed noise, we demonstrate the feasibility of the quantum nondemolition measurement of the phonon number in an originally weak coupled OMS. In addition, the photon-phonon blockade phenomenon is also investigated in this regime, which allows for performing manipulations between photons and phonons. This Letter offers a promising route towards the potential application for the OMS in quantum information processing and quantum networks.

Optimisation of the vibrational response of ultrasonic cutting systems

NASA Astrophysics Data System (ADS)

Cartmell, M. P.; Lim, F. C. N.; Cardoni, A.; Lucas, M.

2005-10-01

This paper provides an account of an investigation into possible dynamic interactions between two coupled non-linear sub-systems, each possessing opposing non-linear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two-degree-of-freedom Duffing oscillator in which certain non-linear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently non-linear, and which is coupled to a bar- or block-horn, and to one or more material cutting blades, for example. The horn/blade configurations are also non-linear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two-degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall non-linear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also been shown experimentally that coupling of ultrasonic components with different non-linear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice. Further experiments have shown that a multiple horn/blade configuration can, under certain circumstances, display autoparametric responses based on the forced response of the desired longitudinal mode parametrically exciting an undesired lateral mode. Typical autoparametric response phenomena have been observed and are presented at the end of the paper.

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.

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.

Saturable nonlinear dielectric waveguide with applications to broad-area semiconductor lasers.

PubMed

Mehuys, D; Mittelstein, M; Salzman, J; Yariv, A

1987-11-01

Self-focusing in a passive dielectric waveguide with a saturable nonlinearity is studied. The eigensolutions constitute a good approximation to the lateral modes of broad-area semiconductor lasers under low-duty-cycle pulsed conditions. The laser modes are predicted to consist of adjacent filaments coupled in phase, leading to a single-lobed far field, and to be stable with increased current injection above saturation intensity. The ultimate filament spacing is inversely proportional to the threshold gain, and thus wider filaments are expected in low-threshold broad-area lasers.

Multifrequency Gap Solitons in Nonlinear Photonic Crystals

NASA Astrophysics Data System (ADS)

Xie, Ping; Zhang, Zhao-Qing

2003-11-01

We predict the existence of multifrequency gap solitons (MFGSs) in both one- and two-dimensional nonlinear photonic crystals. A MFGS is a single intrinsic mode possessing multiple frequencies inside the gap. Its existence is a result of synergic nonlinear coupling among solitons or soliton trains at different frequencies. Its formation can either lower the threshold fields of the respective frequency components or stabilize their excitations. These MFGSs form a new class of stable gap solitons.

Lateral hopping of CO on Cu(111) induced by femtosecond laser pulses

NASA Astrophysics Data System (ADS)

Ueba, H.; Ootsuka, Y.; Paulsson, M.; Persson, B. N. J.

2010-09-01

We present a theoretical study of the lateral hopping of a single CO molecule on Cu(111) induced by femtosecond laser pulses by Mehlhorn [Phys. Rev. Lett. 104, 076101 (2010)]10.1103/PhysRevLett.104.076101. Our model assumes an intermode coupling between the CO frustrated translation (FT) and frustrated rotation (FR) modes with a weak and strong electronic friction coupling to hot electrons, respectively, and heat transfer between the FT mode and the substrate phonons. In this model the effective electronic friction coupling of the FT mode depends on the absorbed laser fluence F through the temperature of the FR mode. The calculated hopping yield as a function of F nicely reproduces the nonlinear increase observed above F=4.0J/m2 . It is found that the electronic heating via friction coupling nor the phonon coupling alone cannot explain the experimental result. Both heatings are cooperatively responsible for CO hopping on Cu(111). The electronic heat transfer dominates over the phononic one at high F , where the effective electronic friction coupling becomes larger than the phononic coupling.

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.

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.

Non-linear resonant coupling of tsunami edge waves using stochastic earthquake source models

USGS Publications Warehouse

Geist, Eric L.

2016-01-01

Non-linear resonant coupling of edge waves can occur with tsunamis generated by large-magnitude subduction zone earthquakes. Earthquake rupture zones that straddle beneath the coastline of continental margins are particularly efficient at generating tsunami edge waves. Using a stochastic model for earthquake slip, it is shown that a wide range of edge-wave modes and wavenumbers can be excited, depending on the variability of slip. If two modes are present that satisfy resonance conditions, then a third mode can gradually increase in amplitude over time, even if the earthquake did not originally excite that edge-wave mode. These three edge waves form a resonant triad that can cause unexpected variations in tsunami amplitude long after the first arrival. An M ∼ 9, 1100 km-long continental subduction zone earthquake is considered as a test case. For the least-variable slip examined involving a Gaussian random variable, the dominant resonant triad includes a high-amplitude fundamental mode wave with wavenumber associated with the along-strike dimension of rupture. The two other waves that make up this triad include subharmonic waves, one of fundamental mode and the other of mode 2 or 3. For the most variable slip examined involving a Cauchy-distributed random variable, the dominant triads involve higher wavenumbers and modes because subevents, rather than the overall rupture dimension, control the excitation of edge waves. Calculation of the resonant period for energy transfer determines which cases resonant coupling may be instrumentally observed. For low-mode triads, the maximum transfer of energy occurs approximately 20–30 wave periods after the first arrival and thus may be observed prior to the tsunami coda being completely attenuated. Therefore, under certain circumstances the necessary ingredients for resonant coupling of tsunami edge waves exist, indicating that resonant triads may be observable and implicated in late, large-amplitude tsunami arrivals.

Dynamics in terahertz semiconductor microcavity: quantum noise spectra

NASA Astrophysics Data System (ADS)

Jabri, H.; Eleuch, H.

2018-05-01

We investigate the physics of an optical semiconductor microcavity containing a coupled double quantum well interacting with cavity photons. The photon statistics of the transmitted light by the cavity is explored. We show that the nonlinear interactions in the direct and indirect excitonic modes generate an important squeezing despite the weak nonlinearities. When the strong coupling regime is achieved, the noise spectra of the system is dominated by the indirect exciton distribution. At the opposite, in the weak regime, direct excitons contribute much larger in the noise spectra.

Deterministic quantum nonlinear optics with single atoms and virtual photons

NASA Astrophysics Data System (ADS)

Kockum, Anton Frisk; Miranowicz, Adam; Macrı, Vincenzo; Savasta, Salvatore; Nori, Franco

2017-06-01

We show how analogs of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogs of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and down-conversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. In contrast to most conventional implementations of nonlinear optics, these analogs can reach unit efficiency, only use a minimal number of photons (they do not require any strong external drive), and do not require more than two atomic levels. The strength of the effective coupling in our proposed setups becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling and improvement of coherence times for engineered quantum systems, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogs can be realized with currently available technology.

Selective Coupling Enhances Harmonic Generation of Whispering-Gallery Modes

NASA Astrophysics Data System (ADS)

Trainor, Luke S.; Sedlmeir, Florian; Peuntinger, Christian; Schwefel, Harald G. L.

2018-02-01

We demonstrate second-harmonic generation (SHG) in an x -cut congruent lithium niobate (LN) whispering-gallery mode (WGM) resonator. First, we show theoretically that independent control of the coupling of the pump and signal modes is optimal for high conversion rates. A coupling scheme based on our earlier work [F. Sedlmeir et al., Phys. Rev. Applied 7, 024029 (2017), 10.1103/PhysRevApplied.7.024029] is then implemented experimentally to verify this improvement. Thereby, we are able to improve on the efficiency of SHG by more than an order of magnitude by selectively outcoupling using a LN prism, utilizing the birefringence of it and the resonator in kind. This method is also applicable to other nonlinear processes in WGM resonators.

Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential.

PubMed

Xu, Si-Liu; Zhao, Guo-Peng; Belić, Milivoj R; He, Jun-Rong; Xue, Li

2017-04-17

We analyze three-dimensional (3D) vector solitary waves in a system of coupled nonlinear Schrödinger equations with spatially modulated diffraction and nonlinearity, under action of a composite self-consistent trapping potential. Exact vector solitary waves, or light bullets (LBs), are found using the self-similarity method. The stability of vortex 3D LB pairs is examined by direct numerical simulations; the results show that only low-order vortex soliton pairs with the mode parameter values n ≤ 1, l ≤ 1 and m = 0 can be supported by the spatially modulated interaction in the composite trap. Higher-order LBs are found unstable over prolonged distances.

CW all optical self switching in nonlinear chalcogenide nano plasmonic directional coupler

NASA Astrophysics Data System (ADS)

Motamed-Jahromi, Leila; Hatami, Mohsen

2018-04-01

In this paper we obtain the coupling coefficient of plasmonic directional coupler (PDC) made up of two parallel monolayer waveguides filled with high nonlinear chalcogenide material for TM mode in continues wave (CW) regime. In addition, we assume each waveguides acts as a perturbation to other waveguide. Four nonlinear-coupled equations are derived. Transfer distances are numerically calculated and used for deriving length of all optical switch. The length of designed switch is in the range of 10-1000 μm, and the switching power is in the range of 1-100 W/m. Obtained values are suitable for designing all optical elements in the integrated optical circuits.

Longwave Stability of Two Liquid Layers Coating Both Sides of a Thick Wall in the Absence of Gravity

NASA Astrophysics Data System (ADS)

Dávalos-Orozco, L. A.

2018-05-01

A system of two coupled nonlinear equations was calculated to describe the thermocapillary evolution of the free surface deformations of two liquid layers coating both sides of a wall of finite thickness and thermal conductivity in the absence of gravity. The equations were obtained under the small wavenumber approximation. A temperature gradient appears perpendicular to the liquid-wall-liquid system due to the temperature difference between the atmospheres outside the free surfaces of both fluid layers. The linear growth rate of the system was investigated with respect to a variety of parameters. Under some conditions, two stationary modes and one oscillatory mode between them were found. The second stationary mode was concluded to be always stable. It was also found that under different conditions only stationary convection is possible. These results depended on the relative thickness of the two fluid films. It is of interest to know if the coupled free surface perturbations presented a nonlinear sinuous or varicose mode. Thus, a two-dimensional numerical analysis was performed to find out which conditions lead to the sinuous or to the varicose mode of instability.

Parametrically excited motion of a levitated rigid bar over high- Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Shimizu, T.; Sugiura, T.; Ogawa, S.

2006-10-01

High-Tc superconducting levitation systems achieve, under no contact support, stable levitation without control. This feature can be applied to flywheels, magnetically levitated trains, and so on. But no contact support has small damping. So these mechanisms can show complicated phenomena of dynamics due to nonlinearity in their magnetic force. For application to large-scale machines, we need to analyze dynamics of a large levitated body supported at multiple points. This research deals with nonlinearly coupled oscillation of a homogeneous and symmetric rigid bar supported at its both ends by equal electromagnetic forces between superconductors and permanent magnets. In our past study, using a rigid bar, we found combination resonance. Combination resonance happens owing to the asymmetry of the system. But, even if support forces are symmetric, parametric resonance can happen. With a simple symmetric model, this research focuses on especially the parametric resonance, and evaluates nonlinear effect of the symmetric support forces by experiment and numerical analysis. Obtained results show that two modes, caused by coupling of horizontal translation and roll motion, can be excited nonlinearly when the superconductor is excited vertically in the neighborhood of twice the natural frequencies of those modes. We confirmed these resonances have nonlinear characteristics of soft-spring, hysteresis and so on.

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.

Nonlinear behavior of solar gravity modes driven by He-3 in the core. I - Bifurcation analysis

NASA Technical Reports Server (NTRS)

Merryfield, William J.; Gough, Douglas; Toomre, Juri

1990-01-01

The nonlinear development of solar gravity modes driven by He-3 burning in the solar core is investigated by means of an idealized dynamical model. Possible outcomes that have been suggested in the literature include the triggering of subcritical direct convection, leading to core mixing, and the saturation of the excitation processes, leading to sustained finite-amplitude oscillations. The present simple model suggests that the latter is the more likely. The limiting amplitude of the oscillations is estimated, ignoring possible resonances with other gravity modes, to be of order 10 km/s at the solar surface. Such oscillations would be easily observable. That large-amplitude gravity modes have not been observed suggests either that these modes are not unstable in the present era or that they are limited to much smaller amplitudes by resonant coupling.

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

A coherent nonlinear theory of auroral Langmuir-Alfven-whistler (LAW) events in the planetary magnetosphere.

NASA Astrophysics Data System (ADS)

Lopes, S. R.; Chian, A. C.-L.

1996-01-01

A coherent nonlinear theory of three-wave coupling involving Langmuir, Alfven and whistler waves is formulated and applied to the observation of auroral LAW events in the planetary magnetosphere. The effects of pump depletion, dissipation and frequency mismatch in the nonlinear wave dynamics are analyzed. The relevance of this theory for understanding the fine structures of auroral whistler-mode emissions and amplitude modulations of auroral Langmuir waves is discussed.

Interaction of chimera states in a multilayered network of nonlocally coupled oscillators

NASA Astrophysics Data System (ADS)

Goremyko, M. V.; Maksimenko, V. A.; Makarov, V. V.; Ghosh, D.; Bera, B.; Dana, S. K.; Hramov, A. E.

2017-08-01

The processes of formation and evolution of chimera states in the model of a multilayered network of nonlinear elements with complex coupling topology are studied. A two-layered network of nonlocally intralayer-coupled Kuramoto-Sakaguchi phase oscillators is taken as the object of investigation. Different modes implemented in this system upon variation of the degree of interlayer interaction are demonstrated.

Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides.

PubMed

Shin, Heedeuk; Qiu, Wenjun; Jarecki, Robert; Cox, Jonathan A; Olsson, Roy H; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T

2013-01-01

Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of hybrid photonic-phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin scattering is realized-with over 1,000 times larger nonlinearity than reported in previous systems-yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show that radiation pressures, produced by subwavelength modal confinement, yield enhancement of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such enhanced and wideband coherent phonon emission paves the way towards the hybridization of silicon photonics, microelectromechanical systems and CMOS signal-processing technologies on chip.

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;

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

Parametric Excitation of Electrostatic Dust-Modes by Ion-Cyclotron Waves in a Dusty Plasma

NASA Astrophysics Data System (ADS)

Islam, M. K.; Salahuddin, M.; Ferdous, T.; Salimullah, M.

A large amplitude electrostatic ion-cyclotron wave propagating through a magnetized and collisional dusty plasma undergoes strong parametric instability off the low-frequency dust-modes. The presence of the dust-component has effect on the nonlinear coupling via the dust-modes. The ion-neutral collisions are seen to have significant effect on the damping and consequent overall growth of the parametric excitation process.

Entanglement dynamics and position-momentum entropic uncertainty relation of a Λ-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities

NASA Astrophysics Data System (ADS)

Faghihi, M. J.; Tavassoly, M. K.; Hooshmandasl, M. R.

2013-05-01

In this paper, the interaction between a $\\Lambda$-type three-level atom and two-mode cavity field is discussed. The detuning parameters and cross-Kerr nonlinearity are taken into account and it is assumed that atom-field coupling and Kerr medium to be $f$-deformed. Even though the system seems to be complicated, the analytical form of the state vector of the entire system for considered model is exactly obtained. The time evolution of nonclassical properties such as quantum entanglement and position-momentum entropic uncertainty relation (entropy squeezing) of the field are investigated. In each case, the influences of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the latter nonclassicality signs are analyzed, in detail.

Nonlinear evolution of baryon acoustic oscillations

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

Crocce, Martin; Institut de Ciencies de l'Espai, IEEC-CSIC, Campus UAB, Facultat de Ciencies, Torre C5 par-2, Barcelona 08193; Scoccimarro, Roman

2008-01-15

We study the nonlinear evolution of baryon acoustic oscillations in the dark matter power spectrum and the correlation function using renormalized perturbation theory. In a previous paper we showed that renormalized perturbation theory successfully predicts the damping of acoustic oscillations; here we extend our calculation to the enhancement of power due to mode coupling. We show that mode coupling generates additional oscillations that are out of phase with those in the linear spectrum, leading to shifts in the scales of oscillation nodes defined with respect to a smooth spectrum. When Fourier transformed, these out-of-phase oscillations induce percent-level shifts in themore » acoustic peak of the two-point correlation function. We present predictions for these shifts as a function of redshift; these should be considered as a robust lower limit to the more realistic case that includes, in addition, redshift distortions and galaxy bias. We show that these nonlinear effects occur at very large scales, leading to a breakdown of linear theory at scales much larger than commonly thought. We discuss why virialized halo profiles are not responsible for these effects, which can be understood from basic physics of gravitational instability. Our results are in excellent agreement with numerical simulations, and can be used as a starting point for modeling baryon acoustic oscillations in future observations. To meet this end, we suggest a simple physically motivated model to correct for the shifts caused by mode coupling.« less

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

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.

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

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

Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2017-03-01

We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.

Nonlinear dynamics of drops and bubbles and chaotic phenomena

NASA Technical Reports Server (NTRS)

Trinh, Eugene H.; Leal, L. G.; Feng, Z. C.; Holt, R. G.

1994-01-01

Nonlinear phenomena associated with the dynamics of free drops and bubbles are investigated analytically, numerically and experimentally. Although newly developed levitation and measurement techniques have been implemented, the full experimental validation of theoretical predictions has been hindered by interfering artifacts associated with levitation in the Earth gravitational field. The low gravity environment of orbital space flight has been shown to provide a more quiescent environment which can be utilized to better match the idealized theoretical conditions. The research effort described in this paper is a closely coupled collaboration between predictive and guiding theoretical activities and a unique experimental program involving the ultrasonic and electrostatic levitation of single droplets and bubbles. The goal is to develop and to validate methods based on nonlinear dynamics for the understanding of the large amplitude oscillatory response of single drops and bubbles to both isotropic and asymmetric pressure stimuli. The first specific area on interest has been the resonant coupling between volume and shape oscillatory modes isolated gas or vapor bubbles in a liquid host. The result of multiple time-scale asymptotic treatment, combined with domain perturbation and bifurcation methods, has been the prediction of resonant and near-resonant coupling between volume and shape modes leading to stable as well as chaotic oscillations. Experimental investigations of the large amplitude shape oscillation modes of centimeter-size single bubbles trapped in water at 1 G and under reduced hydrostatic pressure, have suggested the possibility of a low gravity experiment to study the direct coupling between these low frequency shape modes and the volume pulsation, sound-radiating mode. The second subject of interest has involved numerical modeling, using the boundary integral method, of the large amplitude shape oscillations of charged and uncharged drops in the presence of a static or time-varying electric field. Theoretically predicted non linearity in the resonant frequency of the fundamental quadrupole mode has been verified by the accompanying experimental studies. Additional phenomena such as hysteresis in the frequency response of ultrasoncially levitated droplets in the presence of a time varying electric field, and mode coupling in the oscillations of ultrasonically modulated droplets, have also been uncovered. One of the results of this ground-based research has been the identification and characterization of phenomena strictly associated with the influence of the gravitational field. This has also allowed us to identify the specific requirements for potential microgravity investigations yielding new information not obtainable on Earth.

Nonlinear dynamics of drops and bubbles and chaotic phenomena

NASA Astrophysics Data System (ADS)

Trinh, Eugene H.; Leal, L. G.; Feng, Z. C.; Holt, R. G.

1994-08-01

Nonlinear phenomena associated with the dynamics of free drops and bubbles are investigated analytically, numerically and experimentally. Although newly developed levitation and measurement techniques have been implemented, the full experimental validation of theoretical predictions has been hindered by interfering artifacts associated with levitation in the Earth gravitational field. The low gravity environment of orbital space flight has been shown to provide a more quiescent environment which can be utilized to better match the idealized theoretical conditions. The research effort described in this paper is a closely coupled collaboration between predictive and guiding theoretical activities and a unique experimental program involving the ultrasonic and electrostatic levitation of single droplets and bubbles. The goal is to develop and to validate methods based on nonlinear dynamics for the understanding of the large amplitude oscillatory response of single drops and bubbles to both isotropic and asymmetric pressure stimuli. The first specific area on interest has been the resonant coupling between volume and shape oscillatory modes isolated gas or vapor bubbles in a liquid host. The result of multiple time-scale asymptotic treatment, combined with domain perturbation and bifurcation methods, has been the prediction of resonant and near-resonant coupling between volume and shape modes leading to stable as well as chaotic oscillations. Experimental investigations of the large amplitude shape oscillation modes of centimeter-size single bubbles trapped in water at 1 G and under reduced hydrostatic pressure, have suggested the possibility of a low gravity experiment to study the direct coupling between these low frequency shape modes and the volume pulsation, sound-radiating mode. The second subject of interest has involved numerical modeling, using the boundary integral method, of the large amplitude shape oscillations of charged and uncharged drops in the presence of a static or time-varying electric field. Theoretically predicted non linearity in the resonant frequency of the fundamental quadrupole mode has been verified by the accompanying experimental studies. Additional phenomena such as hysteresis in the frequency response of ultrasoncially levitated droplets in the presence of a time varying electric field, and mode coupling in the oscillations of ultrasonically modulated droplets, have also been uncovered. One of the results of this ground-based research has been the identification and characterization of phenomena strictly associated with the influence of the gravitational field. This has also allowed us to identify the specific requirements for potential microgravity investigations yielding new information not obtainable on Earth.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

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

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

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.

Quasi-phase-matching and second-harmonic generation enhancement in a semiconductor microresonator array using slow-light effects

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

Dumeige, Yannick

We theoretically analyze the second-harmonic generation process in a sequence of unidirectionnaly coupled doubly resonant whispering gallery mode semiconductor resonators. By using a convenient design, it is possible to coherently sum the second-harmonic fields generated inside each resonator. We show that resonator coupling allows the bandwidth of the phase-matching curve to be increased with respect to single-resonator configurations simultaneously taking advantage of the resonant feature of the resonators. This quasi-phase-matching technique could be applied to obtain small-footprint nonlinear devices with large bandwidth and limited nonlinear losses. The results are discussed in the framework of the slow-light-effect enhancement of second-order opticalmore » nonlinearities.« less

Maximizing entanglement in bosonic Josephson junctions using shortcuts to adiabaticity and optimal control

NASA Astrophysics Data System (ADS)

Stefanatos, Dionisis; Paspalakis, Emmanuel

2018-05-01

In this article we consider a bosonic Josephson junction, a model system composed by two coupled nonlinear quantum oscillators which can be implemented in various physical contexts, initially prepared in a product of weakly populated coherent states. We quantify the maximum achievable entanglement between the modes of the junction and then use shortcuts to adiabaticity, a method developed to speed up adiabatic quantum dynamics, as well as numerical optimization, to find time-dependent controls (the nonlinearity and the coupling of the junction) which bring the system to a maximally entangled state.

Nonlinear coupled mode approach for modeling counterpropagating solitons in the presence of disorder-induced multiple scattering in photonic crystal waveguides

NASA Astrophysics Data System (ADS)

Mann, Nishan; Hughes, Stephen

2018-02-01

We present the analytical and numerical details behind our recently published article [Phys. Rev. Lett. 118, 253901 (2017), 10.1103/PhysRevLett.118.253901], describing the impact of disorder-induced multiple scattering on counterpropagating solitons in photonic crystal waveguides. Unlike current nonlinear approaches using the coupled mode formalism, we account for the effects of intraunit cell multiple scattering. To solve the resulting system of coupled semilinear partial differential equations, we introduce a modified Crank-Nicolson-type norm-preserving implicit finite difference scheme inspired by the transfer matrix method. We provide estimates of the numerical dispersion characteristics of our scheme so that optimal step sizes can be chosen to either minimize numerical dispersion or to mimic the exact dispersion. We then show numerical results of a fundamental soliton propagating in the presence of multiple scattering to demonstrate that choosing a subunit cell spatial step size is critical in accurately capturing the effects of multiple scattering, and illustrate the stochastic nature of disorder by simulating soliton propagation in various instances of disordered photonic crystal waveguides. Our approach is easily extended to include a wide range of optical nonlinearities and is applicable to various photonic nanostructures where power propagation is bidirectional, either by choice, or as a result of multiple scattering.

Tunable phonon-cavity coupling in graphene membranes.

PubMed

De Alba, R; Massel, F; Storch, I R; Abhilash, T S; Hui, A; McEuen, P L; Craighead, H G; Parpia, J M

2016-09-01

A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting the interactions between optical cavities and mechanical resonators. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through phonon-cavity coupling-energy exchange between the modes of a single system mediated by intrinsic material nonlinearity. This has so far been demonstrated primarily for bulk crystalline, high-quality-factor (Q > 10(5)) mechanical systems operated at cryogenic temperatures. Here, we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena, including tunable intermodal coupling. We have fabricated circular graphene membranes and report strong phonon-cavity effects at room temperature, despite the modest Q factor (∼100) of this system. We observe both amplification into parametric instability (mechanical lasing) and the cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize the quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where the observation of such effects has proven elusive.

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.

An inherent curvature-compensated voltage reference using non-linearity of gate coupling coefficient

NASA Astrophysics Data System (ADS)

Hande, Vinayak; Shojaei Baghini, Maryam

2015-08-01

A novel current-mode voltage reference circuit which is capable of generating sub-1 V output voltage is presented. The proposed architecture exhibits the inherent curvature compensation ability. The curvature compensation is achieved by utilizing the non-linear behavior of gate coupling coefficient to compensate non-linear temperature dependence of base-emitter voltage. We have also utilized the developments in CMOS process to reduce power and area consumption. The proposed voltage reference is analyzed theoretically and compared with other existing methods. The circuit is designed and simulated in 180 nm mixed-mode CMOS UMC technology which gives a reference level of 246 mV. The minimum required supply voltage is 1 V with maximum current drawn of 9.24 μA. A temperature coefficient of 9 ppm/°C is achieved over -25 to 125 °C temperature range. The reference voltage varies by ±11 mV across process corners. The reference circuit shows the line sensitivity of 0.9 mV/V with area consumption of 100 × 110 μm2

Engineering non-linear resonator mode interactions in circuit QED by continuous driving: Introduction

NASA Astrophysics Data System (ADS)

Pfaff, Wolfgang; Reagor, Matthew; Heeres, Reinier; Ofek, Nissim; Chou, Kevin; Blumoff, Jacob; Leghtas, Zaki; Touzard, Steven; Sliwa, Katrina; Holland, Eric; Krastanov, Stefan; Frunzio, Luigi; Devoret, Michel; Jiang, Liang; Schoelkopf, Robert

2015-03-01

High-Q microwave resonators show great promise for storing and manipulating quantum states in circuit QED. Using resonator modes as such a resource in quantum information processing applications requires the ability to manipulate the state of a resonator efficiently. Further, one must engineer appropriate coupling channels without spoiling the coherence properties of the resonator. We present an architecture that combines millisecond lifetimes for photonic quantum states stored in a linear resonator with fast measurement provided by a low-Q readout resonator. We demonstrate experimentally how a continuous drive on a transmon can be utilized to generate highly non-classical photonic states inside the high-Q resonator via effective nonlinear resonator mode interactions. Our approach opens new avenues for using modes of long-lived linear resonators in the circuit QED platform for quantum information processing tasks.

Exploring the nonlinear regime of light-matter interaction using electronic spins in diamond

NASA Astrophysics Data System (ADS)

Alfasi, Nir; Masis, Sergei; Winik, Roni; Farfurnik, Demitry; Shtempluck, Oleg; Bar-Gill, Nir; Buks, Eyal

2018-06-01

The coupling between defects in diamond and a superconducting microwave resonator is studied in the nonlinear regime. Both negatively charged nitrogen-vacancy and P1 defects are explored. The measured cavity mode response exhibits strong nonlinearity near a spin resonance. Data is compared with theoretical predictions and a good agreement is obtained in a wide range of externally controlled parameters. The nonlinear effect under study in the current paper is expected to play a role in any cavity-based magnetic resonance imaging technique and to impose a fundamental limit upon its sensitivity.

Nonlinear Excitation of Acoustic Modes by Large Amplitude Alfvén waves in the Large Plasma Device (LAPD)

NASA Astrophysics Data System (ADS)

Dorfman, S.; Carter, T.; Pribyl, P.; Tripathi, S. K. P.; van Compernolle, B.; Vincena, S.; Sydora, R.

2013-10-01

Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in lab and space. While the linear behavior of these waves has been extensively studied, non-linear effects are important in many real systems, including the solar wind and solar corona. In particular, a parametric decay process in which a large amplitude Alfvén wave decays into an ion acoustic wave and backward propagating Alfvén wave may play an important role in coronal heating and/or in establishing the spectrum of solar wind turbulence. Recent counter-propagating Alfvén wave experiments have recorded the first laboratory observation of the Alfvén-acoustic mode coupling at the heart of this parametric decay instability. The resonance in the observed beat process has several features consistent with ponderomotive coupling to an ion acoustic mode, including the measured dispersion relation and spatial profile. Strong damping observed after the pump Alfvén waves are turned off is under investigation. New experiments and simulations also aim to identify decay instabilities from a single large-amplitude Alfvén wave. Supported by DOE and NSF.

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.

Nonlinear Mode Coupling Theory of the Lower-Hybrid-Drift Instability.

DTIC Science & Technology

1983-11-25

University of lows Iowa City, Iowa 52242 Tenerin, Michael Space Science Lab. University of California Berkeley, California 94720 Vlahos, Loukas Dept. of fysics University of Maryland College Park, Maryland 20742 44 FILMED 1=84 DTIC

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

Romera, M.; Monteblanco, E.; Garcia-Sanchez, F.

The influence of dynamic coupling in between magnetic layers of a standard spin torque nano-oscillator composed of a synthetic antiferromagnet (SyF) as a polarizer and an in-plane magnetized free layer has been investigated. Experiments on spin valve nanopillars reveal non-continuous features such as kinks in the frequency field dependence that cannot be explained without such interactions. Comparison of experiments to numerical macrospin simulations shows that this is due to non-linear interaction between the spin torque (STT) driven mode and a damped mode that is mediated via the third harmonics of the STT mode. It only occurs at large applied currentsmore » and thus at large excitation amplitudes of the STT mode. Under these conditions, a hybridized mode characterized by a strong reduction of the linewidth appears. The reduced linewidth can be explained by a reduction of the non-linear contribution to the linewidth via an enhanced effective damping. Interestingly, the effect depends also on the exchange interaction within the SyF. An enhancement of the current range of reduced linewidth by a factor of two and a reduction of the minimum linewidth by a factor of two are predicted from simulation when the exchange interaction strength is reduced by 30%. These results open directions to optimize the design and microwave performances of spin torque nano-oscillators taking advantage of the coupling mechanisms.« less

FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

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

McEwen, Joseph E.; Fang, Xiao; Hirata, Christopher M.

2016-09-01

We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theorymore » and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.« less

Reformulation of time-convolutionless mode-coupling theory near the glass transition

NASA Astrophysics Data System (ADS)

Tokuyama, Michio

2017-10-01

The time-convolutionless mode-coupling theory (TMCT) recently proposed is reformulated under the condition that one of two approximations, which have been used to formulate the original TMCT in addition to the MCT approximations done on a derivation of nonlinear memory function in terms of the intermediate-scattering function, is not employed because it causes unphysical results for intermediate times. The improved TMCT equation is then derived consistently under another approximation. It is first checked that the ergodic to non-ergodic transition obtained by a new equation is exactly the same as that obtained by an old one because the long-time dynamics of both equations coincides with each other. However, it is emphasized that a difference between them appears in the intermediate-time dynamics of physical quantities. Such a difference is explored numerically in the dynamics of a non-Gaussian parameter by employing the Percus-Yevick static structure factor to calculate the nonlinear memory function.

Utilizing strongly absorbing materials for low-loss surface-wave nonlinear optics

NASA Astrophysics Data System (ADS)

Grosse, Nicolai B.; Franz, Philipp; Heckmann, Jan; Pufahl, Karsten; Woggon, Ulrike

2018-04-01

Optical media endowed with large nonlinear susceptibilities are highly prized for their employment in frequency conversion and the generation of nonclassical states of light. Although the presence of an optical resonance can greatly increase the nonlinear response (e.g., in epsilon-near-zero materials), the non-negligible increase in linear absorption often precludes the application of such materials in nonlinear optics. Absorbing materials prepared as thin films, however, can support a low-loss surface wave: the long-range surface exciton polariton (LRSEP). Its propagation lifetime increases with greater intrinsic absorption and reduced film thickness, provided that the film is embedded in a transparent medium (symmetric cladding). We explore LRSEP propagation in a molybdenum film by way of a prism-coupling configuration. Our observations show that excitation of the LRSEP mode leads to a dramatic increase in the yield of second-harmonic generation. This implies that the LRSEP mode is an effective vehicle for utilizing the nonlinear response of absorbing materials.

Giant nonlinear interaction between two optical beams via a quantum dot embedded in a photonic wire

NASA Astrophysics Data System (ADS)

Nguyen, H. A.; Grange, T.; Reznychenko, B.; Yeo, I.; de Assis, P.-L.; Tumanov, D.; Fratini, F.; Malik, N. S.; Dupuy, E.; Gregersen, N.; Auffèves, A.; Gérard, J.-M.; Claudon, J.; Poizat, J.-Ph.

2018-05-01

Optical nonlinearities usually appear for large intensities, but discrete transitions allow for giant nonlinearities operating at the single-photon level. This has been demonstrated in the last decade for a single optical mode with cold atomic gases, or single two-level systems coupled to light via a tailored photonic environment. Here, we demonstrate a two-mode giant nonlinearity with a single semiconductor quantum dot (QD) embedded in a photonic wire antenna. We exploit two detuned optical transitions associated with the exciton-biexciton QD level scheme. Owing to the broadband waveguide antenna, the two transitions are efficiently interfaced with two free-space laser beams. The reflection of one laser beam is then controlled by the other beam, with a threshold power as low as 10 photons per exciton lifetime (1.6 nW ). Such a two-color nonlinearity opens appealing perspectives for the realization of ultralow-power logical gates and optical quantum gates, and could also be implemented in an integrated photonic circuit based on planar waveguides.

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.

Excitation of high wavenumber fluctuations by externally-imposed helical fields in edge pedestal plasmas

NASA Astrophysics Data System (ADS)

Singh, R.; Kim, J.-H.; Jhang, Hogun; Das, S.

2018-03-01

Two-step mode coupling analyses for nonlinear excitation of the ballooning mode (BM) in pedestal plasma by external helical magnetic field perturbation [Resonant Magnetic Perturbations (RMP)] are presented. This technique allows calculating the effect of higher harmonic sidebands generated by interaction of long scale RMP pump and BM. It is shown that RMP field perturbations can modify the BM growth rate and frequency through nonlinear Reynolds stress and magnetic stress. In particular, it is shown that both stresses can efficiently excite high wavenumber BM fluctuations which, in turn, can enhance the transport in the pedestal. Another notable feature of this analysis is the existence of short scale (high- k y ) nonlinear instability at Alfven time scale near the ideal BM threshold boundary.

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.

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

Volkoff, T. J., E-mail: adidasty@gmail.com

We motivate and introduce a class of “hierarchical” quantum superposition states of N coupled quantum oscillators. Unlike other well-known multimode photonic Schrödinger-cat states such as entangled coherent states, the hierarchical superposition states are characterized as two-branch superpositions of tensor products of single-mode Schrödinger-cat states. In addition to analyzing the photon statistics and quasiprobability distributions of prominent examples of these nonclassical states, we consider their usefulness for highprecision quantum metrology of nonlinear optical Hamiltonians and quantify their mode entanglement. We propose two methods for generating hierarchical superpositions in N = 2 coupled microwave cavities, exploiting currently existing quantum optical technology formore » generating entanglement between spatially separated electromagnetic field modes.« less

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.

Coherent perfect absorption in a quantum nonlinear regime of cavity quantum electrodynamics

NASA Astrophysics Data System (ADS)

Wei, Yang-hua; Gu, Wen-ju; Yang, Guoqing; Zhu, Yifu; Li, Gao-xiang

2018-05-01

Coherent perfect absorption (CPA) is investigated in the quantum nonlinear regime of cavity quantum electrodynamics (CQED), in which a single two-level atom couples to a single-mode cavity weakly driven by two identical laser fields. In the strong-coupling regime and due to the photon blockade effect, the weakly driven CQED system can be described as a quantum system with three polariton states. CPA is achieved at a critical input field strength when the frequency of the input fields matches the polariton transition frequency. In the quantum nonlinear regime, the incoherent dissipation processes such as atomic and photon decays place a lower bound for the purity of the intracavity quantum field. Our results show that under the CPA condition, the intracavity field always exhibits the quadrature squeezing property manifested by the quantum nonlinearity, and the outgoing photon flux displays the super-Poissonian distribution.

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.

On non-local energy transfer via zonal flow in the Dimits shift

NASA Astrophysics Data System (ADS)

St-Onge, Denis A.

2017-10-01

The two-dimensional Terry-Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth-Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in an nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.

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

St-Onge, Denis A.

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in anmore » $$\\boldsymbol{E}\\times \\boldsymbol{B}$$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.« less

Cross-verification of the GENE and XGC codes in preparation for their coupling

NASA Astrophysics Data System (ADS)

Jenko, Frank; Merlo, Gabriele; Bhattacharjee, Amitava; Chang, Cs; Dominski, Julien; Ku, Seunghoe; Parker, Scott; Lanti, Emmanuel

2017-10-01

A high-fidelity Whole Device Model (WDM) of a magnetically confined plasma is a crucial tool for planning and optimizing the design of future fusion reactors, including ITER. Aiming at building such a tool, in the framework of the Exascale Computing Project (ECP) the two existing gyrokinetic codes GENE (Eulerian delta-f) and XGC (PIC full-f) will be coupled, thus enabling to carry out first principle kinetic WDM simulations. In preparation for this ultimate goal, a benchmark between the two codes is carried out looking at ITG modes in the adiabatic electron limit. This verification exercise is also joined by the global Lagrangian PIC code ORB5. Linear and nonlinear comparisons have been carried out, neglecting for simplicity collisions and sources. A very good agreement is recovered on frequency, growth rate and mode structure of linear modes. A similarly excellent agreement is also observed comparing the evolution of the heat flux and of the background temperature profile during nonlinear simulations. Work supported by the US DOE under the Exascale Computing Project (17-SC-20-SC).

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.

Enhanced optical nonlinearity and fiber-optical frequency comb controlled by a single atom in a whispering-gallery-mode microtoroid resonator

NASA Astrophysics Data System (ADS)

Li, Jiahua; Zhang, Suzhen; Yu, Rong; Zhang, Duo; Wu, Ying

2014-11-01

Based on a single atom coupled to a fiber-coupled, chip-based microresonator [B. Dayan et al., Science 319, 1062 (2008), 10.1126/science.1152261], we put forward a scheme to generate optical frequency combs at driving laser powers as low as a few nanowatts. Using state-of-the-art experimental parameters, we investigate in detail the influences of different atomic positions and taper-resonator coupling regimes on optical-frequency-comb generation. In addition to numerical simulations demonstrating this effect, a physical explanation of the underlying mechanism is presented. We find that the combination of the atom and the resonator can induce a large third-order nonlinearity which is significantly stronger than Kerr nonlinearity in Kerr frequency combs. Such enhanced nonlinearity can be used to generate optical frequency combs if driven with two continuous-wave control and probe lasers and significantly reduce the threshold of nonlinear optical processes. The comb spacing can be well tuned by changing the frequency beating between the driving control and probe lasers. The proposed method is versatile and can be adopted to different types of resonators, such as microdisks, microspheres, microtoroids or microrings.

Use of the dynamic stiffness method to interpret experimental data from a nonlinear system

NASA Astrophysics Data System (ADS)

Tang, Bin; Brennan, M. J.; Gatti, G.

2018-05-01

The interpretation of experimental data from nonlinear structures is challenging, primarily because of dependency on types and levels of excitation, and coupling issues with test equipment. In this paper, the use of the dynamic stiffness method, which is commonly used in the analysis of linear systems, is used to interpret the data from a vibration test of a controllable compressed beam structure coupled to a test shaker. For a single mode of the system, this method facilitates the separation of mass, stiffness and damping effects, including nonlinear stiffness effects. It also allows the separation of the dynamics of the shaker from the structure under test. The approach needs to be used with care, and is only suitable if the nonlinear system has a response that is predominantly at the excitation frequency. For the structure under test, the raw experimental data revealed little about the underlying causes of the dynamic behaviour. However, the dynamic stiffness approach allowed the effects due to the nonlinear stiffness to be easily determined.

Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides

PubMed Central

Shin, Heedeuk; Qiu, Wenjun; Jarecki, Robert; Cox, Jonathan A.; Olsson, Roy H.; Starbuck, Andrew; Wang, Zheng; Rakich, Peter T.

2013-01-01

Nanoscale modal confinement is known to radically enhance the effect of intrinsic Kerr and Raman nonlinearities within nanophotonic silicon waveguides. By contrast, stimulated Brillouin-scattering nonlinearities, which involve coherent coupling between guided photon and phonon modes, are stifled in conventional nanophotonics, preventing the realization of a host of Brillouin-based signal-processing technologies in silicon. Here we demonstrate stimulated Brillouin scattering in silicon waveguides, for the first time, through a new class of hybrid photonic–phononic waveguides. Tailorable travelling-wave forward-stimulated Brillouin scattering is realized—with over 1,000 times larger nonlinearity than reported in previous systems—yielding strong Brillouin coupling to phonons from 1 to 18 GHz. Experiments show that radiation pressures, produced by subwavelength modal confinement, yield enhancement of Brillouin nonlinearity beyond those of material nonlinearity alone. In addition, such enhanced and wideband coherent phonon emission paves the way towards the hybridization of silicon photonics, microelectromechanical systems and CMOS signal-processing technologies on chip. PMID:23739586

Bicoherence Analysis of Electrostatic Interchange Mode Coupling in a Turbulent Laboratory Magnetosphere

NASA Astrophysics Data System (ADS)

Abler, M. C.; Saperstein, A.; Yan, J. R.; Mauel, M. E.

2017-10-01

Plasmas confined by a strong dipole field exhibit interchange and entropy mode turbulence, which previous experiments have shown respond locally to active feedback. On the Collisionless Terrella Experiment (CTX), this turbulence is characterized by low frequency, low order, quasi-coherent modes with complex spectral dynamics. We apply bicoherence analysis to study nonlinear phase coupling in a variety of scenarios. First, we study the self-interaction of the naturally occurring interchange turbulence; this analysis is then expanded to include the effects of driven modes in the frequency range of the background turbulent oscillations. Initial measurements of coupling coefficients are presented in both cases. Driven low frequency interchange modes are observed to generate multiple harmonics which persist throughout the plasma, becoming weaker as they propagate away from the actuator in the direction of the electron magnetic drift. Future work is also discussed, including application of wavelet bicoherence analysis, excitation of interchange modes at multiple frequencies, and applications to planetary magnetospheres. Supported by NSF-DOE Partnership for Plasma Science Grants DOE-DE-FG02-00ER54585.

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.

Nonlinear Wave Chaos and the Random Coupling Model

NASA Astrophysics Data System (ADS)

Zhou, Min; Ott, Edward; Antonsen, Thomas M.; Anlage, Steven

The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic cavities in the highly over-moded regime. It is of interest to extend the RCM to strongly nonlinear systems. To introduce nonlinearity, an active nonlinear circuit is connected to two ports of the wave chaotic 1/4-bowtie cavity. The active nonlinear circuit consists of a frequency multiplier, an amplifier and several passive filters. It acts to double the input frequency in the range from 3.5 GHz to 5 GHz, and operates for microwaves going in only one direction. Measurements are taken between two additional ports of the cavity and we measure the statistics of the second harmonic voltage over an ensemble of realizations of the scattering system. We developed an RCM-based model of this system as two chaotic cavities coupled by means of a nonlinear transfer function. The harmonics received at the output are predicted to be the product of three statistical quantities that describe the three elements correspondingly. Statistical results from simulation, RCM-based modeling, and direct experimental measurements will be compared. ONR under Grant No. N000141512134, AFOSR under COE Grant FA9550-15-1-0171,0 and the Maryland Center for Nanophysics and Advanced Materials.

Nonlinear Elasticity of Doped Semiconductors

DTIC Science & Technology

2017-02-01

experimental data from the Stanford University group. The obtained results show that the goal of the project has been reached. MSU has full...length extension modes in n-doped silicon (Si) microelectromechanical (MEMS) resonators and have started a comparison with the experimental data from...coupling to shear strain modes. • Tested the theory against the existing in the literature experimental data on the effect of doping on the speed of

Efficiency of energy conversion in model biological pumps. Optimization by linear nonequilibrium thermodynamic relations.

PubMed

Stucki, J W; Compiani, M; Caplan, S R

1983-09-01

Experimental investigations showed linear relations between flows and forces in some biological energy converters operating far from equilibrium. This observation cannot be understood on the basis of conventional nonequilibrium thermodynamics. Therefore, the efficiencies of a linear and a nonlinear mode of operation of an energy converter (a hypothetical redox-driven H+ pump) were compared. This comparison revealed that at physiological values of the forces and degrees of coupling (1) the force ratio permitting optimal efficiency was much higher in the linear than in the nonlinear mode and (2) the linear mode of operation was at least 10(6)-times more efficient that the nonlinear one. These observations suggest that the experimentally observed linear relations between flows and forces, particularly in the case of oxidative phosphorylation, may be due to a feedback regulation maintaining linear thermodynamic relations far from equilibrium. This regulation may have come about as the consequence of an evolutionary drive towards higher efficiency.

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.

Networked dynamical systems with linear coupling: synchronisation patterns, coherence and other behaviours.

PubMed

Judd, Kevin

2013-12-01

Many physical and biochemical systems are well modelled as a network of identical non-linear dynamical elements with linear coupling between them. An important question is how network structure affects chaotic dynamics, for example, by patterns of synchronisation and coherence. It is shown that small networks can be characterised precisely into patterns of exact synchronisation and large networks characterised by partial synchronisation at the local and global scale. Exact synchronisation modes are explained using tools of symmetry groups and invariance, and partial synchronisation is explained by finite-time shadowing of exact synchronisation modes.

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.

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.

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

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.

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.

Fitting and forecasting coupled dark energy in the non-linear regime

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

Casas, Santiago; Amendola, Luca; Pettorino, Valeria

2016-01-01

We consider cosmological models in which dark matter feels a fifth force mediated by the dark energy scalar field, also known as coupled dark energy. Our interest resides in estimating forecasts for future surveys like Euclid when we take into account non-linear effects, relying on new fitting functions that reproduce the non-linear matter power spectrum obtained from N-body simulations. We obtain fitting functions for models in which the dark matter-dark energy coupling is constant. Their validity is demonstrated for all available simulations in the redshift range 0z=–1.6 and wave modes below 0k=1 h/Mpc. These fitting formulas can be used tomore » test the predictions of the model in the non-linear regime without the need for additional computing-intensive N-body simulations. We then use these fitting functions to perform forecasts on the constraining power that future galaxy-redshift surveys like Euclid will have on the coupling parameter, using the Fisher matrix method for galaxy clustering (GC) and weak lensing (WL). We find that by using information in the non-linear power spectrum, and combining the GC and WL probes, we can constrain the dark matter-dark energy coupling constant squared, β{sup 2}, with precision smaller than 4% and all other cosmological parameters better than 1%, which is a considerable improvement of more than an order of magnitude compared to corresponding linear power spectrum forecasts with the same survey specifications.« less

Effects due to induced azimuthal eddy currents in a self-exciting Faraday disk homopolar dynamo with a nonlinear series motor. I.. Two special cases

NASA Astrophysics Data System (ADS)

Hide, Raymond; Moroz, Irene M.

1999-10-01

The elucidation of the behaviour of physically realistic self-exciting Faraday-disk dynamos bears inter alia on attempts by theoretical geophysicists to interpret observations of geomagnetic polarity reversals. Hide [The nonlinear differential equations governing a hierarchy of self-exciting coupled Faraday-disk homopolar dynamos, Phys. Earth Planet. Interiors 103 (1997) 281-291; Nonlinear quenching of current fluctuations in a self-exciting homopolar dynamo, Nonlinear Processes in Geophysics 4 (1998) 201-205] has introduced a novel 4-mode set of nonlinear ordinary differential equations to describe such a dynamo in which a nonlinear electric motor is connected in series with the coil. The applied couple, α, driving the disk is steady and the Lorentz couple driving the motor is a quadratic function, x(1-ɛ)+ɛσx 2, of the dynamo-generated current x, with 0≤ɛ≤1. When there are no additional biasing effects due to background magnetic fields etc., the behaviour of the dynamo is determined by eight independent non-negative control parameters. These include ρ, proportional to the resistance of the disk to azimuthal eddy currents, and β, an inverse measure of the moment of inertia of the armature of the motor. When β=0 (the case when the motor is absent and ɛ and σ are redundant) and ρ -1≠0 , the 4-mode dynamo equations reduce to the 3-mode Lorenz equations, which can behave chaotically [E. Knobloch, Chaos in the segmented disc dynamo, Phys. Lett. A 82 (1981) 439-440]. When β≠0 but ρ -1=0 , the 4-mode set of equations reduces to a 3-mode dynamo [R. Hide (1997), see above], which can also behave chaotically when ɛ=0 [R. Hide, A.C. Skeldon, D.J. Acheson, A study of two novel self-exciting single-disk homopolar dynamos: theory, Proc. R. Soc. Lond. A 452 (1996) 1369-1395] but not when ɛ=1 [R. Hide (1998), see above]. In the latter case, however, all persistent fluctuations are completely quenched [R. Hide (1998), see above]. In this paper we investigate two limiting cases of ɛ=0 and ɛ=1 in the 4-mode dynamo when azimuthal eddy currents are allowed to flow i.e. cases when ρ -1=0 ; in a companion paper [I.M. Moroz, R. Hide, Effects due to induced azimuthal eddy currents in the Faraday disk self-exciting homopolar dynamo with a nonlinear series motor: II The general case, 1999, submitted] we extend the present analysis to the general case of 0≤ɛ≤1. When ɛ=0, chaotic behaviour occurs even more extensively in parameter space in the presence of azimuthal eddy currents than in their absence. When ɛ=1, the quenching of chaotic and all other non-steady dynamo action is no longer complete, for aperiodic solutions are found within limited regions of parameter space where β is very small and α is very large.

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.

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.

Design of cladding rods-assisted depressed-core few-mode fibers with improved modal spacing

NASA Astrophysics Data System (ADS)

Han, Jiawei; Zhang, Jie

2018-03-01

This paper investigates the design details of cladding rods-assisted (CRA) depressed-core (DC) few-mode fibers (FMFs) that feature more equally spaced linearly polarized (LP) modal effective indices, suitable for high-spatial-density weakly-coupled mode-division multiplexing systems. The influences of the index profile of cladding rods on LP mode-resolved effective index, bending sensitivity, and effective area Aeff, are numerically described. Based on the design considerations of LP modal Aeff-dependent spatial efficiency and LP modal bending loss-dependent robustness, the small LP21-LP02 and LP22-LP03 modal spacing limitations, encountered in state-of-the-art weakly-coupled step-index FMFs, have been substantially improved by at least 25%. In addition, the proposed CRA DC FMFs also show sufficiently large effective areas (in excess of 110 μm2) for all guided LP modes, which are expected to exhibit good nonlinear performance.

Coupled equations of electromagnetic waves in nonlinear metamaterial waveguides.

PubMed

Azari, Mina; Hatami, Mohsen; Meygoli, Vahid; Yousefi, Elham

2016-11-01

Over the past decades, scientists have presented ways to manipulate the macroscopic properties of a material at levels unachieved before, and called them metamaterials. This research can be considered an important step forward in electromagnetics and optics. In this study, higher-order nonlinear coupled equations in a special kind of metamaterial waveguides (a planar waveguide with metamaterial core) will be derived from both electric and magnetic components of the transverse electric mode of electromagnetic pulse propagation. On the other hand, achieving the refractive index in this research is worthwhile. It is also shown that the coupled equations are not symmetric with respect to the electric and magnetic fields, unlike these kinds of equations in fiber optics and dielectric waveguides. Simulations on the propagation of a fundamental soliton pulse in a nonlinear metamaterial waveguide near the resonance frequency (a little lower than the magnetic resonant frequency) are performed to study its behavior. These pulses are recommended to practice in optical communications in controlled switching by external voltage, even in low power.

Manipulating Nonlinear Emission and Cooperative Effect of CdSe/ZnS Quantum Dots by Coupling to a Silver Nanorod Complex Cavity

PubMed Central

Nan, Fan; Cheng, Zi-Qiang; Wang, Ya-Lan; Zhang, Qing; Zhou, Li; Yang, Zhong-Jian; Zhong, Yu-Ting; Liang, Shan; Xiong, Qihua; Wang, Qu-Quan

2014-01-01

Colloidal semiconductor quantum dots have three-dimensional confined excitons with large optical oscillator strength and gain. The surface plasmons of metallic nanostructures offer an efficient tool to enhance exciton-exciton coupling and excitation energy transfer at appropriate geometric arrangement. Here, we report plasmon-mediated cooperative emissions of approximately one monolayer of ensemble CdSe/ZnS quantum dots coupled with silver nanorod complex cavities at room temperature. Power-dependent spectral shifting, narrowing, modulation, and amplification are demonstrated by adjusting longitudinal surface plasmon resonance of silver nanorods, reflectivity and phase shift of silver nanostructured film, and mode spacing of the complex cavity. The underlying physical mechanism of the nonlinear excitation energy transfer and nonlinear emissions are further investigated and discussed by using time-resolved photoluminescence and finite-difference time-domain numerical simulations. Our results suggest effective strategies to design active plasmonic complex cavities for cooperative emission nanodevices based on semiconductor quantum dots. PMID:24787617

Multi-faults decoupling on turbo-expander using differential-based ensemble empirical mode decomposition

NASA Astrophysics Data System (ADS)

Li, Hongguang; Li, Ming; Li, Cheng; Li, Fucai; Meng, Guang

2017-09-01

This paper dedicates on the multi-faults decoupling of turbo-expander rotor system using Differential-based Ensemble Empirical Mode Decomposition (DEEMD). DEEMD is an improved version of DEMD to resolve the imperfection of mode mixing. The nonlinear behaviors of the turbo-expander considering temperature gradient with crack, rub-impact and pedestal looseness faults are investigated respectively, so that the baseline for the multi-faults decoupling can be established. DEEMD is then utilized on the vibration signals of the rotor system with coupling faults acquired by numerical simulation, and the results indicate that DEEMD can successfully decouple the coupling faults, which is more efficient than EEMD. DEEMD is also applied on the vibration signal of the misalignment coupling with rub-impact fault obtained during the adjustment of the experimental system. The conclusion shows that DEEMD can decompose the practical multi-faults signal and the industrial prospect of DEEMD is verified as well.

Observation of beat oscillation generation by coupled waves associated with parametric decay during radio frequency wave heating of a spherical tokamak plasma.

PubMed

Nagashima, Yoshihiko; Oosako, Takuya; Takase, Yuichi; Ejiri, Akira; Watanabe, Osamu; Kobayashi, Hiroaki; Adachi, Yuuki; Tojo, Hiroshi; Yamaguchi, Takashi; Kurashina, Hiroki; Yamada, Kotaro; An, Byung Il; Kasahara, Hiroshi; Shimpo, Fujio; Kumazawa, Ryuhei; Hayashi, Hiroyuki; Matsuzawa, Haduki; Hiratsuka, Junichi; Hanashima, Kentaro; Kakuda, Hidetoshi; Sakamoto, Takuya; Wakatsuki, Takuma

2010-06-18

We present an observation of beat oscillation generation by coupled modes associated with parametric decay instability (PDI) during radio frequency (rf) wave heating experiments on the Tokyo Spherical Tokamak-2. Nearly identical PDI spectra, which are characterized by the coexistence of the rf pump wave, the lower-sideband wave, and the low-frequency oscillation in the ion-cyclotron range of frequency, are observed at various locations in the edge plasma. A bispectral power analysis was used to experimentally discriminate beat oscillation from the resonant mode for the first time. The pump and lower-sideband waves have resonant mode components, while the low-frequency oscillation is exclusively excited by nonlinear coupling of the pump and lower-sideband waves. Newly discovered nonlocal transport channels in spectral space and in real space via PDI are described.

Cascading and local-field effects in non-linear optics revisited: a quantum-field picture based on exchange of photons.

PubMed

Bennett, Kochise; Mukamel, Shaul

2014-01-28

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).

Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia

NASA Astrophysics Data System (ADS)

Ben Amar, Martine; Bianca, Carlo

2016-09-01

We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k0. However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.

Nonlinear microrheology of dense colloidal suspensions: A mode-coupling theory

NASA Astrophysics Data System (ADS)

Gazuz, I.; Fuchs, M.

2013-03-01

A mode-coupling theory for the motion of a strongly forced probe particle in a dense colloidal suspension is presented. Starting point is the Smoluchowski equation for N bath and a single probe particle. The probe performs Brownian motion under the influence of a strong constant and uniform external force Fex. It is immersed in a dense homogeneous bath of (different) particles also performing Brownian motion. Fluid and glass states are considered; solvent flow effects are neglected. Based on a formally exact generalized Green-Kubo relation, mode coupling approximations are performed and an integration through transients approach applied. A microscopic theory for the nonlinear velocity-force relations of the probe particle in a dense fluid and for the (de-) localized probe in a glass is obtained. It extends the mode coupling theory of the glass transition to strongly forced tracer motion and describes active microrheology experiments. A force threshold is identified which needs to be overcome to pull the probe particle free in a glass. For the model of hard sphere particles, the microscopic equations for the threshold force and the probability density of the localized probe are solved numerically. Neglecting the spatial structure of the theory, a schematic model is derived which contains two types of bifurcation, the glass transition and the force-induced delocalization, and which allows for analytical and numerical solutions. We discuss its phase diagram, forcing effects on the time-dependent correlation functions, and the friction increment. The model was successfully applied to simulations and experiments on colloidal hard sphere systems [Gazuz , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.102.248302 102, 248302 (2009)], while we provide detailed information on its derivation and general properties.

Signal Processing, Pattern Formation and Adaptation in Neural Oscillators

DTIC Science & Technology

2016-11-29

nonlinear oscillations of outer hair cells. We obtained analytical forms for auditory tuning curves of both unidirectionally and bidirectionally coupled...oscillations of outer hair cells in the cochlea, mode-locking of chopper cells to sound in the cochlear nucleus, and entrainment of cortical...oscillations of outer hair cells (e.g., Fredrickson-Hemsing, Ji, Bruinsma, & Bozovic, 2012), mode-locking of choppers in the cochlear nucleus (e.g., Laudanski

Tunable phonon-induced transparency in bilayer graphene nanoribbons.

PubMed

Yan, Hugen; Low, Tony; Guinea, Francisco; Xia, Fengnian; Avouris, Phaedon

2014-08-13

In the phenomenon of plasmon-induced transparency, which is a classical analogue of electromagnetically induced transparency (EIT) in atomic gases, the coherent interference between two plasmon modes results in an optical transparency window in a broad absorption spectrum. With the requirement of contrasting lifetimes, typically one of the plasmon modes involved is a dark mode that has limited coupling to the electromagnetic radiation and possesses relatively longer lifetime. Plasmon-induced transparency not only leads to light transmission at otherwise opaque frequency regions but also results in the slowing of light group velocity and enhanced optical nonlinearity. In this article, we report an analogous behavior, denoted as phonon-induced transparency (PIT), in AB-stacked bilayer graphene nanoribbons. Here, light absorption due to the plasmon excitation is suppressed in a narrow window due to the coupling with the infrared active Γ-point optical phonon, whose function here is similar to that of the dark plasmon mode in the plasmon-induced transparency. We further show that PIT in bilayer graphene is actively tunable by electrostatic gating and estimate a maximum slow light factor of around 500 at the phonon frequency of 1580 cm(-1), based on the measured spectra. Our demonstration opens an avenue for the exploration of few-photon nonlinear optics and slow light in this novel two-dimensional material.

Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers

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

Campione, Salvatore; Wendt, Joel R.; Keeler, Gordon Arthur

Epsilon-near-zero (ENZ) modes provide a new path for tailoring light–matter interactions at the nanoscale. In this paper, we analyze a strongly coupled system at near-infrared frequencies comprising plasmonic metamaterial resonators and ENZ modes supported by degenerately doped semiconductor nanolayers. In strongly coupled systems that combine optical cavities and intersubband transitions, the polariton splitting (i.e., the ratio of Rabi frequency to bare cavity frequency) scales with the square root of the wavelength, thus favoring the long-wavelength regime. In contrast, we observe that the polariton splitting in ENZ/metamaterial resonator systems increases linearly with the thickness of the nanolayer supporting the ENZ modes.more » In this work, we employ an indium-tin-oxide nanolayer and observe a large experimental polariton splitting of approximately 30% in the near-infrared. As a result, this approach opens up many promising applications, including nonlinear optical components and tunable optical filters based on controlling the polariton splitting by adjusting the frequency of the ENZ mode.« less

Near-infrared strong coupling between metamaterials and epsilon-near-zero modes in degenerately doped semiconductor nanolayers

DOE PAGES

Campione, Salvatore; Wendt, Joel R.; Keeler, Gordon Arthur; ...

2016-01-14

Epsilon-near-zero (ENZ) modes provide a new path for tailoring light–matter interactions at the nanoscale. In this paper, we analyze a strongly coupled system at near-infrared frequencies comprising plasmonic metamaterial resonators and ENZ modes supported by degenerately doped semiconductor nanolayers. In strongly coupled systems that combine optical cavities and intersubband transitions, the polariton splitting (i.e., the ratio of Rabi frequency to bare cavity frequency) scales with the square root of the wavelength, thus favoring the long-wavelength regime. In contrast, we observe that the polariton splitting in ENZ/metamaterial resonator systems increases linearly with the thickness of the nanolayer supporting the ENZ modes.more » In this work, we employ an indium-tin-oxide nanolayer and observe a large experimental polariton splitting of approximately 30% in the near-infrared. As a result, this approach opens up many promising applications, including nonlinear optical components and tunable optical filters based on controlling the polariton splitting by adjusting the frequency of the ENZ mode.« less

Controllability in tunable chains of coupled harmonic oscillators

NASA Astrophysics Data System (ADS)

Buchmann, L. F.; Mølmer, K.; Petrosyan, D.

2018-04-01

We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N -1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach any desired Gaussian state requires at most 3 N (N -1 )/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides.

Finding structure in the dark: Coupled dark energy, weak lensing, and the mildly nonlinear regime

NASA Astrophysics Data System (ADS)

Miranda, Vinicius; González, Mariana Carrillo; Krause, Elisabeth; Trodden, Mark

2018-03-01

We reexamine interactions between the dark sectors of cosmology, with a focus on robust constraints that can be obtained using only mildly nonlinear scales. While it is well known that couplings between dark matter and dark energy can be constrained to the percent level when including the full range of scales probed by future optical surveys, calibrating matter power spectrum emulators to all possible choices of potentials and couplings requires many computationally expensive n-body simulations. Here we show that lensing and clustering of galaxies in combination with the cosmic microwave background (CMB) are capable of probing the dark sector coupling to the few percent level for a given class of models, using only linear and quasilinear Fourier modes. These scales can, in principle, be described by semianalytical techniques such as the effective field theory of large-scale structure.

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)

Semiconductor quantum well irradiated by a two-mode electromagnetic field as a terahertz emitter

NASA Astrophysics Data System (ADS)

Mandal, S.; Liew, T. C. H.; Kibis, O. V.

2018-04-01

We study theoretically the nonlinear optical properties of a semiconductor quantum well (QW) irradiated by a two-mode electromagnetic wave consisting of a strong resonant dressing field and a weak off-resonant driving field. In the considered strongly coupled electron-field system, the dressing field opens dynamic Stark gaps in the electron energy spectrum of the QW, whereas the driving field induces electron oscillations in the QW plane. Since the gapped electron spectrum restricts the amplitude of the oscillations, the emission of a frequency comb from the QW appears. Therefore, the doubly driven QW operates as a nonlinear optical element which can be used, particularly, for optically controlled generation of terahertz radiation.

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

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

Weinberg, Nevin N.; Arras, Phil; Burkart, Joshua, E-mail: nevin@mit.edu

2013-06-01

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

Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper.

PubMed

Barclay, Paul; Srinivasan, Kartik; Painter, Oskar

2005-02-07

A technique is demonstrated which efficiently transfers light between a tapered standard single-mode optical fiber and a high-Q, ultra-small mode volume, silicon photonic crystal resonant cavity. Cavity mode quality factors of 4.7x10(4) are measured, and a total fiber-to-cavity coupling efficiency of 44% is demonstrated. Using this efficient cavity input and output channel, the steady-state nonlinear absorption and dispersion of the photonic crystal cavity is studied. Optical bistability is observed for fiber input powers as low as 250 microW, corresponding to a dropped power of 100 microW and 3 fJ of stored cavity energy. A high-density effective free-carrier lifetime for these silicon photonic crystal resonators of ~ 0.5 ns is also estimated from power dependent loss and dispersion measurements.

Nonlinear magnetic electron tripolar vortices in streaming plasmas.

PubMed

Vranjes, J; Marić, G; Shukla, P K

2000-06-01

Magnetic electron modes in nonuniform magnetized and unmagnetized streaming plasmas, with characteristic frequencies between the ion and electron plasma frequencies and at spatial scales of the order of the collisionless skin depth, are studied. Two coupled equations, for the perturbed (in the case of magnetized plasma) or self-generated (for the unmagnetized plasma case) magnetic field, and the temperature, are solved in the strongly nonlinear regime and stationary traveling solutions in the form of tripolar vortices are found.

Observation of Quasi-Two-Dimensional Nonlinear Interactions in a Drift-Wave Streamer

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

Yamada, T.; Nagashima, Y.; Itoh, S.-I.

2010-11-26

A streamer, which is a bunching of drift-wave fluctuations, and its mediator, which generates the streamer by coupling with other fluctuations, have been observed in a cylindrical magnetized plasma. Their radial structures were investigated in detail by using the biphase analysis. Their quasi-two-dimensional structures were revealed to be equivalent with a pair of fast and slow modes predicted by a nonlinear Schroedinger equation based on the Hasegawa-Mima model.

Post-filament self-trapping of ultrashort laser pulses.

PubMed

Mitrofanov, A V; Voronin, A A; Sidorov-Biryukov, D A; Andriukaitis, G; Flöry, T; Pugžlys, A; Fedotov, A B; Mikhailova, J M; Panchenko, V Ya; Baltuška, A; Zheltikov, A M

2014-08-15

Laser filamentation is understood to be self-channeling of intense ultrashort laser pulses achieved when the self-focusing because of the Kerr nonlinearity is balanced by ionization-induced defocusing. Here, we show that, right behind the ionized region of a laser filament, ultrashort laser pulses can couple into a much longer light channel, where a stable self-guiding spatial mode is sustained by the saturable self-focusing nonlinearity. In the limiting regime of negligibly low ionization, this post-filamentation beam dynamics converges to a large-scale beam self-trapping scenario known since the pioneering work on saturable self-focusing nonlinearities.

A possible mechanism of current termination in a reversed field pinch

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

Nagata, A.; Masamune, S.; Arimoto, H.

1989-10-01

A rapid growth of magnetic fluctuations resulting from the {ital m}=1 and {ital m}=2 modes and succeeding stop of rotation of these modes have been found as the precursor phenomena of current termination in the STP-3(M) (Trans. Inst. Elec. Eng. Jpn. {bold 107}-{bold B}, 469 (1987)) reversed field pinch. By deepening the field reversal at the wall, these precursors disappear and the current duration becomes much longer. It is found that sudden current termination is caused by a rapid growth of resistive tearing modes mainly because of nonlinear coupling of the {ital m}=1 mode.

Amplitude Modulation of Pulsation Modes in Delta Scuti Stars

NASA Astrophysics Data System (ADS)

Bowman, Dominic M.

2017-10-01

The pulsations in δ Sct stars are excited by a heat engine driving mechanism caused by increased opacity in their surface layers, and have pulsation periods of order a few hours. Space based observations in the last decade have revealed a diverse range of pulsational behaviour in these stars, which is investigated using an ensemble of 983 δ Sct stars observed continuously for 4 yr by the Kepler Space Telescope. A statistical search for amplitude modulation of pulsation modes is carried out and it is shown that 61.3 per cent of the 983 δ Sct stars exhibit significant amplitude modulation in at least a single pulsation mode, and that this is uncorrelated with effective temperature and surface gravity. Hence, the majority of δ Sct stars exhibit amplitude modulation, with time-scales of years and longer demonstrated to be significant in these stars both observationally and theoretically. An archetypal example of amplitude modulation in a δ Sct star is KIC 7106205, which contains only a single pulsation mode that varies significantly in amplitude whilst all other pulsation modes stay constant in amplitude and phase throughout the 4-yr Kepler data set. Therefore, the visible pulsational energy budget in this star, and many others, is not conserved over 4 yr. Models of beating of close-frequency pulsation modes are used to identify δ Sct stars with frequencies that lie closer than 0.001 d^{-1}, which are barely resolved using 4 yr of Kepler observations, and maintain their independent identities over 4 yr. Mode coupling models are used to quantify the strength of coupling and distinguish between non-linearity in the form of combination frequencies and non-linearity in the form of resonant mode coupling for families of pulsation modes in several stars. The changes in stellar structure caused by stellar evolution are investigated for two high amplitude δ Sct (HADS) stars in the Kepler data set, revealing a positive quadratic change in phase for the fundamental and first overtone radial modes in KIC 5950759. The observed phase modulation of the radial modes in this star is two orders of magnitude larger than predicted by stellar evolutionary models, yet is consistent with the prediction of increasing periods of radial modes for stars on the main sequence. The statistical analysis of 983 δ Sct stars, including the results from the search for amplitude modulation, is a valuable resource for ongoing and future space missions such as K2, TESS and PLATO, because the high quality 4-yr Kepler data set will not be surpassed for some time. The observational studies of individual stars in this thesis provide strong evidence that non-linear processes are clearly at work in the majority of δ Sct stars, and provide valuable constraints for future asteroseismic modelling.

Transfer of dipolar gas through the discrete localized mode.

PubMed

Bai, Xiao-Dong; Zhang, Ai-Xia; Xue, Ju-Kui

2013-12-01

By considering the discrete nonlinear Schrödinger model with dipole-dipole interactions for dipolar condensate, the existence, the types, the stability, and the dynamics of the localized modes in a nonlinear lattice are discussed. It is found that the contact interaction and the dipole-dipole interactions play important roles in determining the existence, the type, and the stability of the localized modes. Because of the coupled effects of the contact interaction and the dipole-dipole interactions, rich localized modes and their stability nature can exist: when the contact interaction is larger and the dipole-dipole interactions is smaller, a discrete bright breather occurs. In this case, while the on-site interaction can stabilize the discrete breather, the dipole-dipole interactions will destabilize the discrete breather; when both the contact interaction and the dipole-dipole interactions are larger, a discrete kink appears. In this case, both the on-site interaction and the dipole-dipole interactions can stabilize the discrete kink, but the discrete kink is more unstable than the ordinary discrete breather. The predicted results provide a deep insight into the dynamics of blocking, filtering, and transfer of the norm in nonlinear lattices for dipolar condensates.

On non-local energy transfer via zonal flow in the Dimits shift

DOE PAGES

St-Onge, Denis A.

2017-10-10

The two-dimensional Terry–Horton equation is shown to exhibit the Dimits shift when suitably modified to capture both the nonlinear enhancement of zonal/drift-wave interactions and the existence of residual Rosenbluth–Hinton states. This phenomenon persists through numerous simplifications of the equation, including a quasilinear approximation as well as a four-mode truncation. It is shown that the use of an appropriate adiabatic electron response, for which the electrons are not affected by the flux-averaged potential, results in anmore » $$\\boldsymbol{E}\\times \\boldsymbol{B}$$ nonlinearity that can efficiently transfer energy non-locally to length scales of the order of the sound radius. The size of the shift for the nonlinear system is heuristically calculated and found to be in excellent agreement with numerical solutions. The existence of the Dimits shift for this system is then understood as an ability of the unstable primary modes to efficiently couple to stable modes at smaller scales, and the shift ends when these stable modes eventually destabilize as the density gradient is increased. This non-local mechanism of energy transfer is argued to be generically important even for more physically complete systems.« less

Magnetic and velocity fluctuations from nonlinearly coupled tearing modes in the reversed field pinch with and without the reversal surface

NASA Astrophysics Data System (ADS)

Craig, D.; Martin, D.; Den Hartog, D. J.; Nornberg, M. D.; Reusch, J. A.

2017-08-01

We investigate the role of poloidal mode number m = 0 fluctuations on m = 1 velocity and magnetic field fluctuations in the Reversed Field Pinch (RFP). Removing the m = 0 resonant surface in the Madison Symmetric Torus (MST), results in suppressed m = 0 activity without a reduction in m = 1 magnetic activity. However, the m = 1 velocity fluctuations and fluctuation-induced mean emf are reduced as m = 0 modes are suppressed. Velocity fluctuations are measured directly using fast Doppler spectroscopy. Similar results are seen in visco-resistive MHD simulation with the DEBS code. An artificial line-averaged velocity diagnostic is developed for DEBS simulations to facilitate direct comparisons with experimental measurements. The sensitivity of the m = 1 velocity fluctuations and corresponding emf to changes in m = 0 mode activity is a feature of tearing modes in the nonlinear regime with a spectrum of interacting modes. These results have implications for RFP sustainment strategies and inform our understanding of the role of magnetic turbulence in astrophysical contexts.

Nonlinear amplitude dynamics in flagellar beating

NASA Astrophysics Data System (ADS)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear amplitude dynamics in flagellar beating.

PubMed

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear amplitude dynamics in flagellar beating

PubMed Central

Casademunt, Jaume

2017-01-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating. PMID:28405357

Analytical formulation of orbiter-payload models coupled by trunnion joints with Coulomb friction

NASA Technical Reports Server (NTRS)

Liu, Frank C.

1987-01-01

An orbiter and its payload substructure are linked together by five trunnion joints which have thirty degrees-of-freedom. Geometric compatibility conditions require fourteen of the interface physical coordinates of the orbiter and payload to be equal to each other and the remaining sixteen are free to have relative motions under Coulomb friction. The component modes synthesis method using fourteen inertia relief attachment modes for the formulation of the coupled system is presented. The exact nonlinear friction function is derived based on the characteristics of the joints. Formulation is applicable to an orbiter that carries any number of payload substructures.

Analytical formulation of orbiter-payload coupled by trunnion joints with Coulomb friction

NASA Technical Reports Server (NTRS)

Liu, Frank C.

1986-01-01

An orbiter and its payload substructure are linked together by five trunnion joints which have thirty degrees-of-freedom. Geometric compatibility conditions require fourteen of the interface physical coordinates of the orbiter and payload to be equal to each other and the remaining sixteen are free to have relative motions under Coulomb friction. The component modes synthesis method using fourteen inertia relief attachment modes for the formulation of the coupled system is presented. The exact nonlinear friction function is derived based on the characteristics of the joints. Formulation is applicable to an orbiter that carries any number of payload substructures.

Optimal antibunching in passive photonic devices based on coupled nonlinear resonators

NASA Astrophysics Data System (ADS)

Ferretti, S.; Savona, V.; Gerace, D.

2013-02-01

We propose the use of weakly nonlinear passive materials for prospective applications in integrated quantum photonics. It is shown that strong enhancement of native optical nonlinearities by electromagnetic field confinement in photonic crystal resonators can lead to single-photon generation only exploiting the quantum interference of two coupled modes and the effect of photon blockade under resonant coherent driving. For realistic system parameters in state of the art microcavities, the efficiency of such a single-photon source is theoretically characterized by means of the second-order correlation function at zero-time delay as the main figure of merit, where major sources of loss and decoherence are taken into account within a standard master equation treatment. These results could stimulate the realization of integrated quantum photonic devices based on non-resonant material media, fully integrable with current semiconductor technology and matching the relevant telecom band operational wavelengths, as an alternative to single-photon nonlinear devices based on cavity quantum electrodynamics with artificial atoms or single atomic-like emitters.

Coupled ion acoustic and drift waves in magnetized superthermal electron-positron-ion plasmas

NASA Astrophysics Data System (ADS)

Adnan, Muhammad; Mahmood, S.; Qamar, Anisa

2014-09-01

Linear and nonlinear coupled drift-ion acoustic waves are investigated in a nonuniform magnetoplasma having kappa distributed electrons and positrons. In the linear regime, the role of kappa distribution and positron content on the dispersion relation has been highlighted; it is found that strong superthermality (low value of κ) and addition of positrons lowers the phase velocity via decreasing the fundamental scalelengths of the plasmas. In the nonlinear regime, first, coherent nonlinear structure in the form of dipoles and monopoles are obtained and the boundary conditions (boundedness) in the context of superthermality and positron concentrations are discussed. Second, in case of scalar nonlinearity, a Korteweg-de Vries-type equation is obtained, which admit solitary wave solution. It is found that both compressive and rarefactive solitons are formed in the present model. The present work may be useful to understand the low frequency electrostatic modes in inhomogeneous electron positron ion plasmas, which exist in astrophysical plasma situations such as those found in the pulsar magnetosphere.

Linear and nonlinear dynamics of current-driven waves in dusty plasmas

NASA Astrophysics Data System (ADS)

Ahmad, Ali; Ali Shan, S.; Haque, Q.; Saleem, H.

2012-09-01

The linear and nonlinear dynamics of a recently proposed plasma mode of dusty plasma is studied using kappa distribution for electrons. This electrostatic wave can propagate in the plasma due to the sheared flow of electrons and ions parallel to the external magnetic field in the presence of stationary dust. The coupling of this wave with the usual drift wave and ion acoustic wave is investigated. D'Angelo's mode is also modified in the presence of superthermal electrons. In the nonlinear regime, the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn's magnetosphere corresponding to negatively charged dust grains. But the theoretical model is applicable for positively charged dust as well. This work will be useful for future observations and studies of dusty environments of planets and comets.

Coupled multi-disciplinary simulation of composite engine structures in propulsion environment

NASA Technical Reports Server (NTRS)

Chamis, Christos C.; Singhal, Surendra N.

1992-01-01

A computational simulation procedure is described for the coupled response of multi-layered multi-material composite engine structural components which are subjected to simultaneous multi-disciplinary thermal, structural, vibration, and acoustic loadings including the effect of hostile environments. The simulation is based on a three dimensional finite element analysis technique in conjunction with structural mechanics codes and with acoustic analysis methods. The composite material behavior is assessed at the various composite scales, i.e., the laminate/ply/constituents (fiber/matrix), via a nonlinear material characterization model. Sample cases exhibiting nonlinear geometrical, material, loading, and environmental behavior of aircraft engine fan blades, are presented. Results for deformed shape, vibration frequency, mode shapes, and acoustic noise emitted from the fan blade, are discussed for their coupled effect in hot and humid environments. Results such as acoustic noise for coupled composite-mechanics/heat transfer/structural/vibration/acoustic analyses demonstrate the effectiveness of coupled multi-disciplinary computational simulation and the various advantages of composite materials compared to metals.

Numerical simulations of an elastica pendulum

NASA Astrophysics Data System (ADS)

Sinclair, R.

Folklore would have it that a massless clamped-free elastica undergoing planar motion with a point end mass possesses periodic solutions corresponding to a single mode of oscillation. We present a battery of numerical simulations leading to the single conclusion that these supposed periodic solutions do not exist, due to a strong nonlinear coupling of two modes, the frequency of one of which is apparently inversely proportional to the magnitude of the force acting on the elastica.

State and Parameter Estimation for a Coupled Ocean--Atmosphere Model

NASA Astrophysics Data System (ADS)

Ghil, M.; Kondrashov, D.; Sun, C.

2006-12-01

The El-Nino/Southern-Oscillation (ENSO) dominates interannual climate variability and plays, therefore, a key role in seasonal-to-interannual prediction. Much is known by now about the main physical mechanisms that give rise to and modulate ENSO, but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean--atmosphere model of ENSO. The coupled model consists of an upper-ocean, reduced-gravity model of the Tropical Pacific and a steady-state atmospheric response to the sea surface temperature (SST). The model errors are assumed to be mainly in the atmospheric wind stress, and assimilated data are equatorial Pacific SSTs. Model behavior is very sensitive to two key parameters: (i) μ, the ocean-atmosphere coupling coefficient between SST and wind stress anomalies; and (ii) δs, the surface-layer coefficient. Previous work has shown that δs determines the period of the model's self-sustained oscillation, while μ measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Estimation of these parameters is tested first on synthetic data and allows us to recover the delayed-oscillator mode starting from model parameter values that correspond to the westward-propagating case. Assimilation of SST data from the NCEP-NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean--atmosphere GCMs will be discussed.

Long distance transmission in few-mode fibers.

PubMed

Yaman, Fatih; Bai, Neng; Zhu, Benyuan; Wang, Ting; Li, Guifang

2010-06-07

Using multimode fibers for long-haul transmission is proposed and demonstrated experimentally. In particular few-mode fibers (FMFs) are demonstrated as a good compromise since they are sufficiently resistant to mode coupling compared to standard multimode fibers but they still can have large core diameters compared to single-mode fibers. As a result these fibers can have significantly less nonlinearity and at the same time they can have the same performance as single-mode fibers in terms of dispersion and loss. In the absence of mode coupling it is possible to use these fibers in the single-mode operation where all the data is carried in only one of the spatial modes throughout the fiber. It is shown experimentally that the single-mode operation is achieved simply by splicing single-mode fibers to both ends of a 35-km-long dual-mode fiber at 1310 nm. After 35 km of transmission, no modal dispersion or excess loss was observed. Finally the same fiber is placed in a recirculating loop and 3 WDM channels each carrying 6 Gb/s BPSK data were transmitted through 1050 km of the few-mode fiber without modal dispersion.

Amplitude mode oscillations in pump-probe photoemission spectra from a d -wave superconductor

NASA Astrophysics Data System (ADS)

Nosarzewski, B.; Moritz, B.; Freericks, J. K.; Kemper, A. F.; Devereaux, T. P.

2017-11-01

Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time- and angle-resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d -wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d -wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. We comment on the necessary conditions for detecting the amplitude mode in trARPES experiments.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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.

Nonlinear High-Energy Pulse Propagation in Graded-Index Multimode Optical Fibers for Mode-Locked Fiber Lasers

DTIC Science & Technology

2014-12-23

coupled for d = 2λ . Results are shown for the TE polarization , where the transverse electric field vector is pointing in the vertical direction in these...16, 42–44 (1991). 6. D. U. Noske, N. Pandit, and J. R. Taylor, “Subpicosecond soliton pulse formation from self-mode- locked erbium fibre laser using...High-Energy Pulse Propagation in Graded-Index Multimode Optical Fibers for Mode- Locked Fiber Lasers 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1

Anomalous vibrational modes in acetanilide: a F.D.S. incoherent inelastic neutron scattering study

NASA Astrophysics Data System (ADS)

Barthes, Mariette; Eckert, Juergen; Johnson, Susanna W.; Moret, Jacques; Swanson, Basil I.; Unkefer, Clifford J.

The origin of the anomalous infra-red and Raman modes in acetanilide (C6H5NHCOCH3, or ACN)(1) , remains a subject of considerable controversy. One family of theoretical models involves Davydov-like solitons (2) nonlinear vibrational coupling (3), or "polaronic" localized modes (4)(5). An alternative interpretation of the extra-bands in terms of a Fermi resonance was proposed (6) and recently the existence of slightly non-degenerate hydrogen atom configurations (7) in the H-bond was suggested as an explanation for the anomalies.

Quantum lattice representations for vector solitons in external potentials

NASA Astrophysics Data System (ADS)

Vahala, George; Vahala, Linda; Yepez, Jeffrey

2006-03-01

A quantum lattice algorithm is developed to examine the effect of an external potential well on exactly integrable vector Manakov solitons. It is found that the exact solutions to the coupled nonlinear Schrodinger equations act like quasi-solitons in weak potentials, leading to mode-locking, trapping and untrapping. Stronger potential wells will lead to the emission of radiation modes from the quasi-soliton initial conditions. If the external potential is applied to that particular mode polarization, then the radiation will be trapped within the potential well. The algorithm developed leads to a finite difference scheme that is unconditionally stable. The Manakov system in an external potential is very closely related to the Gross-Pitaevskii equation for the ground state wave functions of a coupled BEC state at T=0 K.

Nonlinear Two Fluid and Kinetic ELM Simulations

NASA Astrophysics Data System (ADS)

Strauss, H. R.; Sugiyama, L.; Chang, C. S.; Ku, S.; Hientzsch, B.; Breslau, J.; Park, W.; Samtaney, R.; Adams, M.; Jardin, S.

2006-04-01

Simulations of ELMs using dissipative MHD, two fluid MHD, and neoclassical kinetic physics models are being carried out using the M3D code [1]. Resistive MHD simulations of nonlinear edge pressure and current driven instabilities have been performed, initialized with realistic DIIID equilibria. Simulations show the saturation of the modes and relaxation of equilbrium profiles. Linear simulations including two fluid effects show the stabilization of toroidal mode number n = 10 modes, when the Hall parameter H, the ratio of ion skin depth to major radius, exceeds a threshhold. Nonlinear simulations are being done including gyroviscous stabilization. Kinetic effects are incorporated by coupling with the XGC code [2], which is able to simulate the edge plasma density and pressure pedestal buildup. These profiles are being used to initialize M3D simulations of an ELM crash and pedestal relaxation. The goal is to simulate an ELM cycle. [1] Park, W., Belova, E.V., Fu, G.Y., Tang, X.Z., Strauss, H.R., Sugiyama, L.E., Phys. Plas. 6, 1796 (1999).[2] Chang, C.S., Ku, S., and Weitzner, H., Phys. Plas. 11, 2649 (2004)

Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1992-10-01

If signal analyses were perfect without noise and clutters, then any transform can be equally chosen to represent the signal without any loss of information. However, if the analysis using Fourier transform (FT) happens to be a nonlinear dynamic phenomenon, the effect of nonlinearity must be postponed until a later time when a complicated mode-mode coupling is attempted without the assurance of any convergence. Alternatively, there exists a new paradigm of linear transforms called wavelet transform (WT) developed for French oil explorations. Such a WT enjoys the linear superposition principle, the computational efficiency, and the signal/noise ratio enhancement for a nonsinusoidal and nonstationary signal. Our extensions to a dynamic WT and furthermore to an adaptive WT are possible due to the fact that there exists a large set of square-integrable functions that are special solutions of the nonlinear dynamic medium and could be adopted for the WT. In order to analyze nonlinear dynamics phenomena in ocean, we are naturally led to the construction of a soliton mother wavelet. This common sense of 'pay the nonlinear price now and enjoy the linearity later' is certainly useful to probe any nonlinear dynamics. Research directions in wavelets, such as adaptivity, and neural network implementations are indicated, e.g., tailoring an active sonar profile for explorations.

Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials

NASA Astrophysics Data System (ADS)

Yang, Shengyan; Liu, Zhe; Xia, Xiaoxiang; E, Yiwen; Tang, Chengchun; Wang, Yujin; Li, Junjie; Wang, Li; Gu, Changzhi

2016-06-01

We experimentally demonstrate a metamaterial structure composed of two mirror-symmetric joint split ring resonators (JSRRs) that support extremely sharp trapped-mode resonance with a large modulation depth in the terahertz region. Contrary to the regular mirror-arranged SRR arrays in which both the subradiant inductive-capacitive (LC) resonance and quadrupole-mode resonance can be excited, our designed structure features a metallic microstrip bridging the adjacent SRRs, which leads to the emergence of an otherwise inaccessible ultrahigh-quality-factor resonance. The ultrasharp resonance occurs near the Wood-Rayleigh anomaly frequency, and the underlying mechanism can be attributed to the strong coupling between the in-plane propagating collective lattice surface mode originating from the array periodicity and localized surface plasmon resonance in mirror-symmetric coupled JSRRs, which dramatically reduces radiative damping. The ultrasharp resonance shows great potential for multifunctional applications such as plasmonic switching, low-power nonlinear processing, and chemical and biological sensing.

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

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

Femtojoule-scale all-optical latching and modulation via cavity nonlinear optics.

PubMed

Kwon, Yeong-Dae; Armen, Michael A; Mabuchi, Hideo

2013-11-15

We experimentally characterize Hopf bifurcation phenomena at femtojoule energy scales in a multiatom cavity quantum electrodynamical (cavity QED) system and demonstrate how such behaviors can be exploited in the design of all-optical memory and modulation devices. The data are analyzed by using a semiclassical model that explicitly treats heterogeneous coupling of atoms to the cavity mode. Our results highlight the interest of cavity QED systems for ultralow power photonic signal processing as well as for fundamental studies of mesoscopic nonlinear dynamics.

Modal control of an oblique wing aircraft

NASA Technical Reports Server (NTRS)

Phillips, James D.

1989-01-01

A linear modal control algorithm is applied to the NASA Oblique Wing Research Aircraft (OWRA). The control law is evaluated using a detailed nonlinear flight simulation. It is shown that the modal control law attenuates the coupling and nonlinear aerodynamics of the oblique wing and remains stable during control saturation caused by large command inputs or large external disturbances. The technique controls each natural mode independently allowing single-input/single-output techniques to be applied to multiple-input/multiple-output systems.

Triggering of longitudinal combustion instabilities in solid rocket motors: Nonlinear combustion response

NASA Technical Reports Server (NTRS)

Wicker, J. M.; Greene, W. D.; Kim, S. I.; Yang, V.

1995-01-01

Pulsed oscillations in solid rocket motors are investigated with emphasis on nonlinear combustion response. The study employs a wave equation governing the unsteady motions in a two-phase flow, and a solution technique based on spatial- and time-averaging. A wide class of combustion response functions is studied to second-order in fluctuation amplitude to determine if, when, and how triggered instabilities arise. Conditions for triggering are derived from analysis of limit cycles, and regions of triggering are found in parametric space. Based on the behavior of model dynamical systems, introduction of linear cross-coupling and quadratic self-coupling among the acoustic modes appears to be the manner in which the nonlinear combustion response produces triggering to a stable limit cycle. Regions of initial conditions corresponding to stable pulses were found, suggesting that stability depends on initial phase angle and harmonic content, as well as the composite amplitude, of the pulse.

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.

Plasmonic metamaterials with tuneable optical properties

NASA Astrophysics Data System (ADS)

Zayats, Anatoly

2008-03-01

Negative refraction in metamaterials has recently attracted significant attention due to its possible numerous applications in high-resolution imaging and photolithography with the so-called ``perfect lenses,'' for electromagnetic shielding (invisibility cloak), optical signal manipulation, etc. Among various realizations of negative index materials, plasmonic nanostructures play a prominent role as they allow negative refraction properties to be engineered in the visible and near infrared spectral ranges. The coupling of light to plasmonic modes, that are collective electronic excitations in metallic nanostructures, provides the possibility to confine the electromagnetic field on the sub-wavelength scale and manipulate it with high precision to achieve the desired mode dispersion and, thus, reflection, absorption and transmission properties of the nanostructures. In this talk we will discuss various pathways to control dispersion of the electromagnetic waves in plasmonic metamaterials, including plasmon polaritonic crystals and plasmonic nanorod arrays, and the approaches to active tuneability of their optical properties using optical and electric control signals. Both approaches take advantage of the very high sensitivity of surface plasmon mode dispersion on the refractive index of the dielectric adjacent to metallic nanostructure. Hybridization of plasmonic nanostructures with molecular species exhibiting nonlinear optical response allows the development of metamaterials with high effective nonlinear susceptibility due to the electromagnetic field enhancement related to plasmonic excitations. Signal and control light are then coupled to plasmonic modes that strongly interact via nonlinearity introduced by the hybridization. Concurrently, the use of electro-optically active dielectrics incorporated into plasmonic nanostructures provides the route to control optical signals electronically. Plasmonic metamaterials with tuneable optical properties can be used to control negative refraction and electromagnetic field propagation in various applications in nanophotonics, optoelectronics and optical communications.

Chemical event chain model of coupled genetic oscillators.

PubMed

Jörg, David J; Morelli, Luis G; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Chemical event chain model of coupled genetic oscillators

NASA Astrophysics Data System (ADS)

Jörg, David J.; Morelli, Luis G.; Jülicher, Frank

2018-03-01

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

Quantum information processing with a travelling wave of light

NASA Astrophysics Data System (ADS)

Serikawa, Takahiro; Shiozawa, Yu; Ogawa, Hisashi; Takanashi, Naoto; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We exploit quantum information processing on a traveling wave of light, expecting emancipation from thermal noise, easy coupling to fiber communication, and potentially high operation speed. Although optical memories are technically challenging, we have an alternative approach to apply multi-step operations on traveling light, that is, continuous-variable one-way computation. So far our achievement includes generation of a one-million-mode entangled chain in time-domain, mode engineering of nonlinear resource states, and real-time nonlinear feedforward. Although they are implemented with free space optics, we are also investigating photonic integration and performed quantum teleportation with a passive liner waveguide chip as a demonstration of entangling, measurement, and feedforward. We also suggest a loop-based architecture as another model of continuous-variable computing.

Nonlinear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.

1972-01-01

Two particular cases of nonlinear wave interaction in a plasma column were investigated. The frequencies of the waves were on the order of magnitude of the electron plasma frequency, and ion motion was neglected. The nonlinear coupling of slow waves on a plasma column was studied by means of cold plasma theory, and the case of a plasma column surrounded by an infinite dielectric in the absence of a magnetic field was also examined. Nonlinear scattering from a plasma column in an electromagnetic field having it's magnetic field parallel to the axis of the column was investigated. Some experimental results on mode conversion in the presence of loss are presented along with some observations of nonlinear scattering, The effect of the earth's magnetic field and of discharge symmetry on the radiation pattern are discussed.

Nonlinear optics in organic cavity polaritons (Conference Presentation)

NASA Astrophysics Data System (ADS)

Singer, Kenneth D.; Liu, Bin; Crescimanno, Michael; Twieg, Robert J.

2017-02-01

Coupling between excitons belonging to organic dyes and photons in a microcavities forming cavity polaritons have been receiving attention for their fundamental interest as well as potential applications in coherent light sources. Organic materials are of particular interest as the coupling is particularly strong due to the large oscillator strength of conjugated organic molecules. The resulting coupling in organic materials is routinely in the strong regime. Ultrastrong coupling between photons and excitons in microcavities containing organic dyes and semiconductors has been recently observed in room temperature. We have studied the coupling between cavity pairs in the ultrastrong regime and found that the high order terms in the modified Jaynes-Cummings model result in broken degeneracy between the symmetric and antisymmetric modes. The unusually strong coupling between cavity photons and organic excitons dovetail with the robust nonlinear optical responses of the same materials. This provides a new and promising hybrid material for photonics. We report on measurements of photorefraction in organic cavities containing a derivative of the photorefractive organic glass based on 2-dicyanomethylene-3-cyano-2,5-dihydrofuran (DCDHF).

Communication: Probing non-equilibrium vibrational relaxation pathways of highly excited C≡N stretching modes following ultrafast back-electron transfer.

PubMed

Lynch, Michael S; Slenkamp, Karla M; Khalil, Munira

2012-06-28

Fifth-order nonlinear visible-infrared spectroscopy is used to probe coherent and incoherent vibrational energy relaxation dynamics of highly excited vibrational modes indirectly populated via ultrafast photoinduced back-electron transfer in a trinuclear cyano-bridged mixed-valence complex. The flow of excess energy deposited into four C≡N stretching (ν(CN)) modes of the molecule is monitored by performing an IR pump-probe experiment as a function of the photochemical reaction (τ(vis)). Our results provide experimental evidence that the nuclear motions of the molecule are both coherently and incoherently coupled to the electronic charge transfer process. We observe that intramolecular vibrational relaxation dynamics among the highly excited ν(CN) modes change significantly en route to equilibrium. The experiment also measures a 7 cm(-1) shift in the frequency of a ∼57 cm(-1) oscillation reflecting a modulation of the coupling between the probed high-frequency ν(CN) modes for τ(vis) < 500 fs.

N-H Stretching Excitations in Adenosine-Thymidine Base Pairs in Solution: Base Pair Geometries, Infrared Line Shapes and Ultrafast Vibrational Dynamics

PubMed Central

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

2013-01-01

We explore the N-H stretching vibrations of adenosine-thymidine base pairs in chloroform solution with linear and nonlinear infrared spectroscopy. Based on estimates from NMR measurements and ab initio calculations, we conclude that adenosine and thymidine form hydrogen bonded base pairs in Watson-Crick, reverse Watson-Crick, Hoogsteen and reverse Hoogsteen configurations with similar probability. Steady-state concentration- and temperature dependent linear FT-IR studies, including H/D exchange experiments, reveal that these hydrogen-bonded base pairs have complex N-H/N-D stretching spectra with a multitude of spectral components. Nonlinear 2D-IR spectroscopic results, together with IR-pump-IR-probe measurements, as also corroborated by ab initio calculations, reveal that the number of N-H stretching transitions is larger than the total number of N-H stretching modes. This is explained by couplings to other modes, such as an underdamped low-frequency hydrogen-bond mode, and a Fermi resonance with NH2 bending overtone levels of the adenosine amino-group. Our results demonstrate that modeling based on local N-H stretching vibrations only is not sufficient and call for further refinement of the description of the N-H stretching manifolds of nucleic acid base pairs of adenosine and thymidine, incorporating a multitude of couplings with fingerprint and low-frequency modes. PMID:23234439

Bicoherence Analysis of Electrostatic Interchange Mode Coupling in a Turbulent Laboratory Magnetosphere

NASA Astrophysics Data System (ADS)

Abler, M. C.; Mauel, M. E.; Saperstein, A.

2017-12-01

Plasmas confined by a strong dipole field exhibit interchange and entropy mode turbulence, which previous experiments have shown respond locally to active feedback [1]. On the Collisionless Terrella Experiment (CTX), this turbulence is characterized by low frequency, low order, quasi-coherent modes with complex spectral dynamics. We apply bicoherence analysis [2] to study nonlinear phase coupling in a variety of scenarios. First, we study the self-interaction of the naturally occurring interchange turbulence; this analysis is then expanded to include the effects of single or multiple driven modes in the frequency range of the background turbulent oscillations. Initial measurements of coupling coefficients are presented in both cases. Driven low frequency interchange modes are observed to generate multiple harmonics which persist throughout the plasma, becoming weaker as they propagate away from the actuator in the direction of the electron magnetic drift. Future work is also discussed, including application of wavelet bicoherence analysis and applications to planetary magnetospheres. [1] Roberts, Mauel, and Worstell, Phys Plasmas (2015). [2] Grierson, Worstell, and Mauel, Phys Plasmas (2009). Supported by NSF-DOE Partnership for Plasma Science Grants DOE-DE-FG02-00ER54585 and NSF-PHY-1201896.

Heat perturbation spreading in the Fermi-Pasta-Ulam-β system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity

NASA Astrophysics Data System (ADS)

Xiong, Daxing

2017-06-01

We employ the heat perturbation correlation function to study thermal transport in the one-dimensional Fermi-Pasta-Ulam-β lattice with both nearest-neighbor and next-nearest-neighbor couplings. We find that such a system bears a peculiar phonon dispersion relation, and thus there exists a competition between phonon dispersion and nonlinearity that can strongly affect the heat correlation function's shape and scaling property. Specifically, for small and large anharmoncities, the scaling laws are ballistic and superdiffusive types, respectively, which are in good agreement with the recent theoretical predictions; whereas in the intermediate range of the nonlinearity, we observe an unusual multiscaling property characterized by a nonmonotonic delocalization process of the central peak of the heat correlation function. To understand these multiscaling laws, we also examine the momentum perturbation correlation function and find a transition process with the same turning point of the anharmonicity as that shown in the heat correlation function. This suggests coupling between the momentum transport and the heat transport, in agreement with the theoretical arguments of mode cascade theory.

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/.

Nonlinear dispersive waves in repulsive lattices

NASA Astrophysics Data System (ADS)

Mehrem, A.; Jiménez, N.; Salmerón-Contreras, L. J.; García-Andrés, X.; García-Raffi, L. M.; Picó, R.; Sánchez-Morcillo, V. J.

2017-07-01

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting of an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of the α -Fermi-Pasta-Ulam equation, describing a chain of masses connected by nonlinear quadratic springs and numerical simulations. The results can be extrapolated to other systems described by this equation.

Wave-Wave Coupling and Disasters: The 1985 Mexico Earthquake and the 2001 WTC Collapse

NASA Astrophysics Data System (ADS)

Lomnitz, C.

2002-12-01

Wave-wave coupling occurs in the presence of weak nonlinearity. It can generate quite dramatic, unexpected effects. In the 1985 earthquake disaster in Mexico City more than 400 high-rise buildings collapsed on soft ground with a loss of life of around 10,000. The emergence of a large, monochromatic, coherent ground wave was an unforeseen factor. Linear modeling failed to reproduce the main features of this signal including the prominent spectral peak close to the resonant frequency of the high-rise buildings, and an extremely long time duration (more than five minutes). The signal was apparently due to coupling of a fundamental Rayleigh mode to the quarter-wavelength shear resonance in the surface mud layer through their common frequency at 0.4 Hz. An additional unexpected feature was the low attenuation of these modes in the mud layer, and the presence of prograde particle motion. Prograde rotation, though not necessarily caused by nonlinear effects, will couple with structural modes of vibration that tend to destabilize a tall building, much like a tall ship in ocean waves. Such unanticipated features may play a critical role in earthquake disasters on soft ground. A related case is the World Trade Center disaster of 11 September 2001, which was presumed to be due to gradual heat softening of steel girders. If so, the Twin Towers should have leaned over sideways but actually the collapse occurred vertically and quite suddenly. A likely alternative is coupling between a fireball caused by a phase transition between low- and high-oxygen consumption modes in burning jet fuel: (low-oxygen) 2CnH2n+2 + (n+1)O2 = nC2 + (2n+2)H2O, (1) (high-oxygen) 2CnH2n+2 + (3n+1)O2 = 2nCO2 + (2n+2)H2O, (2) and a pressure pulse propagating vertically inside the tubular structure. The pulse would have taken out the concrete floors, thus initiating collapse by implosion of the structural shell. Linear thinking may fail to anticipate coupling, and thus appropriate preventive measures may not be provided.

Improvement of time-delayed feedback control by periodic modulation: analytical theory of Floquet mode control scheme.

PubMed

Just, Wolfram; Popovich, Svitlana; Amann, Andreas; Baba, Nilüfer; Schöll, Eckehard

2003-02-01

We investigate time-delayed feedback control schemes which are based on the unstable modes of the target state, to stabilize unstable periodic orbits. The periodic time dependence of these modes introduces an external time scale in the control process. Phase shifts that develop between these modes and the controlled periodic orbit may lead to a huge increase of the control performance. We illustrate such a feature on a nonlinear reaction diffusion system with global coupling and give a detailed investigation for the Rössler model. In addition we provide the analytical explanation for the observed control features.

Trend extraction using empirical mode decomposition and statistical empirical mode decomposition: Case study: Kuala Lumpur stock market

NASA Astrophysics Data System (ADS)

Jaber, Abobaker M.

2014-12-01

Two nonparametric methods for prediction and modeling of financial time series signals are proposed. The proposed techniques are designed to handle non-stationary and non-linearity behave and to extract meaningful signals for reliable prediction. Due to Fourier Transform (FT), the methods select significant decomposed signals that will be employed for signal prediction. The proposed techniques developed by coupling Holt-winter method with Empirical Mode Decomposition (EMD) and it is Extending the scope of empirical mode decomposition by smoothing (SEMD). To show performance of proposed techniques, we analyze daily closed price of Kuala Lumpur stock market index.

Nonlinear beat excitation of low frequency wave in degenerate plasmas

NASA Astrophysics Data System (ADS)

Mir, Zahid; Shahid, M.; Jamil, M.; Rasheed, A.; Shahbaz, A.

2018-03-01

The beat phenomenon due to the coupling of two signals at slightly different frequencies that generates the low frequency signal is studied. The linear dispersive properties of the pump and sideband are analyzed. The modified nonlinear dispersion relation through the field coupling of linear modes against the beat frequency is derived in the homogeneous quantum dusty magnetoplasmas. The dispersion relation is used to derive the modified growth rate of three wave parametric instability. Moreover, significant quantum effects of electrons through the exchange-correlation potential, the Bohm potential, and the Fermi pressure evolved in macroscopic three wave interaction are presented. The analytical results are interpreted graphically describing the significance of the work. The applications of this study are pointed out at the end of introduction.

Rectified diode response of a multimode quantum cascade laser integrated terahertz transceiver.

PubMed

Dyer, Gregory C; Norquist, Christopher D; Cich, Michael J; Grine, Albert D; Fuller, Charles T; Reno, John L; Wanke, Michael C

2013-02-25

We characterized the DC transport response of a diode embedded in a THz quantum cascade laser as the laser current was changed. The overall response is described by parallel contributions from the rectification of the laser field due to the non-linearity of the diode I-V and from thermally activated transport. Sudden jumps in the diode response when the laser changes from single mode to multi-mode operation, with no corresponding jumps in output power, suggest that the coupling between the diode and laser field depends on the spatial distribution of internal fields. The results demonstrate conclusively that the internal laser field couples directly to the integrated diode.

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

NASA Technical Reports Server (NTRS)

Cantrell, John H., Jr.; Cantrell, Sean A.

2008-01-01

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Amplitude mode oscillations in pump-probe photoemission spectra from a d -wave superconductor

DOE PAGES

Nosarzewski, B.; Moritz, B.; Freericks, J. K.; ...

2017-11-20

Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time- and angle-resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d-wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d-wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. As a result, we comment on the necessary conditionsmore » for detecting the amplitude mode in trARPES experiments.« less

Amplitude mode oscillations in pump-probe photoemission spectra from a d -wave superconductor

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

Nosarzewski, B.; Moritz, B.; Freericks, J. K.

Recent developments in the techniques of ultrafast pump-probe photoemission have made possible the search for collective modes in strongly correlated systems out of equilibrium. Including inelastic scattering processes and a retarded interaction, we simulate time- and angle-resolved photoemission spectroscopy (trARPES) to study the amplitude mode of a d-wave superconductor, a collective mode excited through the nonlinear light-matter coupling to the pump pulse. We find that the amplitude mode oscillations of the d-wave order parameter occur in phase at a single frequency that is twice the quasi-steady-state maximum gap size after pumping. As a result, we comment on the necessary conditionsmore » for detecting the amplitude mode in trARPES experiments.« less

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.

Design of ultra-broadband terahertz polymer waveguide emitters for telecom wavelengths using coupled mode theory.

PubMed

Vallejo, Felipe A; Hayden, L Michael

2013-03-11

We use coupled mode theory, adequately incorporating optical losses, to model ultra-broadband terahertz (THz) waveguide emitters (0.1-20 THz) based on difference frequency generation of femtosecond infrared (IR) optical pulses. We apply the model to a generic, symmetric, five-layer, metal/cladding/core waveguide structure using transfer matrix theory. We provide a design strategy for an efficient ultra-broadband THz emitter and apply it to polymer waveguides with a nonlinear core composed of a poled guest-host electro-optic polymer composite and pumped by a pulsed fiber laser system operating at 1567 nm. The predicted bandwidths are greater than 15 THz and we find a high conversion efficiency of 1.2 × 10(-4) W(-1) by balancing both the modal phase-matching and effective mode attenuation.

The Study of Dynamical Potentials of Highly Excited Vibrational States of HOBr

PubMed Central

Wang, Aixing; Sun, Lifeng; Fang, Chao; Liu, Yibao

2013-01-01

The vibrational nonlinear dynamics of HOBr in the bending and O–Br stretching coordinates with anharmonicity and Fermi 2:1 coupling are studied with dynamical potentials in this article. The result shows that the H–O stretching vibration mode has significantly different effects on the coupling between the O–Br stretching mode and the H–O–Br bending mode under different Polyad numbers. The dynamical potentials and the corresponding phase space trajectories are obtained when the Polyad number is 27, for instance, and the fixed points in the dynamical potentials of HOBr are shown to govern the various quantal environments in which the vibrational states lie. Furthermore, it is also found that the quantal environments could be identified by the numerical values of action integrals, which is consistent with former research. PMID:23462512

Numerical simulation of plasma response to externally applied resonant magnetic perturbation on the J-TEXT tokamak

NASA Astrophysics Data System (ADS)

Bicheng, LI; Zhonghe, JIANG; Jian, LV; Xiang, LI; Bo, RAO; Yonghua, DING

2018-05-01

Nonlinear magnetohydrodynamic (MHD) simulations of an equilibrium on the J-TEXT tokamak with applied resonant magnetic perturbations (RMPs) are performed with NIMROD (non-ideal MHD with rotation, open discussion). Numerical simulation of plasma response to RMPs has been developed to investigate magnetic topology, plasma density and rotation profile. The results indicate that the pure applied RMPs can stimulate 2/1 mode as well as 3/1 mode by the toroidal mode coupling, and finally change density profile by particle transport. At the same time, plasma rotation plays an important role during the entire evolution process.

Single-photon non-linear optics with a quantum dot in a waveguide

NASA Astrophysics Data System (ADS)

Javadi, A.; Söllner, I.; Arcari, M.; Hansen, S. Lindskov; Midolo, L.; Mahmoodian, S.; Kiršanskė, G.; Pregnolato, T.; Lee, E. H.; Song, J. D.; Stobbe, S.; Lodahl, P.

2015-10-01

Strong non-linear interactions between photons enable logic operations for both classical and quantum-information technology. Unfortunately, non-linear interactions are usually feeble and therefore all-optical logic gates tend to be inefficient. A quantum emitter deterministically coupled to a propagating mode fundamentally changes the situation, since each photon inevitably interacts with the emitter, and highly correlated many-photon states may be created. Here we show that a single quantum dot in a photonic-crystal waveguide can be used as a giant non-linearity sensitive at the single-photon level. The non-linear response is revealed from the intensity and quantum statistics of the scattered photons, and contains contributions from an entangled photon-photon bound state. The quantum non-linearity will find immediate applications for deterministic Bell-state measurements and single-photon transistors and paves the way to scalable waveguide-based photonic quantum-computing architectures.

Nonlinear spatial evolution of inviscid instabilities on hypersonic boundary layers

NASA Technical Reports Server (NTRS)

Wundrow, David W.

1996-01-01

The spatial development of an initially linear vorticity-mode instability on a compressible flat-plate boundary layer is considered. The analysis is done in the framework of the hypersonic limit where the free-stream Mach number M approaches infinity. Nonlinearity is shown to become important locally, in a thin critical layer, when sigma, the deviation of the phase speed from unity, becomes o(M(exp -8/7)) and the magnitude of the pressure fluctuations becomes 0(sigma(exp 5/2)M(exp 2)). The unsteady flow outside the critical layer takes the form of a linear instability wave but with its amplitude completely determined by the nonlinear flow within the critical layer. The coupled set of equations which govern the critical-layer dynamics reflect a balance between spatial-evolution, (linear and nonlinear) convection and nonlinear vorticity-generation terms. The numerical solution to these equations shows that nonlinear effects produce a dramatic reduction in the instability-wave amplitude.

Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity

NASA Astrophysics Data System (ADS)

Karamchandani, Avinash J.; Graham, James N.; Riecke, Hermann

2018-04-01

Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.

Entanglement Criteria of Two Two-Level Atoms Interacting with Two Coupled Modes

NASA Astrophysics Data System (ADS)

Baghshahi, Hamid Reza; Tavassoly, Mohammad Kazem; Faghihi, Mohammad Javad

2015-08-01

In this paper, we study the interaction between two two-level atoms and two coupled modes of a quantized radiation field in the form of parametric frequency converter injecting within an optical cavity enclosed by a medium with Kerr nonlinearity. It is demonstrated that, by applying the Bogoliubov-Valatin canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Then, under particular initial conditions for the atoms (in a coherent superposition of its ground and upper states) and the fields (in a standard coherent state) which may be prepared, the time evolution of state vector of the entire system is analytically evaluated. In order to understand the degree of entanglement between subsystems (atom-field and atom-atom), the dynamics of entanglement through different measures, namely, von Neumann reduced entropy, concurrence and negativity is evaluated. In each case, the effects of Kerr nonlinearity and detuning parameter on the above measures are numerically analyzed, in detail. It is illustrated that the amount of entanglement can be tuned by choosing the evolved parameters, appropriately.

1992 Technical Digest Series. Volume 16. Conference Edition: Summaries of Papers Presented at the Nonlinear Dynamics in Optical Systems Topical Meeting Held in Alpbach, Austria on 22-26 June 1992

DTIC Science & Technology

1992-06-01

Geisler, M. H . Haken, Univ. Stuttgar’, Germany. A geometrical formulation P. Sorenson, P. L. Christiansen, Technical Univ., Denmark; J. of phase...locking, L. A. mode inhomogeneously broadened laser dynamics, B. Melnikov, G. N. Tatarkov, Chernyshevsky State Univ., Russia. Meziane, H . Ladjouze, ENSSAT...coupled laser arrays, D. Nichols, H . Winful, Univ. Michigan. We have studied the effect of nonlinear TuC6 Phase singularities in a Fabry-Perot resonator

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Cantrell, Sean A.

2010-01-01

The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.

Finite amplitude transverse oscillations of a magnetic rope

NASA Astrophysics Data System (ADS)

Kolotkov, Dmitrii Y.; Nisticò, Giuseppe; Rowlands, George; Nakariakov, Valery M.

2018-07-01

The effects of finite amplitudes on the transverse oscillations of a quiescent prominence represented by a magnetic rope are investigated in terms of the model proposed by Kolotkov et al. (2016). We consider a weakly nonlinear case governed by a quadratic nonlinearity, and also analyse the fully nonlinear equations of motion. We treat the prominence as a massive line current located above the photosphere and interacting with the magnetised dipped environment via the Lorentz force. In this concept the magnetic dip is produced by two external current sources located at the photosphere. Finite amplitude horizontal and vertical oscillations are found to be strongly coupled between each other. The coupling is more efficient for larger amplitudes and smaller attack angles between the direction of the driver and the horizontal axis. Spatial structure of oscillations is represented by Lissajous-like curves with the limit cycle of a hourglass shape, appearing in the resonant case, when the frequency of the vertical mode is twice the horizontal mode frequency. A metastable equilibrium of the prominence is revealed, which is stable for small amplitude displacements, and becomes horizontally unstable, when the amplitude exceeds a threshold value. The maximum oscillation amplitudes are also analytically derived and analysed. Typical oscillation periods are determined by the oscillation amplitude, prominence current, its mass and position above the photosphere, and the parameters of the magnetic dip. The main new effects of the finite amplitude are the coupling of the horizontally and vertically polarised transverse oscillations (i.e. the lack of a simple, elliptically polarised regime) and the presence of metastable equilibria of prominences.

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

Mechanism of nonlinear flow pattern selection in moderately non-Boussinesq mixed convection.

PubMed

Suslov, Sergey A

2010-02-01

Nonlinear (non-Boussinesq) variations in fluid's density, viscosity, and thermal conductivity caused by a large temperature gradient in a flow domain lead to a wide variety of instability phenomena in mixed convection channel flow of a simple gas such as air. It is known that in strongly nonisothermal flows, the instabilities and the resulting flow patterns are caused by competing buoyancy and shear effects [see S. A. Suslov and S. Paolucci, J. Fluid Mech. 302, 91 (1995)]. However, as is the case in the Boussinesq limit of small temperature gradients, in moderately non-Boussinesq regimes, only a shear instability mechanism is active. Yet in contrast to Boussinesq flows, multiple instability modes are still detected. By reducing the system of full governing Navier-Stokes equations to a dynamical system of coupled Landau-type disturbance amplitude equations we compute a comprehensive parametric map of various shear-driven instabilities observed in a representative moderately non-Boussinesq regime. Subsequently, we analyze nonlinear interaction of unstable modes and reveal physical reasons for their appearance.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

PubMed

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Class-A dual-frequency VECSEL at telecom wavelength.

PubMed

De, Syamsundar; Baili, Ghaya; Alouini, Mehdi; Harmand, Jean-Christophe; Bouchoule, Sophie; Bretenaker, Fabien

2014-10-01

We report class-A dual-frequency oscillation at 1.55 μm in a vertical external cavity surface emitting laser with more than 100 mW optical power. The two orthogonal linear polarizations of different frequencies oscillate simultaneously as their nonlinear coupling is reduced below unity by spatially separating them inside the active medium. The spectral behavior of the radio frequency beatnote obtained by optically mixing two polarizations and the phase noise of the beatnote have been explored for different coupling strengths between the lasing modes.

Comparing magnetic fluctuation dynamics in nonlinear MHD simulations of low-aspect-ratio RFPs to RELAX experiments

NASA Astrophysics Data System (ADS)

McCollam, K. J.; den Hartog, D. J.; Jacobson, C. M.; Sovinec, C. R.; Masamune, S.; Sanpei, A.

2017-10-01

We present comparisons of magnetic tearing fluctuation activity between RFP experiments on the low-aspect-ratio RELAX device (R / a 2) and nonlinear simulations of zero-beta, single-fluid MHD using the NIMROD code in both cylindrical and toroidal geometries at a Lundquist number of S =104 , nearly as high as experimental values. Time-average fluctuation amplitudes observed in the simulations are similar to those from the experiments, but more rigorous comparisons versus spectral mode numbers are in progress. We also focus on how the spatiotemporal dynamics of the fluctuations vary with RFP equilibrium parameters. Interestingly, at shallow reversal, cylindrical simulations show a relatively uncoupled spectrum of nearly quiescent modes periodically varying in time, whereas the corresponding toroidal cases show a fully chaotic spectrum of strongly nonlinearly interacting modes. We ascribe this to the geometric m = 1 coupling present in the toroidal but not the cylindrical case. We present initial results from convergence studies with increased spatial resolution for both geometries. Simulations at higher S are planned. This work is supported by the U.S. DOE and by the Japan Society for the Promotion of Science.

Anomalous vibrational modes in acetanilide: A F. D. S. incoherent inelastic neutron scattering study

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

Barthes, M.; Moret, J.; Eckert, J.

1991-01-01

The origin of the anomalous infra-red and Raman modes in acetanilide (C{sub 6}H{sub 5}NHCOCH{sub 3}, or ACN), remains a subject of considerable controversy. One family of theoretical models involves Davydov-like solitons nonlinear vibrational coupling, or polaronic'' localized modes. An alternative interpretation of the extra-bands in terms of a Fermi resonance was proposed and recently the existence of slightly non-degenerate hydrogen atom configurations in the H-bond was suggested as an explanation for the anomalies. In this paper we report some new results on the anomalous vibrational modes in ACN that were obtained by inelastic incoherent neutron scattering (INS).

Quantum-limited amplification with a nonlinear cavity detector

NASA Astrophysics Data System (ADS)

Laflamme, C.; Clerk, A. A.

2011-03-01

We consider the quantum measurement properties of a driven cavity with a Kerr-type nonlinearity that is used to amplify a dispersively coupled input signal. Focusing on an operating regime that is near a bifurcation point, we derive simple asymptotic expressions describing the cavity’s noise and response. We show that the cavity’s backaction and imprecision noise allow for quantum-limited linear amplification and position detection only if one is able to utilize the sizable correlations between these quantities. This is possible when one amplifies a nonresonant signal but is not possible in quantum nondemolition qubit detection. We also consider the possibility of using the nonlinear cavity’s backaction for cooling a mechanical mode.

Non-linear wave-particle interactions and fast ion loss induced by multiple Alfvén eigenmodes in the DIII-D tokamak

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

Chen, Xi; Kramer, Gerrit J.; Heidbrink, William W.

2014-05-21

A new non-linear feature has been observed in fast-ion loss from tokamak plasmas in the form of oscillations at the sum, difference and second harmonic frequencies of two independent Alfvén eigenmodes (AEs). Full orbit calculations and analytic theory indicate this non-linearity is due to coupling of fast-ion orbital response as it passes through each AE — a change in wave-particle phase k • r by one mode alters the force exerted by the next. Furthermore, the loss measurement is of barely confined, non-resonant particles, while similar non-linear interactions can occur between well-confined particles and multiple AEs leading to enhanced fast-ionmore » transport.« less

Localization of Stable and Chaotic Nonpropagating Structures in Nonlinear Mesoscopic Lattices.

NASA Astrophysics Data System (ADS)

Greenfield, Alan Barry

Recent developments in the study of non-linear localized states, especially non-propagating ones, are outlined. Theoretical models of linear and nonlinear states in a lattice of coupled pendulums and related systems are reviewed. Particular attention is paid to those states which can be described by the Nonlinear Schrodinger equation as well as states where two modes can coexist and states exhibiting chaos. Measurement of localized stable and chaotic states in a 35 site physical pendulum lattice is reported. Various measurement techniques that were used are explained. States that were measured include the tanh profile or kink soliton, and the corresponding uniform state in the wavelength 2 mode, a similar soliton and uniform state in the wavelength 4 mode, a domain wall between the wavelength 2 and 4 modes and a domain wall between a chaotic state and the wavelength 2 mode. Amplitude profiles were measured for the stable kink and domain wall states and smooth curves were obtained by dividing the kink states by the corresponding uniform states. Return maps were measured for two sites in the chaotic domain wall. Simulation of a chaotic domain wall in a 50 site numerical lattice is reported. This system has the advantage that its parameters can be modified much more easily than those of the physical lattice. An attempt is made at quantifying the level of chaos as a function of lattice site with fractal dimension calculations on return maps embedded in a three dimensional space. The drive plane of the chaotic domain wall is mapped out in the drive amplitude - drive frequency plane. Transitions to various stable and quasiperiodic domain walls are noted.

Theta phase precession and phase selectivity: a cognitive device description of neural coding

NASA Astrophysics Data System (ADS)

Zalay, Osbert C.; Bardakjian, Berj L.

2009-06-01

Information in neural systems is carried by way of phase and rate codes. Neuronal signals are processed through transformative biophysical mechanisms at the cellular and network levels. Neural coding transformations can be represented mathematically in a device called the cognitive rhythm generator (CRG). Incoming signals to the CRG are parsed through a bank of neuronal modes that orchestrate proportional, integrative and derivative transformations associated with neural coding. Mode outputs are then mixed through static nonlinearities to encode (spatio) temporal phase relationships. The static nonlinear outputs feed and modulate a ring device (limit cycle) encoding output dynamics. Small coupled CRG networks were created to investigate coding functionality associated with neuronal phase preference and theta precession in the hippocampus. Phase selectivity was found to be dependent on mode shape and polarity, while phase precession was a product of modal mixing (i.e. changes in the relative contribution or amplitude of mode outputs resulted in shifting phase preference). Nonlinear system identification was implemented to help validate the model and explain response characteristics associated with modal mixing; in particular, principal dynamic modes experimentally derived from a hippocampal neuron were inserted into a CRG and the neuron's dynamic response was successfully cloned. From our results, small CRG networks possessing disynaptic feedforward inhibition in combination with feedforward excitation exhibited frequency-dependent inhibitory-to-excitatory and excitatory-to-inhibitory transitions that were similar to transitions seen in a single CRG with quadratic modal mixing. This suggests nonlinear modal mixing to be a coding manifestation of the effect of network connectivity in shaping system dynamic behavior. We hypothesize that circuits containing disynaptic feedforward inhibition in the nervous system may be candidates for interpreting upstream rate codes to guide downstream processes such as phase precession, because of their demonstrated frequency-selective properties.

Epsilon-near-zero modes for tailored light-matter interaction

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

Campione, Salvatore; Liu, Sheng; Benz, Alexander

Epsilon-near-zero (ENZ) modes arising from condensed-matter excitations such as phonons and plasmons are a new path for tailoring light-matter interactions at the nanoscale. Complex spectral shaping can be achieved by creating such modes in nanoscale semiconductor layers and controlling their interaction with multiple, distinct, dipole resonant systems. Examples of this behavior are presented at midinfrared frequencies for ENZ modes that are strongly coupled to metamaterial resonators and simultaneously strongly coupled to semiconductor phonons or quantum-well intersubband transitions (ISTs), resulting in double- and triple-polariton branches in transmission spectra. For the double-polariton branch case, we find that the best strategy to maximizemore » the Rabi splitting is to use a combination of a doped layer supporting an ENZ feature and a layer supporting ISTs, with overlapping ENZ and IST frequencies. As a result, this design flexibility renders this platform attractive for low-voltage tunable filters, light-emitting diodes, and efficient nonlinear composite materials.« less

Epsilon-near-zero modes for tailored light-matter interaction

DOE PAGES

Campione, Salvatore; Liu, Sheng; Benz, Alexander; ...

2015-10-20

Epsilon-near-zero (ENZ) modes arising from condensed-matter excitations such as phonons and plasmons are a new path for tailoring light-matter interactions at the nanoscale. Complex spectral shaping can be achieved by creating such modes in nanoscale semiconductor layers and controlling their interaction with multiple, distinct, dipole resonant systems. Examples of this behavior are presented at midinfrared frequencies for ENZ modes that are strongly coupled to metamaterial resonators and simultaneously strongly coupled to semiconductor phonons or quantum-well intersubband transitions (ISTs), resulting in double- and triple-polariton branches in transmission spectra. For the double-polariton branch case, we find that the best strategy to maximizemore » the Rabi splitting is to use a combination of a doped layer supporting an ENZ feature and a layer supporting ISTs, with overlapping ENZ and IST frequencies. As a result, this design flexibility renders this platform attractive for low-voltage tunable filters, light-emitting diodes, and efficient nonlinear composite materials.« less

Direct Observation of Optical Field Phase Carving in the Vicinity of Plasmonic Metasurfaces.

PubMed

Dagens, B; Février, M; Gogol, P; Blaize, S; Apuzzo, A; Magno, G; Mégy, R; Lerondel, G

2016-07-13

Plasmonic surfaces are mainly used for their optical intensity concentration properties that allow for enhancement of physical interaction like in nonlinear optics, optical sensors, or tweezers. Phase response in plasmonic resonances can also play a major role, especially in a periodic assembly of plasmonic resonators like metasurfaces. Here we show that localized surface plasmons collectively excited by a guided mode in a metallic nanostructure periodic chain present nonmonotonous phase variation along the 1D metasurface, resulting from both selective Bloch mode coupling and dipolar coupling. As shown by near-field measurements, the phase profile of the highly concentrated optical field is carved out in the vicinity of the metallic metasurface, paving the way to unusual local optical functions.

Measurement of Richtmyer–Meshkov mode coupling under steady shock conditions and at high energy density

DOE PAGES

Di Stefano, Carlos A.; Malamud, G.; Kuranz, C. C.; ...

2015-10-19

Here, we present experiments observing Richtmyer–Meshkov mode coupling and bubble competition in a system arising from well-characterized initial conditions and driven by a strong (Mach ~ 8) shock. These measurements and the analysis method developed to interpret them provide an important step toward the possibility of observing self-similarity under such conditions, as well as a general platform for performing and analyzing hydrodynamic instability experiments. A key feature of these experiments is that the shock is sustained sufficiently long that this nonlinear behavior occurs without decay of the shock velocity or other hydrodynamic properties of the system, which facilitates analysis andmore » allows the results to be used in the study of analytic models.« less

Polarization domain wall pulses in a microfiber-based topological insulator fiber laser

PubMed Central

Liu, Jingmin; Li, Xingliang; Zhang, Shumin; Zhang, Han; Yan, Peiguang; Han, Mengmeng; Pang, Zhaoguang; Yang, Zhenjun

2016-01-01

Topological insulators (TIs), are novel two-dimension materials, which can act as effective saturable absorbers (SAs) in a fiber laser. Moreover, based on the evanescent wave interaction, deposition of the TI on microfiber would create an effective SA, which has combined advantages from the strong nonlinear optical response in TI material together with the sufficiently-long-range interaction length in fiber taper. By using this type of TI SA, various scalar solitons have been obtained in fiber lasers. However, a single mode fiber always exhibits birefringence, and hence can support two orthogonal degenerate modes. Here we investigate experimentally the vector characters of a TI SA fiber laser. Using the saturated absorption and the high nonlinearity of the TI SA, a rich variety of dynamic states, including polarization-locked dark pulses and their harmonic mode locked counterparts, polarization-locked noise-like pulses and their harmonic mode locked counterparts, incoherently coupled polarization domain wall pulses, including bright square pulses, bright-dark pulse pairs, dark pulses and bright square pulse-dark pulse pairs are all observed with different pump powers and polarization states. PMID:27381942

Polarization domain wall pulses in a microfiber-based topological insulator fiber laser

NASA Astrophysics Data System (ADS)

Liu, Jingmin; Li, Xingliang; Zhang, Shumin; Zhang, Han; Yan, Peiguang; Han, Mengmeng; Pang, Zhaoguang; Yang, Zhenjun

2016-07-01

Topological insulators (TIs), are novel two-dimension materials, which can act as effective saturable absorbers (SAs) in a fiber laser. Moreover, based on the evanescent wave interaction, deposition of the TI on microfiber would create an effective SA, which has combined advantages from the strong nonlinear optical response in TI material together with the sufficiently-long-range interaction length in fiber taper. By using this type of TI SA, various scalar solitons have been obtained in fiber lasers. However, a single mode fiber always exhibits birefringence, and hence can support two orthogonal degenerate modes. Here we investigate experimentally the vector characters of a TI SA fiber laser. Using the saturated absorption and the high nonlinearity of the TI SA, a rich variety of dynamic states, including polarization-locked dark pulses and their harmonic mode locked counterparts, polarization-locked noise-like pulses and their harmonic mode locked counterparts, incoherently coupled polarization domain wall pulses, including bright square pulses, bright-dark pulse pairs, dark pulses and bright square pulse-dark pulse pairs are all observed with different pump powers and polarization states.

Orbital angular momentum mode division filtering for photon-phonon coupling

PubMed Central

Zhu, Zhi-Han; Sheng, Li-Wen; Lv, Zhi-Wei; He, Wei-Ming; Gao, Wei

2017-01-01

Stimulated Brillouin scattering (SBS), a fundamental nonlinear interaction between light and acoustic waves occurring in any transparency material, has been broadly studied for several decades and gained rapid progress in integrated photonics recently. However, the SBS noise arising from the unwanted coupling between photons and spontaneous non-coherent phonons in media is inevitable. Here, we propose and experimentally demonstrate this obstacle can be overcome via a method called orbital angular momentum mode division filtering. Owing to the introduction of a new distinguishable degree-of-freedom, even extremely weak signals can be discriminated and separated from a strong noise produced in SBS processes. The mechanism demonstrated in this proof-of-principle work provides a practical way for quasi-noise-free photonic-phononic operation, which is still valid in waveguides supporting multi-orthogonal spatial modes, permits more flexibility and robustness for future SBS devices. PMID:28071736

Rigid-flexible coupling dynamic modeling and investigation of a redundantly actuated parallel manipulator with multiple actuation modes

NASA Astrophysics Data System (ADS)

Liang, Dong; Song, Yimin; Sun, Tao; Jin, Xueying

2017-09-01

A systematic dynamic modeling methodology is presented to develop the rigid-flexible coupling dynamic model (RFDM) of an emerging flexible parallel manipulator with multiple actuation modes. By virtue of assumed mode method, the general dynamic model of an arbitrary flexible body with any number of lumped parameters is derived in an explicit closed form, which possesses the modular characteristic. Then the completely dynamic model of system is formulated based on the flexible multi-body dynamics (FMD) theory and the augmented Lagrangian multipliers method. An approach of combining the Udwadia-Kalaba formulation with the hybrid TR-BDF2 numerical algorithm is proposed to address the nonlinear RFDM. Two simulation cases are performed to investigate the dynamic performance of the manipulator with different actuation modes. The results indicate that the redundant actuation modes can effectively attenuate vibration and guarantee higher dynamic performance compared to the traditional non-redundant actuation modes. Finally, a virtual prototype model is developed to demonstrate the validity of the presented RFDM. The systematic methodology proposed in this study can be conveniently extended for the dynamic modeling and controller design of other planar flexible parallel manipulators, especially the emerging ones with multiple actuation modes.

Nonlinear optical coupler using a doped optical waveguide

DOEpatents

Pantell, Richard H.; Sadowski, Robert W.; Digonnet, Michel J. F.; Shaw, Herbert J.

1994-01-01

An optical mode coupling apparatus includes an Erbium-doped optical waveguide in which an optical signal at a signal wavelength propagates in a first spatial propagation mode and a second spatial propagation mode of the waveguide. The optical signal propagating in the waveguide has a beat length. The coupling apparatus includes a pump source of perturbational light signal at a perturbational wavelength that propagates in the waveguide in the first spatial propagation mode. The perturbational signal has a sufficient intensity distribution in the waveguide that it causes a perturbation of the effective refractive index of the first spatial propagation mode of the waveguide in accordance with the optical Kerr effect. The perturbation of the effective refractive index of the first spatial propagation mode of the optical waveguide causes a change in the differential phase delay in the optical signal propagating in the first and second spatial propagation modes. The change in the differential phase delay is detected as a change in the intensity distribution between two lobes of the optical intensity distribution pattern of an output signal. The perturbational light signal can be selectively enabled and disabled to selectively change the intensity distribution in the two lobes of the optical intensity distribution pattern.

Enhanced localized energetic ion losses resulting from first-orbit linear and non-linear interactions with Alfvén eigenmodes in DIII-D

DOE PAGES

Chen, Xi; Heidbrink, William W.; Kramer, Gerrit J.; ...

2014-08-04

Two key insights into interactions between Alfvén eigenmodes (AEs) and energetic particles in the plasma core are gained from measurements and modeling of first-orbit beam-ion loss in DIII-D. First, the neutral beam-ion first-orbit losses are enhanced by AEs and a single AE can cause large fast-ion displacement. The coherent losses are from born trapped full energy beam-ions being non-resonantly scattered by AEs onto loss orbits within their first poloidal transit. The loss amplitudes scale linearly with the mode amplitude but the slope is different for different modes. The radial displacement of fast-ions by individual AEs can be directly inferred frommore » the measurements. Second, oscillations in the beam-ion first-orbit losses are observed at the sum, difference, and harmonic frequencies of two independent AEs. These oscillations are not plasma modes and are absent in magnetic, density, and temperature fluctuations. The origin of the non-linearity as a wave-particle coupling is confirmed through bi-coherence analysis, which is clearly observed because the coherences are preserved by the first-orbit loss mechanism. Finally, an analytic model and full orbit simulations show that the non-linear features seen in the loss signal can be explained by a non-linear interaction between the fast ions and the two independent AEs.« less

Enhanced localized energetic ion losses resulting from first-orbit linear and non-linear interactions with Alfvén eigenmodes in DIII-D

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

Chen, X.; General Atomics, P.O. Box 85608, San Diego, California 92186; Heidbrink, W. W.

2014-08-15

Two key insights into interactions between Alfvén eigenmodes (AEs) and energetic particles in the plasma core are gained from measurements and modeling of first-orbit beam-ion loss in DIII-D. First, the neutral beam-ion first-orbit losses are enhanced by AEs and a single AE can cause large fast-ion displacement. The coherent losses are from born trapped full energy beam-ions being non-resonantly scattered by AEs onto loss orbits within their first poloidal transit. The loss amplitudes scale linearly with the mode amplitude but the slope is different for different modes. The radial displacement of fast-ions by individual AEs can be directly inferred frommore » the measurements. Second, oscillations in the beam-ion first-orbit losses are observed at the sum, difference, and harmonic frequencies of two independent AEs. These oscillations are not plasma modes and are absent in magnetic, density, and temperature fluctuations. The origin of the non-linearity as a wave-particle coupling is confirmed through bi-coherence analysis, which is clearly observed because the coherences are preserved by the first-orbit loss mechanism. An analytic model and full orbit simulations show that the non-linear features seen in the loss signal can be explained by a non-linear interaction between the fast ions and the two independent AEs.« less

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.

Damping of spin-dipole mode and generation of quadrupole mode excitations in a spin-orbit coupled Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Li, Chuan-Hsun; Blasing, David; Chen, Yong

2017-04-01

In cold atom systems, spin excitations have been shown to be a sensitive probe of interactions and quantum statistical effects, and can be used to study spin transport in both Fermi and Bose gases. In particular, spin-dipole mode (SDM) is a type of excitation that can generate a spin current without a net mass current. We present recent measurements and analysis of SDM in a disorder-free, interacting three-dimensional (3D) 87Rb Bose-Einstein condensate (BEC) by applying spin-dependent synthetic electric fields to actuate head-on collisions between two BECs of different spin states. We experimentally study and compare the behaviors of the system following SDM excitations in the presence as well as absence of synthetic 1D spin-orbit coupling (SOC). We find that in the absence of SOC, SDM is relatively weakly damped, accompanied with collision-induced thermalization which heats up the atomic cloud. However, in the presence of SOC, we find that SDM is more strongly damped with reduced thermalization, and observe excitation of a quadrupole mode that exhibits BEC shape oscillation even after SDM is damped out. Such a mode conversion bears analogies with the Beliaev coupling process or the parametric frequency down conversion of light in nonlinear optics.

Entanglement analysis of a two-atom nonlinear Jaynes-Cummings model with nondegenerate two-photon transition, Kerr nonlinearity, and two-mode Stark shift

NASA Astrophysics Data System (ADS)

Baghshahi, H. R.; Tavassoly, M. K.; Faghihi, M. J.

2014-12-01

An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom-field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom-field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.

Mitigation of wind tunnel wall interactions in subsonic cavity flows

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

Wagner, Justin L.; Casper, Katya Marie; Beresh, Steven J.

In this study, the flow over an open aircraft bay is often represented in a wind tunnel with a cavity. In flight, this flow is unconfined, though in experiments, the cavity is surrounded by wind tunnel walls. If untreated, wind tunnel wall effects can lead to significant distortions of cavity acoustics in subsonic flows. To understand and mitigate these cavity–tunnel interactions, a parametric approach was taken for flow over an L/D = 7 cavity at Mach numbers 0.6–0.8. With solid tunnel walls, a dominant cavity tone was observed, likely due to an interaction with a tunnel duct mode. Furthermore, anmore » acoustic liner opposite the cavity decreased the amplitude of the dominant mode and its harmonics, a result observed by previous researchers. Acoustic dampeners were also placed in the tunnel sidewalls, which further decreased the dominant mode amplitudes and peak amplitudes associated with nonlinear interactions between cavity modes. This then indicates that cavity resonance can be altered by tunnel sidewalls and that spanwise coupling should be addressed when conducting subsonic cavity experiments. Though mechanisms for dominant modes and nonlinear interactions likely exist in unconfined cavity flows, these effects can be amplified by the wind tunnel walls.« less

Mitigation of wind tunnel wall interactions in subsonic cavity flows

DOE PAGES

Wagner, Justin L.; Casper, Katya Marie; Beresh, Steven J.; ...

2015-03-06

In this study, the flow over an open aircraft bay is often represented in a wind tunnel with a cavity. In flight, this flow is unconfined, though in experiments, the cavity is surrounded by wind tunnel walls. If untreated, wind tunnel wall effects can lead to significant distortions of cavity acoustics in subsonic flows. To understand and mitigate these cavity–tunnel interactions, a parametric approach was taken for flow over an L/D = 7 cavity at Mach numbers 0.6–0.8. With solid tunnel walls, a dominant cavity tone was observed, likely due to an interaction with a tunnel duct mode. Furthermore, anmore » acoustic liner opposite the cavity decreased the amplitude of the dominant mode and its harmonics, a result observed by previous researchers. Acoustic dampeners were also placed in the tunnel sidewalls, which further decreased the dominant mode amplitudes and peak amplitudes associated with nonlinear interactions between cavity modes. This then indicates that cavity resonance can be altered by tunnel sidewalls and that spanwise coupling should be addressed when conducting subsonic cavity experiments. Though mechanisms for dominant modes and nonlinear interactions likely exist in unconfined cavity flows, these effects can be amplified by the wind tunnel walls.« less

Weakly nonlinear incompressible Rayleigh-Taylor instability in spherical geometry

NASA Astrophysics Data System (ADS)

Zhang, J.; Wang, L. F.; Ye, W. H.; Wu, J. F.; Guo, H. Y.; Zhang, W. Y.; He, X. T.

2017-06-01

In this research, a weakly nonlinear (WN) model for the incompressible Rayleigh-Taylor instability in cylindrical geometry [Wang et al., Phys. Plasmas 20, 042708 (2013)] is generalized to spherical geometry. The evolution of the interface with an initial small-amplitude single-mode perturbation in the form of Legendre mode (Pn) is analysed with the third-order WN solutions. The transition of the small-amplitude perturbed spherical interface to the bubble-and-spike structure can be observed by our model. For single-mode perturbation Pn, besides the generation of P 2 n and P 3 n , which are similar to the second and third harmonics in planar and cylindrical geometries, many other modes in the range of P0- P 3 n are generated by mode-coupling effects up to the third order. With the same initial amplitude, the bubbles at the pole grow faster than those at the equator in the WN regime. Furthermore, it is found that the behavior of the bubbles at the pole is similar to that of three-dimensional axisymmetric bubbles, while the behavior of the bubbles at the equator is similar to that of two-dimensional bubbles.

Components for monolithic fiber chirped pulse amplification laser systems

NASA Astrophysics Data System (ADS)

Swan, Michael Craig

The first portion of this work develops techniques for generating femtosecond-pulses from conventional fabry-perot laser diodes using nonlinear-spectral-broadening techniques in Yb-doped positive dispersion fiber ampliers. The approach employed an injection-locked fabry-perot laser diode followed by two stages of nonlinear-spectral-broadening to generate sub-200fs pulses. This thesis demonstrated that a 60ps gain-switched fabry-perot laser-diode can be injection-locked to generate a single-longitudinal-mode pulse and compressed by nonlinear spectral broadening to 4ps. Two problems have been identified that must be resolved before moving forward with this approach. First, gain-switched pulses from a standard diode-laser have a number of characteristics not well suited for producing clean self-phase-modulation-broadened pulses, such as an asymmetric temporal shape, which has a long pulse tail. Second, though parabolic pulse formation occurs for any arbitrary temporal input pulse profile, deviation from the optimum parabolic input results in extensively spectrally modulated self-phase-modulation-broadened pulses. In conclusion, the approach of generating self-phase-modulation-broadened pulses from pulsed laser diodes has to be modified from the initial approach explored in this thesis. The first Yb-doped chirally-coupled-core ber based systems are demonstrated and characterized in the second portion of this work. Robust single-mode performance independent of excitation or any other external mode management techniques have been demonstrated in Yb-doped chirally-coupled-core fibers. Gain and power efficiency characteristics are not compromised in any way in this novel fiber structure up to the 87W maximum power achieved. Both the small signal gain at 1064nm of 30.3dB, and the wavelength dependence of the small signal gain were comparable to currently deployed large-mode-area-fiber technology. The efficiencies of the laser and amplifier were measured to be 75% and 54% respectively. With the inherent design tradeoff between the fundamental mode loss and higher order mode suppression, loss effects on system efficiency in different configurations were investigated. From these investigations it was seen that the slope-efficiency depends only on the total loss of the active fiber, and that when loss is present, the counter-propagating configuration has substantial advantages over the co-propagating case. In this thesis chirally-coupled-core fiber as the technological basis for the next generation of monolithic high power fiber laser systems has been established.

Excitation of epsilon-near-zero resonance in ultra-thin indium tin oxide shell embedded nanostructured optical fiber.

PubMed

Minn, Khant; Anopchenko, Aleksei; Yang, Jingyi; Lee, Ho Wai Howard

2018-02-05

We report a novel optical waveguide design of a hollow step index fiber modified with a thin layer of indium tin oxide (ITO). We show an excitation of highly confined waveguide mode in the proposed fiber near the wavelength where permittivity of ITO approaches zero. Due to the high field confinement within thin ITO shell inside the fiber, the epsilon-near-zero (ENZ) mode can be characterized by a peak in modal loss of the hybrid waveguide. Our results show that such in-fiber excitation of ENZ mode is due to the coupling of the guided core mode to the thin-film ENZ mode. We also show that the phase matching wavelength, where the coupling takes place, varies depending on the refractive index of the constituents inside the central bore of the fiber. These ENZ nanostructured optical fibers have many potential applications, for example, in ENZ nonlinear and magneto-optics, as in-fiber wavelength-dependent filters, and as subwavelength fluid channel for optical and bio-photonic sensing.

Mode stabilization in quantum cascade lasers via an intra-cavity cascaded nonlinearity.

PubMed

St-Jean, M Renaudat; Amanti, M I; Bismuto, A; Beck, M; Faist, J; Sirtori, C

2017-02-06

We present self-stabilization of the inter-mode separation of a quantum cascade laser (QCL) emitting at 9 μm via cascaded second order nonlinearity. This effect has been observed in lasers that have the optical cavity embedded into a microwave strip-line. The intermodal beat note spectra narrow with increasing laser output power, up to less than 100 kHz. A flat frequency response to direct modulation up to 14 GHz is reported for these microstrip QCLs. The laser inter-mode spacing can be locked to an external RF signal and tuned by more than 1 MHz from the free-running spacing. A parallel study on the same laser material in a non-microstrip line waveguide shows superior performances of the microstrip QCL in terms of the intermodal spectral locking and stability. Finally by analyzing our results with the theory of the injection locking of coupled oscillators, we deduce that the microwave power injected in the microstrip QCL is 2 orders of magnitude higher than in the reference laser.

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

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

NASA Astrophysics Data System (ADS)

Torre, Emanuele G. Dalla; Diehl, Sebastian; Lukin, Mikhail D.; Sachdev, Subir; Strack, Philipp

2013-02-01

We investigate nonequilibrium phase transitions for driven atomic ensembles interacting with a cavity mode and coupled to a Markovian dissipative bath. In the thermodynamic limit and at low frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path-integral approach that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number N of atoms. For finite N, the photon mode behaves as a damped classical nonlinear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any N and correctly captures the atoms’ depolarization due to dissipative dephasing.

Flexure-FET biosensor to break the fundamental sensitivity limits of nanobiosensors using nonlinear electromechanical coupling

PubMed Central

Jain, Ankit; Nair, Pradeep R.; Alam, Muhammad A.

2012-01-01

In this article, we propose a Flexure-FET (flexure sensitive field effect transistor) ultrasensitive biosensor that utilizes the nonlinear electromechanical coupling to overcome the fundamental sensitivity limits of classical electrical or mechanical nanoscale biosensors. The stiffness of the suspended gate of Flexure-FET changes with the capture of the target biomolecules, and the corresponding change in the gate shape or deflection is reflected in the drain current of FET. The Flexure-FET is configured to operate such that the gate is biased near pull-in instability, and the FET-channel is biased in the subthreshold regime. In this coupled nonlinear operating mode, the sensitivity (S) of Flexure-FET with respect to the captured molecule density (Ns) is shown to be exponentially higher than that of any other electrical or mechanical biosensor. In other words, while , classical electrical or mechanical biosensors are limited to Sclassical ∼ γ3NS or γ4 ln(NS), where γi are sensor-specific constants. In addition, the proposed sensor can detect both charged and charge-neutral biomolecules, without requiring a reference electrode or any sophisticated instrumentation, making it a potential candidate for various low-cost, point-of-care applications. PMID:22623527

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

NASA Astrophysics Data System (ADS)

Tzang, Omer; Caravaca-Aguirre, Antonio M.; Wagner, Kelvin; Piestun, Rafael

2018-06-01

Recent progress in wavefront shaping has enabled control of light propagation inside linear media to focus and image through scattering objects. In particular, light propagation in multimode fibres comprises complex intermodal interactions and rich spatiotemporal dynamics. Control of physical phenomena in multimode fibres and its applications are in their infancy, opening opportunities to take advantage of complex nonlinear modal dynamics. Here, we demonstrate a wavefront shaping approach for controlling nonlinear phenomena in multimode fibres. Using a spatial light modulator at the fibre input, real-time spectral feedback and a genetic algorithm optimization, we control a highly nonlinear multimode stimulated Raman scattering cascade and its interplay with four-wave mixing via a flexible implicit control on the superposition of modes coupled into the fibre. We show versatile spectrum manipulations including shifts, suppression, and enhancement of Stokes and anti-Stokes peaks. These demonstrations illustrate the power of wavefront shaping to control and optimize nonlinear wave propagation.

Nonlinear Electrostatic Steepening of Whistler Waves: The Guiding Factors and Dynamics in Inhomogeneous Systems

NASA Astrophysics Data System (ADS)

Agapitov, O.; Drake, J. F.; Vasko, I.; Mozer, F. S.; Artemyev, A.; Krasnoselskikh, V.; Angelopoulos, V.; Wygant, J.; Reeves, G. D.

2018-03-01

Whistler mode chorus waves are particularly important in outer radiation belt dynamics due to their key role in controlling the acceleration and scattering of electrons over a very wide energy range. The efficiency of wave-particle resonant interactions is defined by whistler wave properties which have been described by the approximation of plane linear waves propagating through the cold plasma of the inner magnetosphere. However, recent observations of extremely high-amplitude whistlers suggest the importance of nonlinear wave-particle interactions for the dynamics of the outer radiation belt. Oblique chorus waves observed in the inner magnetosphere often exhibit drastically nonsinusoidal (with significant power in the higher harmonics) waveforms of the parallel electric field, presumably due to the feedback from hot resonant electrons. We have considered the nature and properties of such nonlinear whistler waves observed by the Van Allen Probes and Time History of Events and Macroscale Interactions define during Substorms in the inner magnetosphere, and we show that the significant enhancement of the wave electrostatic component can result from whistler wave coupling with the beam-driven electrostatic mode through the resonant interaction with hot electron beams. Being modulated by a whistler wave, the electron beam generates a driven electrostatic mode significantly enhancing the parallel electric field of the initial whistler wave. We confirm this mechanism using a self-consistent particle-in-cell simulation. The nonlinear electrostatic component manifests properties of the beam-driven electron acoustic mode and can be responsible for effective electron acceleration in the inhomogeneous magnetic field.

Nonlinear distortion of thin liquid sheets

NASA Astrophysics Data System (ADS)

Mehring, Carsten Ralf

Thin planar, annular and conical liquid sheets or films are analyzed, in a unified manner, by means of a reduced- dimension approach providing governing equations for the nonlinear motion of planar and swirling annular thin inviscid and incompressible liquid sheets in zero gravity and with axial disturbances only. Temporal analyses of periodically disturbed infinite sheets are considered, as well as spatial analyses of semi-infinite sheets modulated at the nozzle exit. Results on planar and swirling annular or conical sheets are presented for a zero density ambient gas. Here, conical sheets are obtained in the nearfield of the nozzle exit by considering sheets or films with swirl in excess of that needed to stabilize the discharging stream in its annular configuration. For nonswirling annular sheets a spatially and/or temporally constant gas-core pressure is assumed. A model extension considering the influence of aerodynamic effects on planar sheets is proposed. For planar and annular sheets, linear analyses of the pure initial- and pure boundary-value problem provide insight into the propagation characteristics of dilational and sinuous waves, the (linear) coupling between both wave modes, the stability limits for the annular configuration, as well as the appearance of particular waves on semi-infinite modulated sheets downstream from the nozzle exit. Nonlinear steady-state solutions for the conical configuration (without modulation) are illustrated. Comparison between nonlinear and linear numerical and linear analytical solutions for temporally or spatially developing sheets provides detailed information on the nonlinear distortion characteristics including nonlinear wave propagation and mode-coupling for all the considered geometric configurations and for a variety of parameter configurations. Sensitivity studies on the influence of Weber number, modulation frequency, annular radius, forcing amplitude and sheet divergence on breakup or collapse length and times are reported for modulated semi-infinite annular and conical sheets. Comparisons between the different geometric configurations are made. For periodically disturbed planar sheets, accuracy of the employed reduced-dimension approach is demonstrated by comparison with more accurate two-dimensional vortex dynamics simulations.

Mechanics of inter-modal tunneling in nonlinear waveguides

NASA Astrophysics Data System (ADS)

Jiao, Weijian; Gonella, Stefano

2018-02-01

In this article, we investigate the mechanics of nonlinearly induced inter-modal energy tunneling between flexurally-dominated and axially-dominated modes in phononic waveguides. Special attention is devoted to elucidating the role played by the coupling between axial and flexural degrees of freedom in the determination of the available mode hopping conditions and the associated mechanisms of deformation. Waveguides offer an ideal test bed to investigate the mechanics of nonlinear energy tunneling, due to the fact that they naturally feature, even at low frequencies, families of modes (flexural and axial) that are intrinsically characterized by extreme complementarity. Moreover, thanks to their geometric simplicity, their behavior can be explained by resorting to intuitive structural mechanics models that effectively capture the dichotomy and interplay between flexural and axial mechanisms. After having delineated the fundamental mechanics of flexural-to-axial hopping using the benchmark example of a homogeneous structure, we adapt the analysis to the case of periodic waveguides, in which the complex dispersive behavior due to periodicity results in additional richness of mode hopping mechanisms. We finally extend the analysis to periodic waveguides with internal resonators, in which the availability of locally-resonant bandgaps implies the possibility to activate the resonators even at relatively low frequencies, thus increasing the degree of modal complementarity that is available in the acoustic range. In this context, inter-modal tunneling provides an unprecedented mechanism to transfer conspicuous packets of energy to the resonating microstructure.

Air-coupled laser vibrometry: analysis and applications.

PubMed

Solodov, Igor; Döring, Daniel; Busse, Gerd

2009-03-01

Acousto-optic interaction between a narrow laser beam and acoustic waves in air is analyzed theoretically. The photoelastic relation in air is used to derive the phase modulation of laser light in air-coupled reflection vibrometry induced by angular spatial spectral components comprising the acoustic beam. Maximum interaction was found for the zero spatial acoustic component propagating normal to the laser beam. The angular dependence of the imaging efficiency is determined for the axial and nonaxial acoustic components with the regard for the laser beam steering in the scanning mode. The sensitivity of air-coupled vibrometry is compared with conventional "Doppler" reflection vibrometry. Applications of the methodology for visualization of linear and nonlinear air-coupled fields are demonstrated.

Spatiotemporal splitting of global eigenmodes due to cross-field coupling via vortex dynamics in drift wave turbulence.

PubMed

Brandt, C; Thakur, S C; Light, A D; Negrete, J; Tynan, G R

2014-12-31

Spatiotemporal splitting events of drift wave (DW) eigenmodes due to nonlinear coupling are investigated in a cylindrical helicon plasma device. DW eigenmodes in the radial-azimuthal cross section have been experimentally observed to split at radial locations and recombine into the global eigenmode with a time shorter than the typical DW period (t≪fDW(-1)). The number of splits correlates with the increase of turbulence. The observed dynamics can be theoretically reproduced by a Kuramoto-type model of a network of radially coupled azimuthal eigenmodes. Coupling by E×B-vortex convection cell dynamics and ion gyro radii motion leads to cross-field synchronization and occasional mode splitting events.

Tunable resonant and non-resonant interactions between a phase qubit and LC resonator

NASA Astrophysics Data System (ADS)

Allman, Michael Shane; Whittaker, Jed D.; Castellanos-Beltran, Manuel; Cicak, Katarina; da Silva, Fabio; Defeo, Michael; Lecocq, Florent; Sirois, Adam; Teufel, John; Aumentado, Jose; Simmonds, Raymond W.

2014-03-01

We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current (dc) SQUID to generate strong resonant and non-resonant tunable interactions between a phase qubit and a lumped-element resonator. The rf-SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling rates from zero to near the ultra-strong coupling regime. By modulating the magnetic susceptibility, non-resonant parametric coupling achieves rates > 100 MHz . Nonlinearity of the magnetic susceptibility also leads to parametric coupling at subharmonics of the qubit-resonator detuning. Controllable coupling is generically important for constructing coupled-mode systems ubiquitous in physics, useful for both, quantum information architectures and quantum simulators. This work supported by NIST and NSA grant EAO140639.

Mode structure symmetry breaking of energetic particle driven beta-induced Alfvén eigenmode

NASA Astrophysics Data System (ADS)

Lu, Z. X.; Wang, X.; Lauber, Ph.; Zonca, F.

2018-01-01

The mode structure symmetry breaking of energetic particle driven Beta-induced Alfvén Eigenmode (BAE) is studied based on global theory and simulation. The weak coupling formula gives a reasonable estimate of the local eigenvalue compared with global hybrid simulation using XHMGC. The non-perturbative effect of energetic particles on global mode structure symmetry breaking in radial and parallel (along B) directions is demonstrated. With the contribution from energetic particles, two dimensional (radial and poloidal) BAE mode structures with symmetric/asymmetric tails are produced using an analytical model. It is demonstrated that the symmetry breaking in radial and parallel directions is intimately connected. The effects of mode structure symmetry breaking on nonlinear physics, energetic particle transport, and the possible insight for experimental studies are discussed.

Stability of elastic bending and torsion of uniform cantilever rotor blades in hover with variable structural coupling

NASA Technical Reports Server (NTRS)

Hodges, D. H., Roberta.

1976-01-01

The stability of elastic flap bending, lead-lag bending, and torsion of uniform, untwisted, cantilever rotor blades without chordwise offsets between the elastic, mass, tension, and areodynamic center axes is investigated for the hovering flight condition. The equations of motion are obtained by simplifying the general, nonlinear, partial differential equations of motion of an elastic rotating cantilever blade. The equations are adapted for a linearized stability analysis in the hovering flight condition by prescribing aerodynamic forces, applying Galerkin's method, and linearizing the resulting ordinary differential equations about the equilibrium operating condition. The aerodynamic forces are obtained from strip theory based on a quasi-steady approximation of two-dimensional unsteady airfoil theory. Six coupled mode shapes, calculated from free vibration about the equilibrium operating condition, are used in the linearized stability analysis. The study emphasizes the effects of two types of structural coupling that strongly influence the stability of hingeless rotor blades. The first structural coupling is the linear coupling between flap and lead-lag bending of the rotor blade. The second structural coupling is a nonlinear coupling between flap bending, lead-lag bending, and torsion deflections. Results are obtained for a wide variety of hingeless rotor configurations and operating conditions in order to provide a reasonably complete picture of hingeless rotor blade stability characteristics.

Numerical simulation of turbulence and terahertz magnetosonic waves generation in collisionless plasmas

NASA Astrophysics Data System (ADS)

Kumar, Narender; Singh, Ram Kishor; Sharma, Swati; Uma, R.; Sharma, R. P.

2018-01-01

This paper presents numerical simulations of laser beam (x-mode) coupling with a magnetosonic wave (MSW) in a collisionless plasma. The coupling arises through ponderomotive non-linearity. The pump beam has been perturbed by a periodic perturbation that leads to the nonlinear evolution of the laser beam. It is observed that the frequency spectra of the MSW have peaks at terahertz frequencies. The simulation results show quite complex localized structures that grow with time. The ensemble averaged power spectrum has also been studied which indicates that the spectral index follows an approximate scaling of the order of ˜ k-2.1 at large scales and scaling of the order of ˜ k-3.6 at smaller scales. The results indicate considerable randomness in the spatial structure of the magnetic field profile which gives sufficient indication of turbulence.

Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

NASA Astrophysics Data System (ADS)

Vila, J.; Fernández-Sáez, J.; Zaera, R.

2018-04-01

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

A triangular thin shell finite element: Nonlinear analysis. [structural analysis

NASA Technical Reports Server (NTRS)

Thomas, G. R.; Gallagher, R. H.

1975-01-01

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Rational solitons in deep nonlinear optical Bragg grating.

PubMed

Alatas, H; Iskandar, A A; Tjia, M O; Valkering, T P

2006-06-01

We have examined the rational solitons in the Generalized Coupled Mode model for a deep nonlinear Bragg grating. These solitons are the degenerate forms of the ordinary solitons and appear at the transition lines in the parameter plane. A simple formulation is presented for the investigation of the bifurcations induced by detuning the carrier wave frequency. The analysis yields among others the appearance of in-gap dark and antidark rational solitons unknown in the nonlinear shallow grating. The exact expressions for the corresponding rational solitons are also derived in the process, which are characterized by rational algebraic functions. It is further demonstrated that certain effects in the soliton energy variations are to be expected when the frequency is varied across the values where the rational solitons appear.

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

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

Arefiev, A. V.; Dodin, I. Y.; Kohn, A.

Spherical tokamak plasmas are typically overdense and thus inaccessible to externally-injected microwaves in the electron cyclotron range. The electrostatic electron Bernstein wave (EBW), however, provides a method to access the plasma core for heating and diagnostic purposes. Understanding the details of the coupling process to electromagnetic waves is thus important both for the interpretation of microwave diagnostic data and for assessing the feasibility of EBW heating and current drive. While the coupling is reasonably well–understood in the linear regime, nonlinear physics arising from high input power has not been previously quantified. To tackle this problem, we have performed one- andmore » two-dimensional fully kinetic particle-in-cell simulations of the two possible coupling mechanisms, namely X-B and O-X-B mode conversion. We find that the ion dynamics has a profound effect on the field structure in the nonlinear regime, as high amplitude short-scale oscillations of the longitudinal electric field are excited in the region below the high-density cut-off prior to the arrival of the EBW. We identify this effect as the instability of the X wave with respect to resonant scattering into an EBW and a lower-hybrid wave. Finally, we calculate the instability rate analytically and find this basic theory to be in reasonable agreement with our simulation results.« less

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.

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

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

Nankali, Amir; Grosh, Karl; Department of Biomedical Engineering, University of Michigan, Ann Arbor, Michigan

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

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

DOE PAGES

Arefiev, A. V.; Dodin, I. Y.; Kohn, A.; ...

2017-08-09

Spherical tokamak plasmas are typically overdense and thus inaccessible to externally-injected microwaves in the electron cyclotron range. The electrostatic electron Bernstein wave (EBW), however, provides a method to access the plasma core for heating and diagnostic purposes. Understanding the details of the coupling process to electromagnetic waves is thus important both for the interpretation of microwave diagnostic data and for assessing the feasibility of EBW heating and current drive. While the coupling is reasonably well–understood in the linear regime, nonlinear physics arising from high input power has not been previously quantified. To tackle this problem, we have performed one- andmore » two-dimensional fully kinetic particle-in-cell simulations of the two possible coupling mechanisms, namely X-B and O-X-B mode conversion. We find that the ion dynamics has a profound effect on the field structure in the nonlinear regime, as high amplitude short-scale oscillations of the longitudinal electric field are excited in the region below the high-density cut-off prior to the arrival of the EBW. We identify this effect as the instability of the X wave with respect to resonant scattering into an EBW and a lower-hybrid wave. Finally, we calculate the instability rate analytically and find this basic theory to be in reasonable agreement with our simulation results.« less

Tunable all-optical plasmonic rectifier in nanoscale metal-insulator-metal waveguides.

PubMed

Xu, Yi; Wang, Xiaomeng; Deng, Haidong; Guo, Kangxian

2014-10-15

We propose a tunable all-optical plasmonic rectifier based on the nonlinear Fano resonance in a metal-insulator-metal plasmonic waveguide and cavities coupling system. We develop a theoretical model based on the temporal coupled-mode theory to study the device physics of the nanoscale rectifier. We further demonstrate via the finite difference time domain numerical experiment that our idea can be realized in a plasmonic system with an ultracompact size of ~120×800  nm². The tunable plasmonic rectifier could facilitate the all-optical signal processing in nanoscale.

Exploiting elastic anharmonicity in aluminum nitride matrix for phase-synchronous frequency reference generation

NASA Astrophysics Data System (ADS)

Ghatge, Mayur; Tabrizian, Roozbeh

2018-03-01

A matrix of aluminum-nitride (AlN) waveguides is acoustically engineered to realize electrically isolated phase-synchronous frequency references through nonlinear wave-mixing. AlN rectangular waveguides are cross-coupled through a periodically perforated plate that is engineered to have a wide acoustic bandgap around a desirable frequency ( f1≈509 MHz). While the coupling plate isolates the matrix from resonant vibrations of individual waveguide constituents at f1, it is transparent to the third-order harmonic waves (3f1) that are generated through nonlinear wave-mixing. Therefore, large-signal excitation of the f1 mode in a constituent waveguide generates acoustic waves at 3f1 with an efficiency defined by elastic anharmonicity of the AlN film. The phase-synchronous propagation of the third harmonic through the matrix is amplified by a high quality-factor resonance mode at f2≈1529 MHz, which is sufficiently close to 3f1 (f2 ≅ 3f1). Such an architecture enables realization of frequency-multiplied and phase-synchronous, yet electrically and spectrally isolated, references for multi-band/carrier and spread-spectrum wireless communication systems.

Gyrokinetic GDC turbulence simulations: confirming a new instability regime in LAPD plasmas

NASA Astrophysics Data System (ADS)

Pueschel, M. J.; Rossi, G.; Told, D.; Terry, P. W.; Jenko, F.; Carter, T. A.

2016-10-01

Recent high-beta experiments at the LArge Plasma Device have found significant parallel magnetic fluctuations in the region of large pressure gradients. Linear gyrokinetic simulations show the dominant instability at these radii to be the gradient-driven drift coupling (GDC) mode, a non-textbook mode driven by pressure gradients and destabilized by the coupling of ExB and grad-B∥ drifts. Unlike in previous studies, the large parallel extent of the device allows for finite-kz versions of this instability in addition to kz = 0 . The locations of maximum linear growth match very well with experimentally observed peaks of B∥ fluctuations. Local nonlinear simulations reproduce many features of the observations fairly well, with the exception of Bperp fluctuations, for which experimental profiles suggest a source unrelated to pressure gradients. In toto, the results presented here show that turbulence and transport in these experiments are driven by the GDC instability, that important characteristics of the linear instability carry over to nonlinear simulations, and - in the context of validation - that the gyrokinetic framework performs surprisingly well far outside its typical area of application, increasing confidence in its predictive abilities. Supported by U.S. DOE.

Finite element analysis of hysteresis effects in piezoelectric transducers

NASA Astrophysics Data System (ADS)

Simkovics, Reinhard; Landes, Hermann; Kaltenbacher, Manfred; Hoffelner, Johann; Lerch, Reinhard

2000-06-01

The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.

Excitation of a nonlinear plasma ion wake by intense energy sources with applications to the crunch-in regime

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

Sahai, Aakash A.

We show the excitation of a nonlinear ion-wake mode by plasma electron modes in the bubble regime driven by intense energy sources, using analytical theory and simulations. The ion wake is shown to be a driven nonlinear ion-acoustic wave in the form of a long-lived cylindrical ion soliton which limits the repetition rate of a plasma-based particle accelerator in the bubble regime. We present the application of this evacuated and radially outwards propagating ion-wake channel with an electron skin-depth scale radius for the “crunch-in” regime of hollow-channel plasma. It is shown that the time-asymmetric focusing force phases in the bubblemore » couple to ion motion significantly differently than in the linear electron mode. The electron compression in the back of the bubble sucks in the ions whereas the space charge within the bubble cavity expels them, driving a cylindrical ion-soliton structure at the bubble radius. Once formed, the soliton is sustained and driven radially outwards by the thermal pressure of the wake energy in electrons. Particle-in-cell simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration in the crunch-in regime.« less

Excitation of a nonlinear plasma ion wake by intense energy sources with applications to the crunch-in regime

DOE PAGES

Sahai, Aakash A.

2017-08-23

We show the excitation of a nonlinear ion-wake mode by plasma electron modes in the bubble regime driven by intense energy sources, using analytical theory and simulations. The ion wake is shown to be a driven nonlinear ion-acoustic wave in the form of a long-lived cylindrical ion soliton which limits the repetition rate of a plasma-based particle accelerator in the bubble regime. We present the application of this evacuated and radially outwards propagating ion-wake channel with an electron skin-depth scale radius for the “crunch-in” regime of hollow-channel plasma. It is shown that the time-asymmetric focusing force phases in the bubblemore » couple to ion motion significantly differently than in the linear electron mode. The electron compression in the back of the bubble sucks in the ions whereas the space charge within the bubble cavity expels them, driving a cylindrical ion-soliton structure at the bubble radius. Once formed, the soliton is sustained and driven radially outwards by the thermal pressure of the wake energy in electrons. Particle-in-cell simulations are used to study the ion-wake soliton structure, its driven propagation and its use for positron acceleration in the crunch-in regime.« less

Generation of filamentary structures by beam-plasma interaction

NASA Astrophysics Data System (ADS)

Wang, X. Y.; Lin, Y.

2006-05-01

The previous simulations by Wang and Lin [Phys. Plasmas. 10, 3528, (2003)] showed that filaments, frequently observed in space plasmas, can form via the interaction between an ion beam and a background plasma. In this study, the physical mechanism for the generation of the filaments is investigated by a two-dimensional hybrid simulation, in which a field-aligned ion beam with relative beam density nb=0.1 and beam velocity Vb=10VA is initiated in a uniform plasma. Right-hand nonresonant ion beam modes, consistent with the linear theory, are found to be dominant in the linear stage of the beam-plasma interaction. In the later nonlinear stage, the nonresonant modes decay and the resonant modes grow through a nonlinear wave coupling. The interaction among the resonant modes leads to the formation of filamentary structures, which are the field-aligned structures (k⊥B) of magnetic field B, density, and temperature in the final stage. The filaments are nonlinearly generated in a prey-predator fashion by the parallel and oblique resonant ion beam modes, which meanwhile evolve into two types of shear Alfvén modes, with one mainly propagating along the background field B0 and the other obliquely propagating. The filamentary structures are found to be phase standing in the plasma frame, but their amplitude oscillates with time. In the dominant filament mode, fluctuations in the background ion density, background ion temperature, and beam density are in phase with the fluctuations in B, whereas the significantly enhanced beam temperature is antiphase with B. It is found that the filaments are produced by the interaction of at least two ion beam modes with comparable amplitudes, not by only one single mode, thus their generation mechanism is different from other mechanisms such as the stimulated excitation by the decay of an Alfvén wave.

Oscillation Mode Variability in Evolved Compact Pulsators from Kepler Photometry. I. The Hot B Subdwarf Star KIC 3527751

NASA Astrophysics Data System (ADS)

Zong, Weikai; Charpinet, Stéphane; Fu, Jian-Ning; Vauclair, Gérard; Niu, Jia-Shu; Su, Jie

2018-02-01

We present the first results of an ensemble and systematic survey of oscillation mode variability in pulsating hot B subdwarf (sdB) and white dwarf stars observed with the original Kepler mission. The satellite provides uninterrupted high-quality photometric data with a time baseline that can reach up to 4 yr collected on pulsating stars. This is a unique opportunity to characterize long-term behaviors of oscillation modes. A mode modulation in amplitude and frequency can be independently inferred by its fine structure in the Fourier spectrum, from the sLSP, or with prewhitening methods applied to various parts of the light curve. We apply all these techniques to the sdB star KIC 3527751, a long-period-dominated hybrid pulsator. We find that all the detected modes with sufficiently large amplitudes to be thoroughly studied show amplitude and/or frequency variations. Components of three identified quintuplets around 92, 114, and 253 μHz show signatures that can be linked to nonlinear interactions according to the resonant mode coupling theory. This interpretation is further supported by the fact that many oscillation modes are found to have amplitudes and frequencies showing correlated or anticorrelated variations, a behavior that can be linked to the amplitude equation formalism, where nonlinear frequency corrections are determined by their amplitude variations. Our results suggest that oscillation modes varying with diverse patterns are a very common phenomenon in pulsating sdB stars. Close structures around main frequencies therefore need to be carefully interpreted in light of this finding to secure a robust identification of real eigenfrequencies, which is crucial for seismic modeling. The various modulation patterns uncovered should encourage further developments in the field of nonlinear stellar oscillation theory. It also raises a warning to any long-term project aiming at measuring the rate of period change of pulsations caused by stellar evolution, or at discovering stellar (planetary) companions around pulsating stars using timing methods, as both require very stable pulsation modes.

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.

Two-component vector solitons in defocusing Kerr-type media with spatially modulated nonlinearity

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

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A and M University at Qatar, P.O. Box 23874 Doha; Belić, Milivoj

2014-12-15

We present a class of exact solutions to the coupled (2+1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity and a special external potential, which describe the evolution of two-component vector solitons in defocusing Kerr-type media. We find a robust soliton solution, constructed with the help of Whittaker functions. For specific choices of the topological charge, the radial mode number and the modulation depth, the solitons may exist in various forms, such as the half-moon, necklace-ring, and sawtooth vortex-ring patterns. Our results show that the profile of such solitons can be effectively controlled by the topological charge, the radial mode number,more » and the modulation depth. - Highlights: • Two-component vector soliton clusters in defocusing Kerr-type media are reported. • These soliton clusters are constructed with the help of Whittaker functions. • The half-moon, necklace-ring and vortex-ring patterns are found. • The profile of these solitons can be effectively controlled by three soliton parameters.« less

Phase locking of multi-helicity neoclassical tearing modes in tokamak plasmas

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

Fitzpatrick, Richard

2015-04-15

The attractive “hybrid” tokamak scenario combines comparatively high q{sub 95} operation with improved confinement compared with the conventional H{sub 98,y2} scaling law. Somewhat unusually, hybrid discharges often exhibit multiple neoclassical tearing modes (NTMs) possessing different mode numbers. The various NTMs are eventually observed to phase lock to one another, giving rise to a significant flattening, or even an inversion, of the core toroidal plasma rotation profile. This behavior is highly undesirable because the loss of core plasma rotation is known to have a deleterious effect on plasma stability. This paper presents a simple, single-fluid, cylindrical model of the phase lockingmore » of two NTMs with different poloidal and toroidal mode numbers in a tokamak plasma. Such locking takes place via a combination of nonlinear three-wave coupling and conventional toroidal coupling. In accordance with experimental observations, the model predicts that there is a bifurcation to a phase-locked state when the frequency mismatch between the modes is reduced to one half of its original value. In further accordance, the phase-locked state is characterized by the permanent alignment of one of the X-points of NTM island chains on the outboard mid-plane of the plasma, and a modified toroidal angular velocity profile, interior to the outermost coupled rational surface, which is such that the core rotation is flattened, or even inverted.« less

Soliton interactions and complexes for coupled nonlinear Schrödinger equations.

PubMed

Jiang, Yan; Tian, Bo; Liu, Wen-Jun; Sun, Kun; Li, Min; Wang, Pan

2012-03-01

Under investigation in this paper are the coupled nonlinear Schrödinger (CNLS) equations, which can be used to govern the optical-soliton propagation and interaction in such optical media as the multimode fibers, fiber arrays, and birefringent fibers. By taking the 3-CNLS equations as an example for the N-CNLS ones (N≥3), we derive the analytic mixed-type two- and three-soliton solutions in more general forms than those obtained in the previous studies with the Hirota method and symbolic computation. With the choice of parameters for those soliton solutions, soliton interactions and complexes are investigated through the asymptotic and graphic analysis. Soliton interactions and complexes with the bound dark solitons in a mode or two modes are observed, including that (i) the two bright solitons display the breatherlike structures while the two dark ones stay parallel, (ii) the two bright and dark solitons all stay parallel, and (iii) the states of the bound solitons change from the breatherlike structures to the parallel one even with the distance between those solitons smaller than that before the interaction with the regular one soliton. Asymptotic analysis is also used to investigate the elastic and inelastic interactions between the bound solitons and the regular one soliton. Furthermore, some discussions are extended to the N-CNLS equations (N>3). Our results might be helpful in such applications as the soliton switch, optical computing, and soliton amplification in the nonlinear optics.

Fingering patterns in magnetic fluids: Perturbative solutions and the stability of exact stationary shapes

NASA Astrophysics Data System (ADS)

Anjos, Pedro H. A.; Lira, Sérgio A.; Miranda, José A.

2018-04-01

We examine the formation of interfacial patterns when a magnetic liquid droplet (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. By using a vortex-sheet formalism, we find exact stationary solutions for the fluid-fluid interface in the form of n -fold polygonal shapes. A weakly nonlinear, mode-coupling method is then utilized to find time-evolving perturbative solutions for the interfacial patterns. The stability of such nonzero surface tension exact solutions is checked and discussed, by trying to systematically approach the exact stationary shapes through perturbative solutions containing an increasingly larger number of participating Fourier modes. Our results indicate that the exact stationary solutions of the problem are stable, and that a good matching between exact and perturbative shape solutions is achieved just by using a few Fourier modes. The stability of such solutions is substantiated by a linearization process close to the stationary shape, where a system of mode-coupling equations is diagonalized, determining the eigenvalues which dictate the stability of a fixed point.

Quantum statistics for a two-mode magnon system with microwave pumping: application to coupled ferromagnetic nanowires.

PubMed

Haghshenasfard, Zahra; Cottam, M G

2017-05-17

A microscopic (Hamiltonian-based) method for the quantum statistics of bosonic excitations in a two-mode magnon system is developed. Both the exchange and the dipole-dipole interactions, as well as the Zeeman term for an external applied field, are included in the spin Hamiltonian, and the model also contains the nonlinear effects due to parallel pumping and four-magnon interactions. The quantization of spin operators is achieved through the Holstein-Primakoff formalism, and then a coherent magnon state representation is used to study the occupation magnon number and the quantum statistical behaviour of the system. Particular attention is given to the cross correlation between the two coupled magnon modes in a ferromagnetic nanowire geometry formed by two lines of spins. Manipulation of the collapse-and-revival phenomena for the temporal evolution of the magnon number as well as the control of the cross correlation between the two magnon modes is demonstrated by tuning the parallel pumping field amplitude. The role of the four-magnon interactions is particularly interesting and leads to anti-correlation in some cases with coherent states.

Coupled harmonic oscillators and their quantum entanglement.

PubMed

Makarov, Dmitry N

2018-04-01

A system of two coupled quantum harmonic oscillators with the Hamiltonian H[over ̂]=1/2(1/m_{1}p[over ̂]_{1}^{2}+1/m_{2}p[over ̂]_{2}^{2}+Ax_{1}^{2}+Bx_{2}^{2}+Cx_{1}x_{2}) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H[over ̂]Ψ=iℏ∂Ψ/∂t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

Coupled harmonic oscillators and their quantum entanglement

NASA Astrophysics Data System (ADS)

Makarov, Dmitry N.

2018-04-01

A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.

Modulational instabilities in acetanilide taking into account both the N H and the C=O vibrational self-trappings

NASA Astrophysics Data System (ADS)

Simo, Elie

2007-02-01

A model of crystalline acetanilide, ACN accounting for the C=O and N-H vibrational self-trappings is presented. We develop a fully discrete version of ACN. We show that ACN can be described by a set of two coupled discrete nonlinear Schrödinger (DNLS) equations. Modulational instabilities (MI) are studied both theoretically and numerically. Dispersion laws for the wavenumbers and frequencies of the linear modulation waves are determined. We also derived the criterion for the existence of MI. Numerical simulations are carried out for a variety of selected wave amplitudes in the unstable zone. It is shown that instabilities grow as the wavenumbers and amplitudes of the modulated waves increase. MI grow faster in the N-H mode than in the C=O mode. Temporal evolution of the density probabilities of the vibrational excitons are obtained by the numerical integration of the coupled DNLS equations governing the ACN molecule. These investigations confirm the generation of localized modes by the phenomenon of MI and the predominance of the N-H vibrational mode in the MI process of the ACN.

Sigma omega meson coupling and properties of nuclei and nuclear matter

NASA Astrophysics Data System (ADS)

Haidari, Maryam M.; Sharma, Madan M.

2008-05-01

We have constructed a Lagrangian model with a coupling of σ and ω mesons in the relativistic mean-field theory. Properties of finite nuclei and nuclear matter are explored with the new Lagrangian model SIG-OM. The study shows that an excellent description of binding energies and charge radii of nuclei over a large range of isospin is achieved with SIG-OM. With an incompressibility of nuclear matter K=265 MeV, it is also able to describe the breathing-mode isoscalar giant monopole resonance energies appropriately. It is shown that the high-density behaviour of the equation of state of nuclear and neutron matter with the σ-ω coupling is much softer than that of the non-linear scalar coupling model.

Effects of Equilibrium Toroidal Flow on Locked Mode and Plasma Response in a Tokamak

NASA Astrophysics Data System (ADS)

Zhu, Ping; Huang, Wenlong; Yan, Xingting

2016-10-01

It is widely believed that plasma flow plays significant roles in regulating the processes of mode locking and plasma response in a tokamak in presence of external resonant magnetic perturbations (RMPs). Recently a common analytic relation for both locked mode and plasma response has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance. The analytic relation predicts the size of the magnetic island of a locked mode or a static nonlinear plasma response for a given RMP amplitude, and rigorously proves a screening effect of the equilibrium toroidal flow. To test the theory, we solve for the locked mode and the nonlinear plasma response in presence of RMP for a circular-shaped limiter tokamak equilibrium with constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. The comparison between the simulation results and the theory prediction, in terms of the quantitative screening effects of equilibrium toroidal flow, will be reported and discussed. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

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.

Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system

NASA Astrophysics Data System (ADS)

He, Qiongyi; Ficek, Zbigniew

2014-02-01

We study multipartite entanglement, the generation of Einstein-Podolsky-Rosen (EPR) states, and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beam-splitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuator of the output fields. The threshold is determined by the ratio of the coupling strengths of the cavity mode to the mirror and to the atomic ensemble. It is shown that above the threshold, the system effectively behaves as a two-mode system in which a perfect bipartite EPR state can be generated, while it is impossible below the threshold. Furthermore, a fully inseparable tripartite entanglement and even further a genuine tripartite entanglement can be produced above and below the threshold. In addition, we consider quantum steering and examine the monogamy relations that quantify the amount of bipartite steering that can be shared between different modes. It is found that the mirror is more capable for steering of entanglement than the cavity mode. The two-way steering is found between the mirror and the atomic ensemble despite the fact that they are not directly coupled to each other, while it is impossible between the output of cavity mode and the ensemble which are directly coupled to each other.

Nonlinear evolution of energetic-particles-driven waves in collisionless plasmas

NASA Astrophysics Data System (ADS)

Li, Shuhan; Liu, Jinyuan; Wang, Feng; Shen, Wei; Li, Dong

2018-06-01

A one-dimensional electrostatic collisionless particle-in-cell code has been developed to study the nonlinear interaction between electrostatic waves and energetic particles (EPs). For a single wave, the results are clear and agree well with the existing theories. For coexisting two waves, although the mode nonlinear coupling between two wave fields is ignored, the second-order phase space islands can still exist between first-order islands generated by the two waves. However, the second-order phase islands are not formed by the superposed wave fields and the perturbed motions of EPs induced by the combined effect of two main resonances make these structures in phase space. Owing to these second-order islands, energy can be transferred between waves, even if the overlap of two main resonances never occurs. Depending on the distance between the main resonance islands in velocity space, the second-order island can affect the nonlinear dynamics and saturations of waves.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

The contribution of NOAA/CMDL ground-based measurements to understanding long-term stratospheric changes

NASA Astrophysics Data System (ADS)

Montzka, S. A.; Butler, J. H.; Dutton, G.; Thompson, T. M.; Hall, B.; Mondeel, D. J.; Elkins, J. W.

2005-05-01

The El-Nino/Southern-Oscillation (ENSO) dominates interannual climate variability and plays, therefore, a key role in seasonal-to-interannual prediction. Much is known by now about the main physical mechanisms that give rise to and modulate ENSO, but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean--atmosphere model of ENSO. The coupled model consists of an upper-ocean, reduced-gravity model of the Tropical Pacific and a steady-state atmospheric response to the sea surface temperature (SST). The model errors are assumed to be mainly in the atmospheric wind stress, and assimilated data are equatorial Pacific SSTs. Model behavior is very sensitive to two key parameters: (i) μ, the ocean-atmosphere coupling coefficient between SST and wind stress anomalies; and (ii) δs, the surface-layer coefficient. Previous work has shown that δs determines the period of the model's self-sustained oscillation, while μ measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Estimation of these parameters is tested first on synthetic data and allows us to recover the delayed-oscillator mode starting from model parameter values that correspond to the westward-propagating case. Assimilation of SST data from the NCEP-NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean--atmosphere GCMs will be discussed.

Symmetry blockade and its breakdown in energy equipartition of square graphene resonators

NASA Astrophysics Data System (ADS)

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

2018-03-01

The interaction between flexural modes due to nonlinear potentials is critical to heat conductivity and mechanical vibration of two dimensional materials such as graphene. Much effort has been devoted to understanding the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during the equipartition process. In particular, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes, forming symmetry blockades. As a result, the energy first flows to the modes in the same symmetry class. Breakdown of the symmetry blockade, i.e., inter-class energy flow, starts when the displacement profile becomes complex and the inter-class couplings bear nonneglectable values. The equipartition time follows the stretched exponential law and survives in the thermodynamic limit. 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 contribution in high thermal conductivity and mechanism of energy dissipation that may intrinsically limit the quality factor of the resonator.

Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes.

PubMed

Seitner, Maximilian J; Abdi, Mehdi; Ridolfo, Alessandro; Hartmann, Michael J; Weig, Eva M

2017-06-23

We study locking phenomena of two strongly coupled, high quality factor nanomechanical resonator modes to a common parametric drive at a single drive frequency in different parametric driving regimes. By controlled dielectric gradient forces we tune the resonance frequencies of the flexural in-plane and out-of-plane oscillation of the high stress silicon nitride string through their mutual avoided crossing. For the case of the strong common parametric drive signal-idler generation via nondegenerate parametric two-mode oscillation is observed. Broadband frequency tuning of the very narrow linewidth signal and idler resonances is demonstrated. When the resonance frequencies of the signal and idler get closer to each other, partial injection locking, injection pulling, and complete injection locking to half of the drive frequency occurs depending on the pump strength. Furthermore, satellite resonances, symmetrically offset from the signal and idler by their beat note, are observed, which can be attributed to degenerate four-wave mixing in the highly nonlinear mechanical oscillations.

Single photons from a gain medium below threshold

NASA Astrophysics Data System (ADS)

Ghosh, Sanjib; Liew, Timothy C. H.

2018-06-01

The emission from a nonlinear photonic mode coupled weakly to a gain medium operating below threshold is predicted to exhibit antibunching. In the steady state regime, analytical solutions for the relevant observable quantities are found in accurate agreement with exact numerical results. Under pulsed excitation, the unequal time second-order correlation function demonstrates the triggered probabilistic generation of single photons well separated in time.

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.

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.

Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design.

PubMed

Megam Ngouonkadi, Elie Bertrand; Fotsin, Hilaire Bertrand; Kabong Nono, Martial; Louodop Fotso, Patrick Herve

2016-10-01

In this paper, we report on the synchronization of a pacemaker neuronal ensemble constituted of an AB neuron electrically coupled to two PD neurons. By the virtue of this electrical coupling, they can fire synchronous bursts of action potential. An external master neuron is used to induce to the whole system the desired dynamics, via a nonlinear controller. Such controller is obtained by a combination of sliding mode and feedback control. The proposed controller is able to offset uncertainties in the synchronized systems. We show how noise affects the synchronization of the pacemaker neuronal ensemble, and briefly discuss its potential benefits in our synchronization scheme. An extended Hindmarsh-Rose neuronal model is used to represent a single cell dynamic of the network. Numerical simulations and Pspice implementation of the synchronization scheme are presented. We found that, the proposed controller reduces the stochastic resonance of the network when its gain increases.

Mode-coupling theoretical study on the roles of heterogeneous structure in rheology of ionic liquids.

PubMed

Yamaguchi, Tsuyoshi

2016-03-28

Theoretical calculations of the rheological properties of coarse-grained model ionic liquids were performed using mode-coupling theory. The nonpolar part of the cation was systematically increased in order to clarify the effects of the heterogeneous structure on shear viscosity. The shear viscosity showed a minimum as the function of the size of the nonpolar part, as had been reported in literatures. The minimum was ascribed to the interplay between the increase in the shear relaxation time and the decrease in the high-frequency shear modulus with increasing the size of the nonpolar part of the cation. The ionic liquids with symmetric charge distribution of cations were less viscous than those with asymmetric cations, which is also in harmony with experiments. The theoretical analysis demonstrated that there are two mechanisms for the higher viscosity of the asymmetric model. The first one is the direct coupling between the domain dynamics and the shear stress. The second one is that the microscopic dynamics within the polar domain is retarded due to the nonlinear coupling with the heterogeneous structure.

Vortices at the magnetic equator generated by hybrid Alfvén resonant waves

NASA Astrophysics Data System (ADS)

Hiraki, Yasutaka

2015-01-01

We performed three-dimensional magnetohydrodynamic simulations of shear Alfvén waves in a full field line system with magnetosphere-ionosphere coupling and plasma non-uniformities. Feedback instability of the Alfvén resonant modes showed various nonlinear features under the field line cavities: (i) a secondary flow shear instability occurs at the magnetic equator, (ii) trapping of the ionospheric Alfvén resonant modes facilitates deformation of field-aligned current structures, and (iii) hybrid Alfvén resonant modes grow to cause vortices and magnetic oscillations around the magnetic equator. Essential features in the initial brightening of auroral arc at substorm onsets could be explained by the dynamics of Alfvén resonant modes, which are the nature of the field line system responding to a background rapid change.

Sensitivity of a Wave Structure to Initial Conditions

NASA Technical Reports Server (NTRS)

Duval, Walter M. B.; Duval, Walter M. B. (Technical Monitor)

2000-01-01

Microgravity experiments aimed at quantifying effects of gentler via controlled sinusoidal forcing transmitted on the interface between two miscible liquids have shown the evolution of a quasi -stationary four-mode wave structure oriented vertically. The sensitivity of the wave structure to phase angle variation is investigated computationally. We show that a slight variation of the phase angle is sufficient to cause a bifurcation to a two-mode structure. The dependence of phase angle on wave structure is attributed to sensitivity on initial conditions due to the strong nonlinearity of the coupled field equations for the parametric space of interest.

Linear and non-linear flow mode in Pb-Pb collisions at √{sNN} = 2.76 TeV

NASA Astrophysics Data System (ADS)

Acharya, S.; Adamová, D.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, N.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Alba, J. L. B.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Alme, J.; Alt, T.; Altenkamper, L.; Altsybeev, I.; Alves Garcia Prado, C.; An, M.; Andrei, C.; Andreou, D.; Andrews, H. A.; Andronic, A.; Anguelov, V.; Anson, C.; Antičić, T.; Antinori, F.; Antonioli, P.; Anwar, R.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Baldisseri, A.; Ball, M.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barioglio, L.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartsch, E.; Basile, M.; Bastid, N.; Basu, S.; Bathen, B.; Batigne, G.; Batista Camejo, A.; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Beltran, L. G. E.; Belyaev, V.; Bencedi, G.; Beole, S.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Blair, J. T.; Blau, D.; Blume, C.; Boca, G.; Bock, F.; Bogdanov, A.; Boldizsár, L.; Bombara, M.; Bonomi, G.; Bonora, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buhler, P.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Caines, H.; Caliva, A.; Calvo Villar, E.; Camerini, P.; Capon, A. A.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cerello, P.; Chandra, S.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Chowdhury, T.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Concas, M.; Conesa Balbastre, G.; Conesa Del Valle, Z.; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Costanza, S.; Crkovská, J.; Crochet, P.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; de, S.; de Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; de Falco, A.; de Gruttola, D.; De Marco, N.; de Pasquale, S.; de Souza, R. D.; Degenhardt, H. F.; Deisting, A.; Deloff, A.; Deplano, C.; Dhankher, P.; di Bari, D.; di Mauro, A.; di Nezza, P.; di Ruzza, B.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Doremalen, L. V. V.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Duggal, A. K.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erhardt, F.; Espagnon, B.; Esumi, S.; Eulisse, G.; Eum, J.; Evans, D.; Evdokimov, S.; Fabbietti, L.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernández Téllez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Francisco, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gajdosova, K.; Gallio, M.; Galvan, C. D.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Garg, K.; Garg, P.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Gay Ducati, M. B.; Germain, M.; Ghosh, J.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; Gonzalez, V.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Graczykowski, L. K.; Graham, K. L.; Greiner, L.; Grelli, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grion, N.; Gronefeld, J. M.; Grosa, F.; Grosse-Oetringhaus, J. F.; Grosso, R.; Gruber, L.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Guzman, I. B.; Haake, R.; Hadjidakis, C.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hassan, H.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Herrmann, F.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hills, C.; Hippolyte, B.; Hladky, J.; Hohlweger, B.; Horak, D.; Hornung, S.; Hosokawa, R.; Hristov, P.; Hughes, C.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Iga Buitron, S. A.; Ilkaev, R.; Inaba, M.; Ippolitov, M.; Irfan, M.; Isakov, V.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacak, B.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jaelani, S.; Jahnke, C.; Jakubowska, M. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Jercic, M.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Ketzer, B.; Khabanova, Z.; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Khatun, A.; Khuntia, A.; Kielbowicz, M. M.; Kileng, B.; Kim, D.; Kim, D. W.; Kim, D. J.; Kim, H.; Kim, J. S.; Kim, J.; Kim, M.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Konyushikhin, M.; Kopcik, M.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Koyithatta Meethaleveedu, G.; Králik, I.; Kravčáková, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kundu, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kushpil, S.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Lagana Fernandes, C.; Lai, Y. S.; Lakomov, I.; Langoy, R.; Lapidus, K.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lavicka, R.; Lazaridis, L.; Lea, R.; Leardini, L.; Lee, S.; Lehas, F.; Lehner, S.; Lehrbach, J.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; León Monzón, I.; Lévai, P.; Li, S.; Li, X.; Lien, J.; Lietava, R.; Lim, B.; Lindal, S.; Lindenstruth, V.; Lindsay, S. W.; Lippmann, C.; Lisa, M. A.; Litichevskyi, V.; Ljunggren, H. M.; Llope, W. J.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Loncar, P.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lupi, M.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Mao, Y.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martinengo, P.; Martinez, J. A. L.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Masson, E.; Mastroserio, A.; Mathis, A. M.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzilli, M.; Mazzoni, M. A.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Mhlanga, S.; Miake, Y.; Mieskolainen, M. M.; Mihaylov, D.; Mihaylov, D. L.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Miśkowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Mohisin Khan, M.; Montes, E.; Moreira de Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Münning, K.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Myers, C. J.; Myrcha, J. W.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Narayan, A.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Negrao de Oliveira, R. A.; Nellen, L.; Nesbo, S. V.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Nobuhiro, A.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Ohlson, A.; Okubo, T.; Olah, L.; Oleniacz, J.; Oliveira da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Pachmayer, Y.; Pacik, V.; Pagano, D.; Pagano, P.; Paić, G.; Palni, P.; Pan, J.; Pandey, A. K.; Panebianco, S.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, J.; Parmar, S.; Passfeld, A.; Pathak, S. P.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Peng, X.; Pereira, L. G.; Pereira da Costa, H.; Peresunko, D.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrov, V.; Petrovici, M.; Petta, C.; Pezzi, R. P.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Płoskoń, M.; Planinic, M.; Pliquett, F.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Poppenborg, H.; Porteboeuf-Houssais, S.; Porter, J.; Pozdniakov, V.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Rana, D. B.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Ratza, V.; Ravasenga, I.; Read, K. F.; Redlich, K.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rodríguez Cahuantzi, M.; Røed, K.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Rokita, P. S.; Ronchetti, F.; Rosas, E. D.; Rosnet, P.; Rossi, A.; Rotondi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rueda, O. V.; Rui, R.; Russo, R.; Rustamov, A.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Saha, S. K.; Sahlmuller, B.; Sahoo, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Sandoval, A.; Sarkar, D.; Sarkar, N.; Sarma, P.; Sas, M. H. P.; Scapparone, E.; Scarlassara, F.; Scharenberg, R. P.; Scheid, H. S.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schmidt, M. O.; Schmidt, M.; Schuchmann, S.; Schukraft, J.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sett, P.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shahoyan, R.; Shaikh, W.; Shangaraev, A.; Sharma, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singhal, V.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Soramel, F.; Sorensen, S.; Sozzi, F.; Spiriti, E.; Sputowska, I.; Srivastava, B. K.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Suzuki, K.; Swain, S.; Szabo, A.; Szarka, I.; Szczepankiewicz, A.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thakur, D.; Thakur, S.; Thomas, D.; Tieulent, R.; Tikhonov, A.; Timmins, A. R.; Toia, A.; Tripathy, S.; Trogolo, S.; Trombetta, G.; Tropp, L.; Trubnikov, V.; Trzaska, W. H.; Trzeciak, B. A.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Umaka, E. N.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; van der Maarel, J.; van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vázquez Doce, O.; Vechernin, V.; Veen, A. M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vernet, R.; Vértesi, R.; Vickovic, L.; Vigolo, S.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Virgili, T.; Vislavicius, V.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Voscek, D.; Vranic, D.; Vrláková, J.; Wagner, B.; Wagner, J.; Wang, H.; Wang, M.; Watanabe, D.; Watanabe, Y.; Weber, M.; Weber, S. G.; Weiser, D. F.; Wenzel, S. C.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Willems, G. A.; Williams, M. C. S.; Willsher, E.; Windelband, B.; Witt, W. E.; Yalcin, S.; Yamakawa, K.; Yang, P.; Yano, S.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yurchenko, V.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zhu, X.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zmeskal, J.; Zou, S.; Alice Collaboration

2017-10-01

The second and the third order anisotropic flow, V2 and V3, are mostly determined by the corresponding initial spatial anisotropy coefficients, ε2 and ε3, in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, Vn (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow Vn for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range | η | < 0.8 and the transverse momentum range 0.2

Linear and non-linear flow mode in Pb–Pb collisions at s NN = 2.76  TeV

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

Acharya, S.; Adamová, D.; Adolfsson, J.

The second and the third order anisotropic flow, V 2 and V 3, are mostly determined by the corresponding initial spatial anisotropy coefficients, and , in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, V n (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider.more » The measurements are done for particles in the pseudorapidity range |η| < 0.8 and the transverse momentum range 0.2 < p T < 5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.« less

Extraction and prediction of indices for monsoon intraseasonal oscillations: an approach based on nonlinear Laplacian spectral analysis

NASA Astrophysics Data System (ADS)

Sabeerali, C. T.; Ajayamohan, R. S.; Giannakis, Dimitrios; Majda, Andrew J.

2017-11-01

An improved index for real-time monitoring and forecast verification of monsoon intraseasonal oscillations (MISOs) is introduced using the recently developed nonlinear Laplacian spectral analysis (NLSA) technique. Using NLSA, a hierarchy of Laplace-Beltrami (LB) eigenfunctions are extracted from unfiltered daily rainfall data from the Global Precipitation Climatology Project over the south Asian monsoon region. Two modes representing the full life cycle of the northeastward-propagating boreal summer MISO are identified from the hierarchy of LB eigenfunctions. These modes have a number of advantages over MISO modes extracted via extended empirical orthogonal function analysis including higher memory and predictability, stronger amplitude and higher fractional explained variance over the western Pacific, Western Ghats, and adjoining Arabian Sea regions, and more realistic representation of the regional heat sources over the Indian and Pacific Oceans. Real-time prediction of NLSA-derived MISO indices is demonstrated via extended-range hindcasts based on NCEP Coupled Forecast System version 2 operational output. It is shown that in these hindcasts the NLSA MISO indices remain predictable out to ˜3 weeks.

Linear and non-linear flow mode in Pb–Pb collisions at s NN = 2.76  TeV

DOE PAGES

Acharya, S.; Adamová, D.; Adolfsson, J.; ...

2017-08-04

The second and the third order anisotropic flow, V 2 and V 3, are mostly determined by the corresponding initial spatial anisotropy coefficients, and , in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, V n (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider.more » The measurements are done for particles in the pseudorapidity range |η| < 0.8 and the transverse momentum range 0.2 < p T < 5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.« less

Nonlinear Response of the Stratosphere and the North Atlantic-European Climate to Global Warming

NASA Astrophysics Data System (ADS)

Manzini, E.; Karpechko, A. Yu.; Kornblueh, L.

2018-05-01

The response of the northern winter atmospheric circulation for two consecutive global warming periods of 2 K is examined in a grand ensemble (68 members) of idealized CO2 increase experiments performed with the same climate model. The comparison of the atmospheric responses for the two periods shows remarkable differences, indicating the nonlinearity of the response. The nonlinear signature of the atmospheric and surface responses is reminiscent of the positive phase of the annular mode of variability. The stratospheric vortex response shifts from an easterly wind change for the first 2 K to a westerly wind change for the second 2 K. The North Atlantic storm track shifts poleward only in the second period. A weaker November Arctic amplification during the second period suggests that differences in Arctic sea ice changes can act to trigger the atmospheric nonlinear response. Stratosphere-troposphere coupling thereafter can provide for the persistence of this nonlinearity throughout the winter.

Tunable room temperature THz sources based on nonlinear mixing in a hybrid optical and THz micro-ring resonator.

PubMed

Sinha, Raju; Karabiyik, Mustafa; Al-Amin, Chowdhury; Vabbina, Phani K; Güney, Durdu Ö; Pala, Nezih

2015-03-24

We propose and systematically investigate a novel tunable, compact room temperature terahertz (THz) source based on difference frequency generation in a hybrid optical and THz micro-ring resonator. We describe detailed design steps of the source capable of generating THz wave in 0.5-10 THz with a tunability resolution of 0.05 THz by using high second order optical susceptibility (χ((2))) in crystals and polymers. In order to enhance THz generation compared to bulk nonlinear material, we employ a nonlinear optical micro-ring resonator with high-Q resonant modes for infrared input waves. Another ring oscillator with the same outer radius underneath the nonlinear ring with an insulation of SiO2 layer supports the generated THz with resonant modes and out-couples them into a THz waveguide. The phase matching condition is satisfied by engineering both the optical and THz resonators with appropriate effective indices. We analytically estimate THz output power of the device by using practical values of susceptibility in available crystals and polymers. The proposed source can enable tunable, compact THz emitters, on-chip integrated spectrometers, inspire a broader use of THz sources and motivate many important potential THz applications in different fields.

Tunable Room Temperature THz Sources Based on Nonlinear Mixing in a Hybrid Optical and THz Micro-Ring Resonator

PubMed Central

Sinha, Raju; Karabiyik, Mustafa; Al-Amin, Chowdhury; Vabbina, Phani K.; Güney, Durdu Ö.; Pala, Nezih

2015-01-01

We propose and systematically investigate a novel tunable, compact room temperature terahertz (THz) source based on difference frequency generation in a hybrid optical and THz micro-ring resonator. We describe detailed design steps of the source capable of generating THz wave in 0.5–10 THz with a tunability resolution of 0.05 THz by using high second order optical susceptibility (χ(2)) in crystals and polymers. In order to enhance THz generation compared to bulk nonlinear material, we employ a nonlinear optical micro-ring resonator with high-Q resonant modes for infrared input waves. Another ring oscillator with the same outer radius underneath the nonlinear ring with an insulation of SiO2 layer supports the generated THz with resonant modes and out-couples them into a THz waveguide. The phase matching condition is satisfied by engineering both the optical and THz resonators with appropriate effective indices. We analytically estimate THz output power of the device by using practical values of susceptibility in available crystals and polymers. The proposed source can enable tunable, compact THz emitters, on-chip integrated spectrometers, inspire a broader use of THz sources and motivate many important potential THz applications in different fields. PMID:25800287

Formation of vortices in the presence of sheared electron flows in the earth's ionosphere

NASA Astrophysics Data System (ADS)

Farid, T.; Shukla, P. K.; Sakanaka, P. H.; Mirza, A. M.

2000-12-01

It is shown that sheared electron flows can generate long as well as short wavelength (in comparison with the ion gyroradius) electrostatic waves in a nonuniform magnetplasma. For this purpose, we derive dispersion relations by employing two-fluid and hybrid models; in the two-fluid model the dynamics of both the electrons and ions are governed by the hydrodynamic equations and the guiding center fluid drifts, whereas the hybrid model assumes kinetic ions and fluid electrons. Explicit expressions for the growth rates and thresholds are presented. Linearly excited waves attain finite amplitudes and start interacting among themselves. The interaction is governed by the nonlinear equations containing the Jacobian nonlinearities. Stationary solutions of the nonlinear mode coupling equations can be represented in the form of a dipolar vortex and a vortex street. Conditions under which the latter arise are given. Numerical results for the growth rates of linearly excited modes as well as for various types of vortices are displayed for the parameters that are relevant for the F-region of the Earth's ionosphere. It is suggested that the results of the present investigation are useful in understanding the properties of nonthermal electrostatic waves and associated nonlinear vortex structures in the Earth's ionosphere.

Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the "phoenix soliton".

PubMed

Peleg, Or; Segev, Mordechai; Bartal, Guy; Christodoulides, Demetrios N; Moiseyev, Nimrod

2009-04-24

We formulate wave propagation in arrays of subwavelength waveguides with sharp index contrasts and demonstrate the collapse of bands into evanescent modes and lattice solitons with superluminal phase velocity. We find a self-reviving soliton ("phoenix soliton") comprised of coupled forward- and backward-propagating light, originating solely from evanescent bands. In the linear regime, all Bloch waves comprising this beam decay, whereas a proper nonlinearity assembles them into a propagating self-trapped beam. Finally, we simulate the dynamics of such a beam and observe breakup into temporal pulses, indicating a new kind of slow-light gap solitons, trapped in time and in one transverse dimension.

Three-dimensional vortex-induced vibrations of supported pipes conveying fluid based on wake oscillator models

NASA Astrophysics Data System (ADS)

Wang, L.; Jiang, T. L.; Dai, H. L.; Ni, Q.

2018-05-01

The present study develops a new three-dimensional nonlinear model for investigating vortex-induced vibrations (VIV) of flexible pipes conveying internal fluid flow. The unsteady hydrodynamic forces associated with the wake dynamics are modeled by two distributed van der Pol wake oscillators. In particular, the nonlinear partial differential equations of motion of the pipe and the wake are derived, taking into account the coupling between the structure and the fluid. The nonlinear equations of motion for the coupled system are then discretized by means of the Galerkin technique, resulting in a high-dimensional reduced-order model of the system. It is shown that the natural frequencies for in-plane and out-of-plane motions of the pipe may be different at high internal flow velocities beyond the threshold of buckling instability. The orientation angle of the postbuckling configuration is time-varying due to the disturbance of hydrodynamic forces, thus yielding sometimes unexpected results. For a buckled pipe with relatively low cross-flow velocity, interestingly, examining the nonlinear dynamics of the pipe indicates that the combined effects of the cross-flow-induced resonance of the in-plane first mode and the internal-flow-induced buckling on the IL and CF oscillation amplitudes may be significant. For higher cross-flow velocities, however, the effect of internal fluid flow on the nonlinear VIV responses of the pipe is not pronounced.

Investigations of the role of nonlinear couplings in structure formation and transport regulation in plasma turbulence

NASA Astrophysics Data System (ADS)

Holland, Christopher George

Studies of nonlinear couplings and dynamics in plasma turbulence are presented. Particular areas of focus are analytic studies of coherent structure formation in electron temperature gradient turbulence, measurement of nonlinear energy transfer in simulations of plasma turbulence, and bispectral analysis of experimental and computational data. The motivation for these works has been to develop and expand the existing theories of plasma transport, and verify the nonlinear predictions of those theories in simulation and experiment. In Chapter II, we study electromagnetic secondary instabilities of electron temperature gradient turbulence. The growth rate for zonal flow generation via modulational instability of electromagnetic ETG turbulence is calculated, as well as that for zonal (magnetic) field generation. In Chapter III, the stability and saturation of streamers in ETG turbulence is considered, and shown to depend sensitively upon geometry and the damping rates of the Kelvin-Helmholtz mode. Requirements for a credible theory of streamer transport are presented. In addition, a self-consistent model for interactions between ETG and ITG (ion temperature gradient) turbulence is presented. In Chapter IV, the nonlinear transfer of kinetic and internal energy is measured in simulations of plasma turbulence. The regulation of turbulence by radial decorrelation due to zonal flows and generation of zonal flows via the Reynolds stress are explicitly demonstrated, and shown to be symmetric facets of a single nonlinear process. Novel nonlinear saturation mechanisms for zonal flows are discussed. In Chapter V, measurements of fluctuation bicoherence in the edge of the DIII-D tokamak are presented. It is shown that the bicoherence increases transiently before a L-H transition, and decays to its initial value after the barrier has formed. The increase in bicoherence is localized to the region where the transport barrier forms, and shows strong coupling between well-separated frequencies. These results are qualitatively reproduced in a simple numerical "thought experiment," described in Chapter VI, which suggests that zonal flows may trigger the L-H transition.

Limitations and Tolerances in Optical Devices

NASA Astrophysics Data System (ADS)

Jackman, Neil Allan

The performance of optical systems is limited by the imperfections of their components. Many of the devices in optical systems including optical fiber amplifiers, multimode transmission lines and multilayered media such as mirrors, windows and filters, are modeled by coupled line equations. This investigation includes: (i) a study of the limitations imposed on a wavelength multiplexed unidirectional ring by the non-uniformities of the gain spectra of Erbium-doped optical fiber amplifiers. We find numerical solutions for non-linear coupled power differential equations and use these solutions to compare the signal -to-noise ratios and signal levels at different nodes. (ii) An analytical study of the tolerances of imperfect multimode media which support forward traveling modes. The complex mode amplitudes are related by linear coupled differential equations. We use analytical methods to derive extended equations for the expected mode powers and give heuristic limits for their regions of validity. These results compare favorably to exact solutions found for a special case. (iii) A study of the tolerances of multilayered media in the presence of optical thickness imperfections. We use analytical methods including Kronecker producers, to calculate the reflection and transmission statistics of the media. Monte Carlo simulations compare well to our analytical method.

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.

Solitons of the coupled Schrödinger-Korteweg-de Vries system with arbitrary strengths of the nonlinearity and dispersion

NASA Astrophysics Data System (ADS)

Gromov, Evgeny; Malomed, Boris

2017-11-01

New two-component soliton solutions of the coupled high-frequency (HF)—low-frequency (LF) system, based on Schrödinger-Korteweg-de Vries (KdV) system with the Zakharov's coupling, are obtained for arbitrary relative strengths of the nonlinearity and dispersion in the LF component. The complex HF field is governed by the linear Schrödinger equation with a potential generated by the real LF component, which, in turn, is governed by the KdV equation including the ponderomotive coupling term, representing the feedback of the HF field onto the LF component. First, we study the evolution of pulse-shaped pulses by means of direct simulations. In the case when the dispersion of the LF component is weak in comparison to its nonlinearity, the input gives rise to several solitons in which the HF component is much broader than its LF counterpart. In the opposite case, the system creates a single soliton with approximately equal widths of both components. Collisions between stable solitons are studied too, with a conclusion that the collisions are inelastic, with a greater soliton getting still stronger, and the smaller one suffering further attenuation. Robust intrinsic modes are excited in the colliding solitons. A new family of approximate analytical two-component soliton solutions with two free parameters is found for an arbitrary relative strength of the nonlinearity and dispersion of the LF component, assuming weak feedback of the HF field onto the LF component. Further, a one-parameter (non-generic) family of exact bright-soliton solutions, with mutually proportional HF and LF components, is produced too. Intrinsic dynamics of the two-component solitons, induced by a shift of their HF component against the LF one, is also studied, by means of numerical simulations, demonstrating excitation of a robust intrinsic mode. In addition to the above-mentioned results for LF-dominated two-component solitons, which always run in one (positive) velocities, we produce HF-dominated soliton complexes, which travel in the opposite (negative) direction. They are obtained in a numerical form and by means of a quasi-adiabatic analytical approximation. The solutions with positive and negative velocities correspond, respectively, to super- and subsonic Davydov-Scott solitons.

Theoretical Advances in Sequential Data Assimilation for the Atmosphere and Oceans

NASA Astrophysics Data System (ADS)

Ghil, M.

2007-05-01

We concentrate here on two aspects of advanced Kalman--filter-related methods: (i) the stability of the forecast- assimilation cycle, and (ii) parameter estimation for the coupled ocean-atmosphere system. The nonlinear stability of a prediction-assimilation system guarantees the uniqueness of the sequentially estimated solutions in the presence of partial and inaccurate observations, distributed in space and time; this stability is shown to be a necessary condition for the convergence of the state estimates to the true evolution of the turbulent flow. The stability properties of the governing nonlinear equations and of several data assimilation systems are studied by computing the spectrum of the associated Lyapunov exponents. These ideas are applied to a simple and an intermediate model of atmospheric variability and we show that the degree of stabilization depends on the type and distribution of the observations, as well as on the data assimilation method. These results represent joint work with A. Carrassi, A. Trevisan and F. Uboldi. Much is known by now about the main physical mechanisms that give rise to and modulate the El-Nino/Southern- Oscillation (ENSO), but the values of several parameters that enter these mechanisms are an important unknown. We apply Extended Kalman Filtering (EKF) for both model state and parameter estimation in an intermediate, nonlinear, coupled ocean-atmosphere model of ENSO. Model behavior is very sensitive to two key parameters: (a) "mu", the ocean-atmosphere coupling coefficient between the sea-surface temperature (SST) and wind stress anomalies; and (b) "delta-s", the surface-layer coefficient. Previous work has shown that "delta- s" determines the period of the model's self-sustained oscillation, while "mu' measures the degree of nonlinearity. Depending on the values of these parameters, the spatio-temporal pattern of model solutions is either that of a delayed oscillator or of a westward propagating mode. Assimilation of SST data from the NCEP- NCAR Reanalysis-2 shows that the parameters can vary on fairly short time scales and switch between values that approximate the two distinct modes of ENSO behavior. Rapid adjustments of these parameters occur, in particular, during strong ENSO events. Ways to apply EKF parameter estimation efficiently to state-of-the-art coupled ocean-atmosphere GCMs will be discussed. These results arise from joint work with D. Kondrashov and C.-j. Sun.

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.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-02-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-06-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

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.

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.

Reduced nonlinear prognostic model construction from high-dimensional data

NASA Astrophysics Data System (ADS)

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

2017-04-01

Construction of a data-driven model of evolution operator using universal approximating functions can only be statistically justified when the dimension of its phase space is small enough, especially in the case of short time series. At the same time in many applications real-measured data is high-dimensional, e.g. it is space-distributed and multivariate in climate science. Therefore it is necessary to use efficient dimensionality reduction methods which are also able to capture key dynamical properties of the system from observed data. To address this problem we present a Bayesian approach to an evolution operator construction which incorporates two key reduction steps. First, the data is decomposed into a set of certain empirical modes, such as standard empirical orthogonal functions or recently suggested nonlinear dynamical modes (NDMs) [1], and the reduced space of corresponding principal components (PCs) is obtained. Then, the model of evolution operator for PCs is constructed which maps a number of states in the past to the current state. The second step is to reduce this time-extended space in the past using appropriate decomposition methods. Such a reduction allows us to capture only the most significant spatio-temporal couplings. The functional form of the evolution operator includes separately linear, nonlinear (based on artificial neural networks) and stochastic terms. Explicit separation of the linear term from the nonlinear one allows us to more easily interpret degree of nonlinearity as well as to deal better with smooth PCs which can naturally occur in the decompositions like NDM, as they provide a time scale separation. Results of application of the proposed method to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510

Quadratic resonance in the three-dimensional oscillations of inviscid drops with surface tension

NASA Technical Reports Server (NTRS)

Natarajan, R.; Brown, R. A.

1986-01-01

The moderate-amplitude, three-dimensional oscillations of an inviscid drop are described in terms of spherical harmonics. Specific oscillation modes are resonantly coupled by quadratic nonlinearities caused by inertia, capillarity, and drop deformation. The equations describing the interactions of these modes are derived from the variational principle for the appropriate Lagrangian by expressing the modal amplitudes to be functions of a slow time scale and by preaveraging the Lagrangian over the time scale of the primary oscillations. Stochastic motions are predicted for nonaxisymmetric deformations starting from most initial conditions, even those arbitrarily close to the axisymmetric shapes. The stochasticity is characterized by a redistribution of the energy contained in the initial deformation over all the degrees of freedom of the interacting modes.

Lyapunov modes in extended systems.

PubMed

Yang, Hong-Liu; Radons, Günter

2009-08-28

Hydrodynamic Lyapunov modes, which have recently been observed in many extended systems with translational symmetry, such as hard sphere systems, dynamic XY models or Lennard-Jones fluids, are nowadays regarded as fundamental objects connecting nonlinear dynamics and statistical physics. We review here our recent results on Lyapunov modes in extended system. The solution to one of the puzzles, the appearance of good and 'vague' modes, is presented for the model system of coupled map lattices. The structural properties of these modes are related to the phase space geometry, especially the angles between Oseledec subspaces, and to fluctuations of local Lyapunov exponents. In this context, we report also on the possible appearance of branches splitting in the Lyapunov spectra of diatomic systems, similar to acoustic and optical branches for phonons. The final part is devoted to the hyperbolicity of partial differential equations and the effective degrees of freedom of such infinite-dimensional systems.

Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

NASA Astrophysics Data System (ADS)

Malaeke, Hasan; Moeenfard, Hamid

2016-03-01

The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

NASA Technical Reports Server (NTRS)

Wagner, William (Technical Monitor); Cranmer, Steven R.

2005-01-01

The paper discusses the following: 1. No-cost Extension. The no-cost extension is required to complete the work on the unified model codes (both hydrodynamic and kinetic Monte Carlo) as described in the initial proposal and previous annual reports. 2. Scientific Accomplishments during the Report Period. We completed a comprehensive model of Alfvtn wave reflection that spans the full distance from the photosphere to the distant heliosphere. 3. Comparison of Accomplishments with Proposed Goals. The proposal contained two specific objectives for Year 3: (1) to complete the unified model code, and (2) to apply it to various kinds of coronal holes (and polar plumes within coronal holes). Although the anticipated route toward these two final goals has changed (see accomplishments 2a and 2b above), they remain the major milestones for the extended period of performance. Accomplishments la and IC were necessary prerequisites for the derivation of "physically relevant transport and mode-coupling terms" for the unified model codes (as stated in the proposal Year 3 goals). We have fulfilled the proposed "core work" to study 4 general types of physical processes; in previous years we studied turbulence, mode coupling (Le., non-WKB reflection), and kinetic wave damping, and accomplishment lb provides the fourth topic: nonlinear steepening.

Dynamics and couplings of N-H stretching excitations of guanosine-cytidine base pairs in solution.

PubMed

Yang, Ming; Szyc, Łukasz; Röttger, Katharina; Fidder, Henk; Nibbering, Erik T J; Elsaesser, Thomas; Temps, Friedrich

2011-05-12

N-H stretching vibrations of hydrogen-bonded guanosine-cytidine (G·C) base pairs in chloroform solution are studied with linear and ultrafast nonlinear infrared (IR) spectroscopy. Assignment of the IR-active bands in the linear spectrum is made possible by combining structural information on the hydrogen bonds in G·C base pairs with literature results of density functional theory calculations, and empirical relations connecting frequency shifts and intensity of the IR-active vibrations. A local mode representation of N-H stretching vibrations is adopted, consisting of ν(G)(NH(2))(f) and ν(C)(NH(2))(f) modes for free NH groups of G and C, and of ν(G)(NH(2))(b), ν(G)(NH), and ν(C)(NH(2))(b) modes associated with N-H stretching motions of hydrogen-bonded NH groups. The couplings and relaxation dynamics of the N-H stretching excitations are studied with femtosecond mid-infrared two-dimensional (2D) and pump-probe spectroscopy. The N-H stretching vibrations of the free NH groups of G and C have an average population lifetime of 2.4 ps. Besides a vibrational population lifetime shortening to subpicosecond values observed for the hydrogen-bonded N-H stretching vibrations, the 2D spectra reveal vibrational excitation transfer from the ν(G)(NH(2))(b) mode to the ν(G)(NH) and/or ν(C)(NH(2))(b) modes. The underlying intermode vibrational couplings are on the order of 10 cm(-1).

Stability of metal-rich very massive stars

NASA Astrophysics Data System (ADS)

Goodman, J.; White, Christopher J.

2016-02-01

We revisit the stability of very massive non-rotating main-sequence stars at solar metallicity, with the goal of understanding whether radial pulsations set a physical upper limit to stellar mass. Models of up to 938 solar masses are constructed with the MESA code, and their linear stability in the fundamental mode, assumed to be the most dangerous, is analysed with a fully non-adiabatic method. Models above 100 M⊙ have extended tenuous atmospheres (`shelves') that affect the stability of the fundamental. Even when positive, this growth rate is small, in agreement with previous results. We argue that small growth rates lead to saturation at small amplitudes that are not dangerous to the star. A mechanism for saturation is demonstrated involving non-linear parametric coupling to short-wavelength g-modes and the damping of the latter by radiative diffusion. The shelves are subject to much more rapidly growing strange modes. This also agrees with previous results but is extended here to higher masses. The strange modes probably saturate via shocks rather than mode coupling but have very small amplitudes in the core, where almost all of the stellar mass resides. Although our stellar models are hydrostatic, the structure of their outer parts suggests that optically thick winds, driven by some combination of radiation pressure, transonic convection, and strange modes, are more likely than pulsation in the fundamental mode to limit the main-sequence lifetime.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

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.

Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics.

PubMed

Monat, Christelle; Grillet, Christian; Corcoran, Bill; Moss, David J; Eggleton, Benjamin J; White, Thomas P; Krauss, Thomas F

2010-03-29

Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.

Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

NASA Astrophysics Data System (ADS)

Roux Oliveira, Tiago; Jacoud Peixoto, Alessandro; Hsu, Liu

2015-09-01

This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment.

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.

Optical nonlinearities in plasmonic metamaterials (Conference Presentation)

NASA Astrophysics Data System (ADS)

Zayats, Anatoly V.

2016-04-01

Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.

Low-Dimensional Model of a Cylinder Wake

NASA Astrophysics Data System (ADS)

Luchtenburg, Mark; Cohen, Kelly; Siegel, Stefan; McLaughlin, Tom

2003-11-01

In a two-dimensional cylinder wake, self-excited oscillations in the form of periodic shedding of vortices are observed above a critical Reynolds number of about 47. These flow-induced non-linear oscillations lead to some undesirable effects associated with unsteady pressures such as fluid-structure interactions. An effective way of suppressing the self-excited flow oscillations is by the incorporation of closed-loop flow control. In this effort, a low dimensional, proper orthogonal decomposition (POD) model is based on data obtained from direct numerical simulations of the Navier Stokes equations for the two dimensional circular cylinder wake at a Reynolds number of 100. Three different conditions are examined, namely, the unforced wake experiencing steady-state vortex shedding, the transient behavior of the unforced wake at the startup of the simulation, and transient response to open-loop harmonic forcing by translation. We discuss POD mode selection and the number of modes that need to be included in the low-dimensional model. It is found that the transient dynamics need to be represented by a coupled system that includes an aperiodic mean-flow mode, an aperiodic shift mode and the periodic von Karman modes. Finally, a least squares mapping method is introduced to develop the non-linear state equations. The predictive capability of the state equations demonstrates the ability of the above approach to model the transient dynamics of the wake.

Implementation of a quantum metamaterial using superconducting qubits.

PubMed

Macha, Pascal; Oelsner, Gregor; Reiner, Jan-Michael; Marthaler, Michael; André, Stephan; Schön, Gerd; Hübner, Uwe; Meyer, Hans-Georg; Il'ichev, Evgeni; Ustinov, Alexey V

2014-10-14

The key issue for the implementation of a metamaterial is to demonstrate the existence of collective modes corresponding to coherent oscillations of the meta-atoms. Atoms of natural materials interact with electromagnetic fields as quantum two-level systems. Artificial quantum two-level systems can be made, for example, using superconducting nonlinear resonators cooled down to their ground state. Here we perform an experiment in which 20 of these quantum meta-atoms, so-called flux qubits, are embedded into a microwave resonator. We observe the dispersive shift of the resonator frequency imposed by the qubit metamaterial and the collective resonant coupling of eight qubits. The realized prototype represents a mesoscopic limit of naturally occurring spin ensembles and as such we demonstrate the AC-Zeeman shift of a resonant qubit ensemble. The studied system constitutes the implementation of a basic quantum metamaterial in the sense that many artificial atoms are coupled collectively to the quantized mode of a photon field.

Automatic network coupling analysis for dynamical systems based on detailed kinetic models.

PubMed

Lebiedz, Dirk; Kammerer, Julia; Brandt-Pollmann, Ulrich

2005-10-01

We introduce a numerical complexity reduction method for the automatic identification and analysis of dynamic network decompositions in (bio)chemical kinetics based on error-controlled computation of a minimal model dimension represented by the number of (locally) active dynamical modes. Our algorithm exploits a generalized sensitivity analysis along state trajectories and subsequent singular value decomposition of sensitivity matrices for the identification of these dominant dynamical modes. It allows for a dynamic coupling analysis of (bio)chemical species in kinetic models that can be exploited for the piecewise computation of a minimal model on small time intervals and offers valuable functional insight into highly nonlinear reaction mechanisms and network dynamics. We present results for the identification of network decompositions in a simple oscillatory chemical reaction, time scale separation based model reduction in a Michaelis-Menten enzyme system and network decomposition of a detailed model for the oscillatory peroxidase-oxidase enzyme system.

Linear entropy and collapse–revival phenomenon for a general formalism N-type four-level atom interacting with a single-mode field

NASA Astrophysics Data System (ADS)

Eied, A. A.

2018-05-01

In this paper, the linear entropy and collapse-revival phenomenon through the relation (< {\\hat{a}}+{\\hat{a}} > -{\\bar{n}}) in a system of N-configuration four-level atom interacting with a single-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom-field coupling functional are investigated. A factorization of the initial density operator is assumed, considering the field to be initially in a squeezed coherent states and the atom initially in its most upper excited state. The dynamical behavior of the linear entropy and the time evolution of (< {\\hat{a}}+ {\\hat{a}} > -{\\bar{n}}) are analyzed. In particular, the effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy and the evolution of (< {\\hat{a}}+ {\\hat{a}} > -{\\bar{n}}) are examined.

Hybrid Photon-Plasmon Coupling and Ultrafast Control of Nanoantennas on a Silicon Photonic Chip.

PubMed

Chen, Bigeng; Bruck, Roman; Traviss, Daniel; Khokhar, Ali Z; Reynolds, Scott; Thomson, David J; Mashanovich, Goran Z; Reed, Graham T; Muskens, Otto L

2018-01-10

Hybrid integration of nanoplasmonic devices with silicon photonic circuits holds promise for a range of applications in on-chip sensing, field-enhanced and nonlinear spectroscopy, and integrated nanophotonic switches. Here, we demonstrate a new regime of photon-plasmon coupling by combining a silicon photonic resonator with plasmonic nanoantennas. Using principles from coherent perfect absorption, we make use of standing-wave light fields to maximize the photon-plasmon interaction strength. Precise placement of the broadband antennas with respect to the narrowband photonic racetrack modes results in controlled hybridization of only a subset of these modes. By combining antennas into groups of radiating dipoles with opposite phase, far-field scattering is effectively suppressed. We achieve ultrafast tuning of photon-plasmon hybridization including reconfigurable routing of the standing-wave input between two output ports. Hybrid photonic-plasmonic resonators provide conceptually new approaches for on-chip integrated nanophotonic devices.

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

Photon energy conversion by near-zero permittivity nonlinear materials

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

Luk, Ting S.; Sinclair, Michael B.; Campione, Salvatore

Efficient harmonic light generation can be achieved with ultrathin films by coupling an incident pump wave to an epsilon-near-zero (ENZ) mode of the thin film. As an example, efficient third harmonic generation from an indium tin oxide nanofilm (.lamda./42 thick) on a glass substrate for a pump wavelength of 1.4 .mu.m was demonstrated. A conversion efficiency of 3.3.times.10.sup.-6 was achieved by exploiting the field enhancement properties of the ENZ mode with an enhancement factor of 200. This nanoscale frequency conversion method is applicable to other plasmonic materials and reststrahlen materials in proximity of the longitudinal optical phonon frequencies.

Anderson localization in sigma models

NASA Astrophysics Data System (ADS)

Bruckmann, Falk; Wellnhofer, Jacob

2018-03-01

In QCD above the chiral restoration temperature there exists an Anderson transition in the fermion spectrum from localized to delocalized modes. We investigate whether the same holds for nonlinear sigma models which share properties like dynamical mass generation and asymptotic freedom with QCD. In particular we study the spectra of fermions coupled to (quenched) CP(N-1) configurations at high temperatures. We compare results in two and three space-time dimensions: in two dimensions the Anderson transition is absent, since all fermion modes are localized, while in three dimensions it is present. Our measurements include a more recent observable characterizing level spacings: the distribution of ratios of consecutive level spacings.

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

Kodama, Yuta; Kokubu, Kento; Sawado, Nobuyuki

We construct brane solutions in 6-dimensional Einstein-Skyrme systems. A class of baby-Skyrmion solutions realizes warped compactification of the extra dimensions and gravity localization on the brane for the negative bulk cosmological constant. Coupling of the fermions with brane Skyrmions leads to brane localized fermions. In terms of the level crossing picture, emergence of the massive localized modes are observed. The nonlinear nature of Skyrmions brings richer information for the fermions' level structure. It comprises doubly degenerate lowest plus single excited modes. Three generations of fundamental fermions are associated with this distinctive structure. The mass hierarchy of quarks or leptons appearedmore » in terms of slightly deformed baby Skyrmions with topological charge three.« less

Huge light-enhancement by coupling a Bowtie Nano-antenna's plasmonic resonance to a photonic crystal mode.

PubMed

Eter, Ali El; Grosjean, Thierry; Viktorovitch, Pierre; Letartre, Xavier; Benyattou, Taha; Baida, Fadi I

2014-06-16

We numerically demonstrate a drastic enhancement of the light intensity in the vicinity of the gap of Bowtie Nano-antenna (BA) through its coupling with Photonic Crystal (PC) resonator. The resulting huge energy transfer toward the BA is based on the coupling between two optical resonators (BA and PC membrane) of strongly unbalanced quality factors. Thus, these two resonators are designed so that the PC is only slightly perturbed in term of resonance properties. The proposed hybrid dielectric-plasmonic structure may open new avenues in the generation of deeply subwavelength intense optical sources, with direct applications in various domains such as data storage, non-linear optics, optical trapping and manipulation, microscopy, etc.

Dynamics identification of a piezoelectric vibrational energy harvester by image analysis with a high speed camera

NASA Astrophysics Data System (ADS)

Wolszczak, Piotr; Łygas, Krystian; Litak, Grzegorz

2018-07-01

This study investigates dynamic responses of a nonlinear vibration energy harvester. The nonlinear mechanical resonator consists of a flexible beam moving like an inverted pendulum between amplitude limiters. It is coupled with a piezoelectric converter, and excited kinematically. Consequently, the mechanical energy input is converted into the electrical power output on the loading resistor included in an electric circuit attached to the piezoelectric electrodes. The curvature of beam mode shapes as well as deflection of the whole beam are examined using a high speed camera. The visual identification results are compared with the voltage output generated by the piezoelectric element for corresponding frequency sweeps and analyzed by the Hilbert transform.

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

Collins, Liam; Belianinov, Alex; Proksch, Roger

We develop a full information capture approach for Magnetic Force Microscopy (MFM), referred to as generalized mode (G-Mode) MFM. G-Mode MFM acquires and stores the full data stream from the photodetector at sampling rates approaching the intrinsic photodiode limit. The data can be subsequently compressed, denoised, and analyzed, without information loss. Also, 3 G-Mode MFM is implemented and compared to traditional heterodyne based MFM on model systems including domain structures in ferromagnetic Yttrium Iron Garnet (YIG) and electronically and magnetically inhomogeneous high entropy alloy, CoFeMnNiSn. We investigate the use of information theory to mine the G-Mode MFM data and demonstratemore » its usefulness for extracting information which may be hidden in traditional MFM modes, including signatures of nonlinearities and mode coupling phenomena. Finally we demonstrate detection and separation of magnetic and electrostatic tip-sample interactions from a single G-Mode image, by analyzing the entire frequency response of the cantilever. G-Mode MFM is immediately implementable on any AFM platform and as such is expected to be a useful technique for probing spatiotemporal cantilever dynamics and mapping material properties as well as their mutual interactions.« less

Raman lasing in As₂S₃ high-Q whispering gallery mode resonators.

PubMed

Vanier, Francis; Rochette, Martin; Godbout, Nicolas; Peter, Yves-Alain

2013-12-01

We report the first observation of a nonlinear process in a chalcogenide microresonator. Raman scattering and stimulated Raman scattering leading to laser oscillation is observed in microspheres made of As₂S₃. The coupled pump power threshold is as low as 13 μW using a pump wavelength of 1550 nm. The quality factor of the chalcogenide microresonator is also the highest ever reported with Q>7×10(7).

Millimeter Wave Generation by Relativistic Electron Beams.

DTIC Science & Technology

1984-12-01

frequency and wave vector matching relations for influence of various nonlinear effects on this instability is this four-wave interaction require...following coupled mode equations _ 6 = 6 _ (14)-- v vx (14) ." .’ for the lower hybrid sidebands: v - V 2 - The x component of the resultant vector equation...involves a purely growing modte, a four-wave interaction plitoces is analysed, including a u ap ti wave- vector up-shifted and ilown-shiftes upper

Magnetically coupled flextensional transducer for wideband vibration energy harvesting: Design, modeling and experiments

NASA Astrophysics Data System (ADS)

Zou, Hong-Xiang; Zhang, Wen-Ming; Li, Wen-Bo; Wei, Ke-Xiang; Hu, Kai-Ming; Peng, Zhi-Ke; Meng, Guang

2018-03-01

The combination of nonlinear bistable and flextensional mechanisms has the advantages of wide operating frequency and high equivalent piezoelectric constant. In this paper, three magnetically coupled flextensional vibration energy harvesters (MF-VEHs) are designed from three magnetically coupled vibration systems which utilize a magnetic repulsion, two symmetrical magnetic attractions and multi-magnetic repulsions, respectively. The coupled dynamic models are developed to describe the electromechanical transitions. Simulations under harmonic excitation and random excitation are carried out to investigate the performance of the MF-VEHs with different parameters. Experimental validations of the MF-VEHs are performed under different excitation levels. The experimental results verify that the developed mathematical models can be used to accurately characterize the MF-VEHs for various magnetic coupling modes. A comparison of three MF-VEHs is provided and the results illustrate that a reasonable arrangement of multiple magnets can reduce the threshold excitation intensity and increase the harvested energy.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

NASA Astrophysics Data System (ADS)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

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.

DAVs: Red Edge and Outbursts

NASA Astrophysics Data System (ADS)

Luan, Jing

2018-04-01

As established by ground based surveys, white dwarfs with hydrogen atmospheres pulsate as they cool across the temperature range, 12500K< Teff < 10800K . Known as DAVs or ZZ Ceti stars, their oscillations are attributed to overstable g-modes excited by convective driving. The effective temperature at the blue edge of the instability strip is slightly lower than that at which a surface convection zone appears. The temperature at the red edge is a two-decade old puzzle. Recently, Kepler discovered a number of cool DAVs exhibiting sporadic outbursts separated by days, each lasting several hours, and releasing \\sim 10^{33}-10^{34} {erg}. We provide quantitative explanations for both the red edge and the outbursts. The minimal frequency for overstable modes rises abruptly near the red edge. Although high frequency overstable modes exist below the red edge, their photometric amplitudes are generally too small to be detected by ground based observations. Nevertheless, these overstable parent modes can manifest themselves through nonlinear mode couplings to damped daughter modes which generate limit cycles giving rise to photometric outbursts.

Nonlinearities and noise in micromechanical resonators: From understanding to characterization and design tools

NASA Astrophysics Data System (ADS)

Polunin, Pavel M.

In this work we consider several nonlinearity-based and/or noise-related phenomena that have been recently observed in micro-electromechanical vibratory systems. The main goals are to closely examine these phenomena, develop an understanding of their underlying physics, derive techniques for characterizing parameters in relevant mathematical models, and determine ways to improve the performance of specific classes of micro-electromechanical systems (MEMS) used in applications. The general perspective of this work is based on the fact that nonlinearity and noise represent integral parts of the models needed to describe the response of these systems, and the focus is on situations where these generally undesirable features can be utilized or accounted for in design. We consider three different, but related, topics in this general area. The first topic uses the slowly varying states in a rotating frame of reference where we analyze the stationary probability distribution of a nonlinear parametrically-driven resonator subjected to Poisson pulses and thermal noise. We show that Poisson pulses with low pulse rates, as compared with the resonator decay rate, cause a power-law divergence of the probability density at the resonator equilibrium in both the underdamped (overdamped) regimes, in which the response does (does not) spiral in the rotating frame. We have also found that the shape of the probability distribution away from the equilibrium position is qualitatively different for the overdamped and underdamped cases. In particular, in the overdamped regime, the form of the secondary singularity in the probability distribution depends strongly on the reference phase of the resonator response and the pulse modulation phase, while in the underdamped regime several singular peaks occur in the distribution, and their locations are determined by the resonator frequency and decay rate in the rotating frame. Finally, we show that even weak Gaussian noise smoothens out the singular peaks in the probability distribution. The theoretical results are successfully compared experimental results obtained from collaborators at the Hong Kong University of Science and Technology. Second, we discuss a time-domain technique for characterizing parameters for models that describe the response of a single vibrational mode of micromechanical resonators with symmetric restoring and damping forces. These parameters include coefficients of conservative and dissipative linear and nonlinear terms, as well as the strengths of various noise sources acting on the mode of interest. The method relies on measurements taken during a ringdown response, that is, free vibration, in which the nonlinearities result in an amplitude-dependent frequency and a non-exponential decay of the amplitude, while noise sources cause fluctuations in the resonator amplitude and phase. Analysis of the amplitude of the ringdown response allows one to estimate the quality factor and the dissipative nonlinearity, and the zero-crossing points in the ringdown measurement can be used to characterize the linear natural frequency and the cubic and quintic nonlinearities of the vibrational mode, which typically arise from a combination of mechanical and electrostatic effects. Additionally, we develop and demonstrate a statistical analysis of the zero-crossing points in the resonator response that allows one to separate the effects of additive, multiplicative, and measurement noises and estimate their corresponding intensities. These characterization methods are demonstrated using experimental measurements obtained from collaborators at Stanford University. Finally, we examine the problem of self-induced parametric amplification in ring/disk resonating gyroscopes. We model the dynamics of these gyroscopes by considering flexural (elliptical) vibrations of a thin elastic ring subjected to electrostatic transduction and show that the parametric amplification arises naturally from nonlinear intermodal coupling between the drive and sense modes of the gyroscope. Analysis shows that this coupling results in a substantial increase in the sensitivity of the gyroscope to the external angular rate. This improvement in the gyroscope performance depends strongly on both the modal coupling strength and the operating point of the gyroscope, features which depend on details of nonlinear kinematics of, and forces acting on, the ring. Using the results from this model, we explore ways to enhance the amplification effect by changing the shape of the resonator body and attendant electrodes, and by electrostatic tuning. These results suggest new designs for ring gyros, and a general approach for other geometries, such as disk-resonator-gyros (DRGs), that should offer significant improvements in device sensitivity.

Cooperative Jahn-Teller phase transition of icosahedral molecular units

NASA Astrophysics Data System (ADS)

Nasrollahi, Seyed H.; Vvedensky, Dimitri D.

2017-02-01

Non-linear molecules undergo distortions when the orbital degeneracy of the highest occupied level is lifted by the Jahn-Teller effect. If such molecules or clusters of atoms are coupled to one another, the system may experience a cooperative Jahn-Teller effect (CJTE). In this paper, we describe a model of how the CJTE leads to the crystallization of the disordered phase. The model Hamiltonian is based on a normal mode decomposition of the clusters in order to maintain the symmetry labels. We take account of the electron-strain and the electron-phonon couplings and, by displacing the coordinates of the oscillators, obtain a term that explicitly couples the Jahn-Teller centers, enabling us to perform a mean-field analysis. The calculation of the free energy then becomes straightforward, and obtaining phase diagrams in various regimes follows from the minimization of this free energy. The results show that the character of the phase transition may change from strong to weak first order and even to second-order, depending on the coupling to the vibrational modes. Taken together, these results may serve as a paradigm for crystallization near the transition temperature, where the atoms tend to form clusters of icosahedral symmetry.

Imprint of non-linear effects on HI intensity mapping on large scales

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

Umeh, Obinna, E-mail: umeobinna@gmail.com

Intensity mapping of the HI brightness temperature provides a unique way of tracing large-scale structures of the Universe up to the largest possible scales. This is achieved by using a low angular resolution radio telescopes to detect emission line from cosmic neutral Hydrogen in the post-reionization Universe. We use general relativistic perturbation theory techniques to derive for the first time the full expression for the HI brightness temperature up to third order in perturbation theory without making any plane-parallel approximation. We use this result and the renormalization prescription for biased tracers to study the impact of nonlinear effects on themore » power spectrum of HI brightness temperature both in real and redshift space. We show how mode coupling at nonlinear order due to nonlinear bias parameters and redshift space distortion terms modulate the power spectrum on large scales. The large scale modulation may be understood to be due to the effective bias parameter and effective shot noise.« less

MoS2 /Carbon Nanotube Core-Shell Nanocomposites for Enhanced Nonlinear Optical Performance.

PubMed

Zhang, Xiaoyan; Selkirk, Andrew; Zhang, Saifeng; Huang, Jiawei; Li, Yuanxin; Xie, Yafeng; Dong, Ningning; Cui, Yun; Zhang, Long; Blau, Werner J; Wang, Jun

2017-03-08

Nanocomposites of layered MoS 2 and multi-walled carbon nanotubes (CNTs) with core-shell structure were prepared by a simple solvothermal method. The formation of MoS 2 nanosheets on the surface of coaxial CNTs has been confirmed by scanning electron microscopy, transmission electron microscopy, absorption spectrum, Raman spectroscopy, and X-ray photoelectron spectroscopy. Enhanced third-order nonlinear optical performances were observed for both femtosecond and nanosecond laser pulses over a broad wavelength range from the visible to the near infrared, compared to those of MoS 2 and CNTs alone. The enhancement can be ascribed to the strong coupling effect and the photoinduced charge transfer between MoS 2 and CNTs. This work affords an efficient way to fabricate novel CNTs based nanocomposites for enhanced nonlinear light-matter interaction. The versatile nonlinear properties imply a huge potential of the nanocomposites in the development of nanophotonic devices, such as mode-lockers, optical limiters, or optical switches. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Discriminating cascading processes in nonlinear optics: A QED analysis based on their molecular and geometric origin

NASA Astrophysics Data System (ADS)

Bennett, Kochise; Chernyak, Vladimir Y.; Mukamel, Shaul

2017-03-01

The nonlinear optical response of a system of molecules often contains contributions whereby the products of lower-order processes in two separate molecules give signals that appear on top of a genuine direct higher-order process with a single molecule. These many-body contributions are known as cascading and complicate the interpretation of multidimensional stimulated Raman and other nonlinear signals. In a quantum electrodynamic treatment, these cascading processes arise from second-order expansion in the molecular coupling to vacuum modes of the radiation field, i.e., single-photon exchange between molecules, which also gives rise to other collective effects. We predict the relative phase of the direct and cascading nonlinear signals and its dependence on the microscopic dynamics as well as the sample geometry. This phase may be used to identify experimental conditions for distinguishing the direct and cascading signals by their phase. Higher-order cascading processes involving the exchange of several photons between more than two molecules are discussed.

Imprint of non-linear effects on HI intensity mapping on large scales

NASA Astrophysics Data System (ADS)

Umeh, Obinna

2017-06-01

Intensity mapping of the HI brightness temperature provides a unique way of tracing large-scale structures of the Universe up to the largest possible scales. This is achieved by using a low angular resolution radio telescopes to detect emission line from cosmic neutral Hydrogen in the post-reionization Universe. We use general relativistic perturbation theory techniques to derive for the first time the full expression for the HI brightness temperature up to third order in perturbation theory without making any plane-parallel approximation. We use this result and the renormalization prescription for biased tracers to study the impact of nonlinear effects on the power spectrum of HI brightness temperature both in real and redshift space. We show how mode coupling at nonlinear order due to nonlinear bias parameters and redshift space distortion terms modulate the power spectrum on large scales. The large scale modulation may be understood to be due to the effective bias parameter and effective shot noise.

1/f Noise Inside a Faraday Cage

NASA Astrophysics Data System (ADS)

Handel, Peter H.; George, Thomas F.

2009-04-01

We show that quantum 1/f noise does not have a lower frequency limit given by the lowest free electromagnetic field mode in a Faraday cage, even in an ideal cage. Indeed, quantum 1/f noise comes from the infrared-divergent coupling of the field with the charges, in their joint nonlinear system, where the charges cause the field that reacts back on the charges, and so on. This low-frequency limitation is thus not applicable for the nonlinear system of matter and field in interaction. Indeed, this nonlinear system is governed by Newton's laws, Maxwell's equations, in general also by the diffusion equations for particles and heat, or reaction kinetics given by quantum matrix elements. Nevertheless, all the other quantities can be eliminated in principle, resulting in highly nonlinear integro-differential equations for the electromagnetic field only, which no longer yield a fundamental frequency. Alternatively, we may describe this through the presence of an infinite system of subharmonics. We show how this was proven early in the classical and quantum domains, adding new insight.

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

DOE PAGES

Lott, Martin; Remillieux, Marcel; Garnier, Vincent; ...

2017-07-17

Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists ofmore » the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.« less

Fast and slowly evolving vector solitons in mode-locked fibre lasers.

PubMed

Sergeyev, Sergey V

2014-10-28

We report on a new vector model of an erbium-doped fibre laser mode locked with carbon nanotubes. This model goes beyond the limitations of the previously used models based on either coupled nonlinear Schrödinger or Ginzburg-Landau equations. Unlike the previous models, it accounts for the vector nature of the interaction between an optical field and an erbium-doped active medium, slow relaxation dynamics of erbium ions, linear birefringence in a fibre, linear and circular birefringence of a laser cavity caused by in-cavity polarization controller and light-induced anisotropy caused by elliptically polarized pump field. Interplay of aforementioned factors changes coherent coupling of two polarization modes at a long time scale and so results in a new family of vector solitons (VSs) with fast and slowly evolving states of polarization. The observed VSs can be of interest in secure communications, trapping and manipulation of atoms and nanoparticles, control of magnetization in data storage devices and many other areas. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Nonreciprocal reconfigurable microwave optomechanical circuit.

PubMed

Bernier, N R; Tóth, L D; Koottandavida, A; Ioannou, M A; Malz, D; Nunnenkamp, A; Feofanov, A K; Kippenberg, T J

2017-09-19

Nonreciprocal microwave devices are ubiquitous in radar and radio communication and indispensable in the readout chains of superconducting quantum circuits. Since they commonly rely on ferrite materials requiring large magnetic fields that make them bulky and lossy, there has been significant interest in magnetic-field-free on-chip alternatives, such as those recently implemented using the Josephson nonlinearity. Here, we realize reconfigurable nonreciprocal transmission between two microwave modes using purely optomechanical interactions in a superconducting electromechanical circuit. The scheme relies on the interference in two mechanical modes that mediate coupling between the microwave cavities and requires no magnetic field. We analyse the isolation, transmission and the noise properties of this nonreciprocal circuit. Finally, we show how quantum-limited circulators can be realized with the same principle. All-optomechanically mediated nonreciprocity demonstrated here can also be extended to directional amplifiers, and it forms the basis towards realizing topological states of light and sound.Nonreciprocal optical devices traditionally rely on magnetic fields and magnetic-free approaches are rather recent. Here, Bernier et al. propose and demonstrate a purely optomechanical circulator with reconfigurable transmission without the need for direct coupling between input and output modes.

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.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

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.

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.

High beta effects and nonlinear evolution of the TAE instability

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

Spong, D.A.

1992-12-31

The toroidal Alfven eigenmode has recently been observed experimentally on DIII-D and TFTR when neutral beams are injected near the Alfven velocity. This instability is also of concern for future high {beta} D-T devices where fusion by-product alpha populations will generally be super-Alfvenic. We have developed a gyrofluid model (with Landau closure) of the TAE mode which can include most of the relevant damping mechanisms (continuum damping, ion and electron damping, ion FLR and collisional trapped electron damping) as well as reproducing analytically predicted undamped growth rates relatively accurately. An important consideration in predicting future unstable TAE regimes is themore » effect of finite beta in the background plasma. Due to the Shafranov shift and distortion of the flux surfaces, the location of the stable TAE root and the continuum will shift with increasing {beta}. The net effect of this is to generally enhance continuum damping and stabilize the TAF instability. Also, as the pressure gradient drive from the background becomes increasingly important, coupling between TAE and background driven modes can alter the TAE mode. A further application of our gyrofluid model which will be discussed is the nonlinear evolution of the TAE instability. Gyrofluid models offer a convenient reduced description which is more amenable to computational nonlinear modeling than full kinetic particle models. Our results demonstrate the rise and crash phases of TAE activity similar to experimental observations. The saturation is caused by generation of m=0 n=0 components through nonlinear beatings of the n > 1 modes; these cause modifications to the original equilibrium profiles in such a direction as to decrease the instability drive. This is the gyrofluid analog of direct particle losses. The peak magnetic fluctuation level increases with increasing energetic species beta, resulting in non-resonant stochastization of magnetic field lines.« less

High beta effects and nonlinear evolution of the TAE instability

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

Spong, D.A.

1992-01-01

The toroidal Alfven eigenmode has recently been observed experimentally on DIII-D and TFTR when neutral beams are injected near the Alfven velocity. This instability is also of concern for future high [beta] D-T devices where fusion by-product alpha populations will generally be super-Alfvenic. We have developed a gyrofluid model (with Landau closure) of the TAE mode which can include most of the relevant damping mechanisms (continuum damping, ion and electron damping, ion FLR and collisional trapped electron damping) as well as reproducing analytically predicted undamped growth rates relatively accurately. An important consideration in predicting future unstable TAE regimes is themore » effect of finite beta in the background plasma. Due to the Shafranov shift and distortion of the flux surfaces, the location of the stable TAE root and the continuum will shift with increasing [beta]. The net effect of this is to generally enhance continuum damping and stabilize the TAF instability. Also, as the pressure gradient drive from the background becomes increasingly important, coupling between TAE and background driven modes can alter the TAE mode. A further application of our gyrofluid model which will be discussed is the nonlinear evolution of the TAE instability. Gyrofluid models offer a convenient reduced description which is more amenable to computational nonlinear modeling than full kinetic particle models. Our results demonstrate the rise and crash phases of TAE activity similar to experimental observations. The saturation is caused by generation of m=0 n=0 components through nonlinear beatings of the n > 1 modes; these cause modifications to the original equilibrium profiles in such a direction as to decrease the instability drive. This is the gyrofluid analog of direct particle losses. The peak magnetic fluctuation level increases with increasing energetic species beta, resulting in non-resonant stochastization of magnetic field lines.« less

Bispectral analysis: comparison of two windowing functions

NASA Astrophysics Data System (ADS)

Silvagni, D.; Djerroud, C.; Réveillé, T.; Gravier, E.

2018-02-01

Amongst all the normalized forms of bispectrum, the bicoherence is shown to be a very useful diagnostic tool in experimental studies of nonlinear wave interactions in plasma, as it measures the fraction of wave power due to the quadratic wave coupling in a self-excited fluctuation spectrum [1, 2]. In order to avoid spectral leakage, the application of a windowing function is needed during the bicoherence computation. Spectral leakage from statistically dependent components are of crucial importance in the discrimination between coupled and uncoupled modes, as they will introduce in the bicoherence spectrum phase-coupled modes which in reality do not exist. Therefore, the windowing function plays a key role in the bicoherence estimation. In this paper, two windowing methods are compared: the multiplication of the initial signal by the Hanning function and the subtraction of the straight line which links the two extremities of the signal. The influence of these two windowing methods on both the power spectrum and the bicoherence spectrum is showed. Although both methods give precise results, the Hanning function appears to be the more suitable window.

Improvements in mode-based waveform modeling and application to Eurasian velocity structure

NASA Astrophysics Data System (ADS)

Panning, M. P.; Marone, F.; Kim, A.; Capdeville, Y.; Cupillard, P.; Gung, Y.; Romanowicz, B.

2006-12-01

We introduce several recent improvements to mode-based 3D and asymptotic waveform modeling and examine how to integrate them with numerical approaches for an improved model of upper-mantle structure under eastern Eurasia. The first step in our approach is to create a large-scale starting model including shear anisotropy using Nonlinear Asymptotic Coupling Theory (NACT; Li and Romanowicz, 1995), which models the 2D sensitivity of the waveform to the great-circle path between source and receiver. We have recently improved this approach by implementing new crustal corrections which include a non-linear correction for the difference between the average structure of several large regions from the global model with further linear corrections to account for the local structure along the path between source and receiver (Marone and Romanowicz, 2006; Panning and Romanowicz, 2006). This model is further refined using a 3D implementation of Born scattering (Capdeville, 2005). We have made several recent improvements to this method, in particular introducing the ability to represent perturbations to discontinuities. While the approach treats all sensitivity as linear perturbations to the waveform, we have also experimented with a non-linear modification analogous to that used in the development of NACT. This allows us to treat large accumulated phase delays determined from a path-average approximation non-linearly, while still using the full 3D sensitivity of the Born approximation. Further refinement of shallow regions of the model is obtained using broadband forward finite-difference waveform modeling. We are also integrating a regional Spectral Element Method code into our tomographic modeling, allowing us to move beyond many assumptions inherent in the analytic mode-based approaches, while still taking advantage of their computational efficiency. Illustrations of the effects of these increasingly sophisticated steps will be presented.

Quantum Theories of Self-Localization

NASA Astrophysics Data System (ADS)

Bernstein, Lisa Joan

In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

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.

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.

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

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

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

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

Hyperchaotic Dynamics for Light Polarization in a Laser Diode

NASA Astrophysics Data System (ADS)

Bonatto, Cristian

2018-04-01

It is shown that a highly randomlike behavior of light polarization states in the output of a free-running laser diode, covering the whole Poincaré sphere, arises as a result from a fully deterministic nonlinear process, which is characterized by a hyperchaotic dynamics of two polarization modes nonlinearly coupled with a semiconductor medium, inside the optical cavity. A number of statistical distributions were found to describe the deterministic data of the low-dimensional nonlinear flow, such as lognormal distribution for the light intensity, Gaussian distributions for the electric field components and electron densities, Rice and Rayleigh distributions, and Weibull and negative exponential distributions, for the modulus and intensity of the orthogonal linear components of the electric field, respectively. The presented results could be relevant for the generation of single units of compact light source devices to be used in low-dimensional optical hyperchaos-based applications.

Reconstructing baryon oscillations: A Lagrangian theory perspective

NASA Astrophysics Data System (ADS)

Padmanabhan, Nikhil; White, Martin; Cohn, J. D.

2009-03-01

Recently Eisenstein and collaborators introduced a method to “reconstruct” the linear power spectrum from a nonlinearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to nonlinear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different nonlinear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why miscalibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

Microresonators for Nonlinear Quantum Optics

NASA Astrophysics Data System (ADS)

Vernon, Zachary

In this thesis I study in detail the quantum dynamics of several nonlinear optical processes in microresonator systems. A Heisenberg-picture input-output formalism is developed from first principles that includes the effects of scattering losses and independent quality factors and coupling ratios for different resonances. The task of calculating the device output is then reduced to solving a set of driven, damped, ordinary differential equations for the resonator mode operators alone. This theoretical framework is used to study photon pair generation via spontaneous four-wave mixing in the weakly pumped regime, on which the effects of scattering losses are appraised. A more strongly driven regime is studied for continuous wave pumps, demonstrating when self- and cross-phase modulation and multi-photon pair generation become important, and their effects on the spectral and power scaling properties of the system are examined; A detuning strategy is presented that compensates for some of these effects. The results of the weak-pump regime are applied to study microresonator-based heralded single photon sources. The impact of scattering losses is studied, revealing that typical systems suffer from low heralding efficiency due to these losses. A technique to improve heralding efficiency is presented through over-coupling the resonator-channel system, and a resultant trade-off between heralding rate and heralding efficiency is uncovered. Limitations to the spectral purity of the heralded single photon output for conventional microresonator systems are also analysed, and a more sophisticated coupling scheme presented to overcome the upper bound for spectral purity of 93% that exists in typical systems, permitting the generation of single photons with spectral purity arbitrarily close to 100% without spectral filtering or sophisticated phase-matching techniques. The theory of quantum frequency conversion in microresonators using four-wave mixing is then developed in detail, and the spectral conversion probability and conversion efficiency studied. Efficiencies exceeding 90% using less than 100 mW of pump power are predicted to be achievable with current technology. A dressed mode picture is developed to better understand the conversion dynamics. Rabi-like spectral splitting and temporal oscillations of the intraresonator mean photon number are predicted, exhibiting a novel regime of strongly coupled photonic modes.

The ABC model: a non-hydrostatic toy model for use in convective-scale data assimilation investigations

NASA Astrophysics Data System (ADS)

Petrie, Ruth Elizabeth; Bannister, Ross Noel; Priestley Cullen, Michael John

2017-12-01

In developing methods for convective-scale data assimilation (DA), it is necessary to consider the full range of motions governed by the compressible Navier-Stokes equations (including non-hydrostatic and ageostrophic flow). These equations describe motion on a wide range of timescales with non-linear coupling. For the purpose of developing new DA techniques that suit the convective-scale problem, it is helpful to use so-called toy models that are easy to run and contain the same types of motion as the full equation set. Such a model needs to permit hydrostatic and geostrophic balance at large scales but allow imbalance at small scales, and in particular, it needs to exhibit intermittent convection-like behaviour. Existing toy models are not always sufficient for investigating these issues. A simplified system of intermediate complexity derived from the Euler equations is presented, which supports dispersive gravity and acoustic modes. In this system, the separation of timescales can be greatly reduced by changing the physical parameters. Unlike in existing toy models, this allows the acoustic modes to be treated explicitly and hence inexpensively. In addition, the non-linear coupling induced by the equation of state is simplified. This means that the gravity and acoustic modes are less coupled than in conventional models. A vertical slice formulation is used which contains only dry dynamics. The model is shown to give physically reasonable results, and convective behaviour is generated by localised compressible effects. This model provides an affordable and flexible framework within which some of the complex issues of convective-scale DA can later be investigated. The model is called the ABC model after the three tunable parameters introduced: A (the pure gravity wave frequency), B (the modulation of the divergent term in the continuity equation), and C (defining the compressibility).

Reduction of dissipation in a thermal engine by means of periodic changes of external constraintsa)

NASA Astrophysics Data System (ADS)

Escher, Claus; Ross, John

1985-03-01

We consider a thermal engine driven by chemical reactions, which take place in a continuous flow, stirred tank reactor fitted with a movable piston. Work can be produced by means of a heat engine coupled to the products and to an external heat bath, and by the piston. Two modes of operation are compared, each with fixed input rate of chemicals: one with periodic variation of an external constraint [mode (b)], in which we vary the external pressure, and one without such variation [mode (a)]. We derive equations for the total power output in each of the two modes. The power output in mode (b) can be larger than that of mode (a) for the same chemical throughput and for the same average value of the external pressure. For a particularly simple case it is shown that the total power output in mode (b) is larger than that in (a) if work is done by the piston. At the same time the entropy production is decreased and the efficiency is increased. The possibility of an increased power output is due to the proper control of the relative phase of the externally varied constraint and its conjugate variable, the external pressure and the volume. This control is achieved by the coupling of nonlinear kinetics to the externally varied constraint. Details of specific mechanisms and the occurrence of resonance phenomena are presented in the following article.

A Finite-Difference Time-Domain Model of Artificial Ionospheric Modification

NASA Astrophysics Data System (ADS)

Cannon, Patrick; Honary, Farideh; Borisov, Nikolay

Experiments in the artificial modification of the ionosphere via a radio frequency pump wave have observed a wide range of non-linear phenomena near the reflection height of an O-mode wave. These effects exhibit a strong aspect-angle dependence thought to be associated with the process by which, for a narrow range of off-vertical launch angles, the O-mode pump wave can propagate beyond the standard reflection height at X=1 as a Z-mode wave and excite additional plasma activity. A numerical model based on Finite-Difference Time-Domain method has been developed to simulate the interaction of the pump wave with an ionospheric plasma and investigate different non-linear processes involved in modification experiments. The effects on wave propagation due to plasma inhomogeneity and anisotropy are introduced through coupling of the Lorentz equation of motion for electrons and ions to Maxwell’s wave equations in the FDTD formulation, leading to a model that is capable of exciting a variety of plasma waves including Langmuir and upper-hybrid waves. Additionally, discretized equations describing the time-dependent evolution of the plasma fluid temperature and density are included in the FDTD update scheme. This model is used to calculate the aspect angle dependence and angular size of the radio window for which Z-mode excitation occurs, and the results compared favourably with both theoretical predictions and experimental observations. The simulation results are found to reproduce the angular dependence on electron density and temperature enhancement observed experimentally. The model is used to investigate the effect of different initial plasma density conditions on the evolution of non-linear effects, and demonstrates that the inclusion of features such as small field-aligned density perturbations can have a significant influence on wave propagation and the magnitude of temperature and density enhancements.

Simulation of linear and nonlinear Landau damping of lower hybrid waves

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

Qi, Lei; Wang, X. Y.; Lin, Y.

2013-06-15

The linear physics of lower hybrid waves (LHWs) and their nonlinear interaction with particles through Landau damping are studied with the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model in the electrostatic limit. Unlike most other wave modes, the LHWs can resonantly interact with both electrons and ions, with the former being highly magnetized and latter nearly unmagnetized around the lower hybrid frequency. Direct interactions of LHWs with electrons and/or ions are investigated for cases with various k{sub ∥}/k,T{sub i}/T{sub e}, and wave amplitudes. In the linear electron Landau damping (ELD), the dispersion relation and the linear dampingmore » rate obtained from our simulation agree well with the analytical linear theory. As the wave amplitude increases, the nonlinear Landau effects are present, and a transition from strong decay at smaller amplitudes to weak decay at larger amplitudes is observed. In the nonlinear stage, the LHWs in the long time evolution finally exhibit a steady Bernstein-Greene-Kruskal mode, in which the wave amplitude is saturated above the noise level. While the resonant electrons are trapped in the wave field in the nonlinear ELD, the resonant ions are untrapped in the LHW time scales. The ion Landau damping is thus predominantly in a linear fashion, leading to a wave saturation level significantly lower than that in the ELD. On the long time scales, however, the ions are still weakly trapped. The results show a coupling between the LHW frequency and the ion cyclotron frequency during the long-time LHW evolution.« less

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

The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Liu, Huan

2018-04-01

The Riemann-Hilbert problem for the coupled nonlinear Schrödinger equation is formulated on the basis of the corresponding 3× 3 matrix spectral problem. Using the nonlinear steepest descent method, we obtain leading-order asymptotics for the Cauchy problem of the coupled nonlinear Schrödinger equation.

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.

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.

Research on polarization vector characteristics in a microfiber-based graphene fiber laser

NASA Astrophysics Data System (ADS)

Han, Mengmeng; Zhang, Shumin; Li, Xingliang; Han, Huiyun; Liu, Jingmin; Yan, Dan

2016-11-01

We experimentally investigated the polarization vector characteristics in an Er-doped fiber laser based on graphene that was deposited on microfiber. A variety of dynamic states, including polarization locked fundamental soliton, and polarization domain wall square pulses and their harmonic mode locked counterparts have all been observed with different pump powers and polarization states. These results indicated that the microfiber-based graphene not only could act as a saturable absorber but also could provide high nonlinearity, which is favorable for the cross coupling between the two orthogonal polarization components. It was worth to mention that it is the first time to obtain the polarization domain wall solitons in a mode locked fiber laser.

Dynamics of nonspherical microbubble oscillations above instability threshold

NASA Astrophysics Data System (ADS)

Guédra, Matthieu; Cleve, Sarah; Mauger, Cyril; Blanc-Benon, Philippe; Inserra, Claude

2017-12-01

Time-resolved dynamics of nonspherical oscillations of micrometer-sized bubbles are captured and analyzed using high-speed imaging. The axisymmetry of the bubble shape is ensured with certainty for the first time from the recordings of two synchronous high-speed cameras located at 90∘. The temporal dynamics of finite-amplitude nonspherical oscillations are then analyzed for various acoustic pressures above the instability threshold. The experimental results are compared with recent theories accounting for nonlinearities and mode coupling, highlighting particular effects inherent to these mechanisms (saturation of the instability, triggering of nonparametric shape modes). Finally, the amplitude of the nonspherical oscillations is given as function of the driving pressure both for quadrupolar and octupolar bubbles.

Femtosecond pulses generated from a synchronously pumped chromium-doped forsterite laser

NASA Technical Reports Server (NTRS)

Seas, A.; Petricevic, V.; Alfano, R. R.

1993-01-01

Kerr lens mode-locking (KLM) has become a standard method to produce femtosecond pulses from tunable solid state lasers. High power inside the laser resonator propagating through the laser-medium with nonlinear index of refraction, coupled with the stability conditions of the laser modes in the resonator, result in a passive amplitude modulation which explains the mechanism for pulse shortening. Recently, chromium doped forsterite was shown to exhibit similar pulse behavior. A successful attempt to generate femtosecond pulses from a synchronously pumped chromium-doped forsterite laser with intracavity dispersion compensation is reported. Stable, transform limited pulses with duration of 105 fs were routinely generated, tunable between 1240 to 1270 nm.

A morphological study of waves in the thermosphere using DE-2 observations

NASA Technical Reports Server (NTRS)

Gross, S. H.; Kuo, S. P.; Shmoys, J.

1986-01-01

Theoretical model and data analysis of DE-2 observations for determining the correlation between the neutral wave activity and plasma irregularities have been presented. The relationships between the observed structure of the sources, precipitation and joule heating, and the fluctuations in neutral and plasma parameters are obtained by analyzing two measurements of neutral atmospheric wave activity and plasma irregularities by DE-2 during perigee passes at an altitude on the order of 300 to 350 km over the polar cap. A theoretical model based on thermal nonlinearity (joule heating) to give mode-mode coupling is developed to explore the role of neutral disturbance (winds and gravity waves) on the generation of plasma irregularities.

Magnetic domain wall gratings for magnetization reversal tuning and confined dynamic mode localization.

PubMed

Trützschler, Julia; Sentosun, Kadir; Mozooni, Babak; Mattheis, Roland; McCord, Jeffrey

2016-08-04

High density magnetic domain wall gratings are imprinted in ferromagnetic-antiferromagnetic thin films by local ion irradiation by which alternating head-to-tail-to-head-to-tail and head-to-head-to-tail-to-tail spatially overlapping domain wall networks are formed. Unique magnetic domain processes result from the interaction of anchored domain walls. Non-linear magnetization response is introduced by the laterally distributed magnetic anisotropy phases. The locally varying magnetic charge distribution gives rise to localized and guided magnetization spin-wave modes directly constrained by the narrow domain wall cores. The exchange coupled multiphase material structure leads to unprecedented static and locally modified dynamic magnetic material properties.

Magnetic domain wall gratings for magnetization reversal tuning and confined dynamic mode localization

NASA Astrophysics Data System (ADS)

Trützschler, Julia; Sentosun, Kadir; Mozooni, Babak; Mattheis, Roland; McCord, Jeffrey

2016-08-01

High density magnetic domain wall gratings are imprinted in ferromagnetic-antiferromagnetic thin films by local ion irradiation by which alternating head-to-tail-to-head-to-tail and head-to-head-to-tail-to-tail spatially overlapping domain wall networks are formed. Unique magnetic domain processes result from the interaction of anchored domain walls. Non-linear magnetization response is introduced by the laterally distributed magnetic anisotropy phases. The locally varying magnetic charge distribution gives rise to localized and guided magnetization spin-wave modes directly constrained by the narrow domain wall cores. The exchange coupled multiphase material structure leads to unprecedented static and locally modified dynamic magnetic material properties.

G-mode magnetic force microscopy: Separating magnetic and electrostatic interactions using big data analytics

DOE PAGES

Collins, Liam; Belianinov, Alex; Proksch, Roger; ...

2016-05-09

We develop a full information capture approach for Magnetic Force Microscopy (MFM), referred to as generalized mode (G-Mode) MFM. G-Mode MFM acquires and stores the full data stream from the photodetector at sampling rates approaching the intrinsic photodiode limit. The data can be subsequently compressed, denoised, and analyzed, without information loss. Also, 3 G-Mode MFM is implemented and compared to traditional heterodyne based MFM on model systems including domain structures in ferromagnetic Yttrium Iron Garnet (YIG) and electronically and magnetically inhomogeneous high entropy alloy, CoFeMnNiSn. We investigate the use of information theory to mine the G-Mode MFM data and demonstratemore » its usefulness for extracting information which may be hidden in traditional MFM modes, including signatures of nonlinearities and mode coupling phenomena. Finally we demonstrate detection and separation of magnetic and electrostatic tip-sample interactions from a single G-Mode image, by analyzing the entire frequency response of the cantilever. G-Mode MFM is immediately implementable on any AFM platform and as such is expected to be a useful technique for probing spatiotemporal cantilever dynamics and mapping material properties as well as their mutual interactions.« less

Numerical Simulation of the ``Fluid Mechanical Sewing Machine''

NASA Astrophysics Data System (ADS)

Brun, Pierre-Thomas; Audoly, Basile; Ribe, Neil

2011-11-01

A thin thread of viscous fluid falling onto a moving conveyor belt generates a wealth of complex ``stitch'' patterns depending on the belt speed and the fall height. To understand the rich nonlinear dynamics of this system, we have developed a new numerical code for simulating unsteady viscous threads, based on a discrete description of the geometry and a variational formulation for the viscous stresses. The code successfully reproduces all major features of the experimental state diagram of Morris et al. (Phys. Rev. E 2008). Fourier analysis of the motion of the thread's contact point with the belt suggests a new classification of the observed patterns, and reveals that the system behaves as a nonlinear oscillator coupling the pendulum modes of the thread.

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

NASA Astrophysics Data System (ADS)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

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.

Advanced specialty fiber designs for high power fiber lasers

NASA Astrophysics Data System (ADS)

Gu, Guancheng

The output power of fiber lasers has increased rapidly over the last decade. There are two major limiting factors, namely nonlinear effects and transverse mode instability, prohibiting the power scaling capability of fiber lasers. The nonlinear effects, originating from high optical intensity, primarily limit the peak power scaling. The mode instability, on the other hand, arises from quantum-defect driven heating, causing undesired mode coupling once the power exceeds the threshold and degradation of beam quality. The mode instability has now become the bottleneck for average output power scaling of fiber lasers. Mode area scaling is the most effective way to mitigate nonlinear effects. However, the use of large mode area may increase the tendency to support multiple modes in the core, resulting in lower mode instability threshold. Therefore, it is critical to maintain single mode operation in a large mode area fiber. Sufficient higher order mode suppression can lead to effective single-transverse-mode propagation. In this dissertation, we explore the feasibility of using specialty fiber to construct high power fiber lasers with robust single-mode output. The first type of fiber discussed is the resonantly-enhanced leakage channel fiber. Coherent reflection at the fiber outer boundary can lead to additional confinement especially for highly leaky HOM, leading to lower HOM losses than what are predicted by conventional finite element mothod mode solver considering infinite cladding. In this work, we conducted careful measurements of HOM losses in two leakage channel fibers (LCF) with circular and rounded hexagonal boundary shapes respectively. Impact on HOM losses from coiling, fiber boundary shapes and coating indexes were studied in comparison to simulations. This work demonstrates the limit of the simulation method commonly used in the large-mode-area fiber designs and the need for an improved approach. More importantly, this work also demonstrates that a deviation from circular fiber outer shape may be an effective method to mitigate HOM loss reduction from coherent reflection from fiber outer boundary. In an all-solid photonic bandgap fiber, modes are only guided due to anti-resonance of cladding photonic crystal lattice. This provides strongly mode-dependent guidance, leading to very high differential mode losses, which is essential for lasing far from the gain peak and suppression of stimulated Raman scattering. We will show that all-solid photonic bandgap fibers with effective mode area of 920microm2 can be made with excellent higher order mode suppression. We then demonstrate a 50microm-core-diameter Yb-doped all-solid photonic bandgap fiber laser. 75W output power has been generated with a diffraction-limited beam and an efficiency of 70% relative to the launched pump power. We have also experimentally confirmed that a robust single-mode regime exists near the high frequency edge of the bandgap. It is well known that incorporation of additional smaller cores in the cladding can be used to resonantly out-couple higher-order modes from a main core to suppress higher-order-mode propagation in the main core. Using a novel design with multiple coupled smaller cores in the cladding, we further scaled up the mode area and have successfully demonstrated a single-mode photonic bandgap fiber with record effective mode area of 2650microm2. Detailed numeric studies have been conducted for multiple cladding designs. For the optimal designs, the simulated minimum higher-order-mode losses are well over two orders of magnitudes higher than that of fundamental mode when expressed in dBs. We have also experimentally validated one of the designs. M 2<1.08 across the transmission band was demonstrated. Lowering quantum defect heating is another approach to mitigate mode instability. Highly-efficient high-power fiber lasers operating at wavelength below 1020nm are critical for tandem-pumping in >10kW fiber lasers to provide high pump brightness and low thermal loading. Using an ytterbium-doped-phosphosilicate double-clad leakage-channel fiber with 50microm core and 420microm cladding, we have achieved 70% optical-to-optical efficiency at 1018nm. The much larger cladding than those in previous reports demonstrates the much lower required pump brightness, a key for efficient kW operation. The demonstrated 1018nm fiber laser has ASE suppression of 41dB. This is higher than previous reports and further demonstrates the advantages of the fiber used. Limiting factors to efficiency are also systematically studied.

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

Strong quantum squeezing of mechanical resonator via parametric amplification and coherent feedback

NASA Astrophysics Data System (ADS)

You, Xiang; Li, Zongyang; Li, Yongmin

2017-12-01

A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

NASA Technical Reports Server (NTRS)

Ballabrera-Poy, J.; Busalacchi, A.; Murtugudde, R.

2000-01-01

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model of Zebiak and Cane. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Application of a Reduced Order Kalman Filter to Initialize a Coupled Atmosphere-Ocean Model: Impact on the Prediction of El Nino

NASA Technical Reports Server (NTRS)

Ballabrera-Poy, Joaquim; Busalacchi, Antonio J.; Murtugudde, Ragu

2000-01-01

A reduced order Kalman Filter, based on a simplification of the Singular Evolutive Extended Kalman (SEEK) filter equations, is used to assimilate observed fields of the surface wind stress, sea surface temperature and sea level into the nonlinear coupled ocean-atmosphere model. The SEEK filter projects the Kalman Filter equations onto a subspace defined by the eigenvalue decomposition of the error forecast matrix, allowing its application to high dimensional systems. The Zebiak and Cane model couples a linear reduced gravity ocean model with a single vertical mode atmospheric model of Zebiak. The compatibility between the simplified physics of the model and each observed variable is studied separately and together. The results show the ability of the model to represent the simultaneous value of the wind stress, SST and sea level, when the fields are limited to the latitude band 10 deg S - 10 deg N. In this first application of the Kalman Filter to a coupled ocean-atmosphere prediction model, the sea level fields are assimilated in terms of the Kelvin and Rossby modes of the thermocline depth anomaly. An estimation of the error of these modes is derived from the projection of an estimation of the sea level error over such modes. This method gives a value of 12 for the error of the Kelvin amplitude, and 6 m of error for the Rossby component of the thermocline depth. The ability of the method to reconstruct the state of the equatorial Pacific and predict its time evolution is demonstrated. The method is shown to be quite robust for predictions I up to six months, and able to predict the onset of the 1997 warm event fifteen months before its occurrence.

Observation of finite-. beta. MHD phenomena in tokamaks

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

McGuire, K.M.

1984-09-01

Stable high-beta plasmas are required for the tokamak to attain an economical fusion reactor. Recently, intense neutral beam heating experiments in tokamaks have shown new effects on plasma stability and confinement associated with high beta plasmas. The observed spectrum of MHD fluctuations at high beta is clearly dominated by the n = 1 mode when the q = 1 surface is in the plasma. The m/n = 1/1 mode drives other n = 1 modes through toroidal coupling and n > 1 modes through nonlinear coupling. On PDX, with near perpendicular injection, a resonant interaction between the n = 1more » internal kink and the trapped fast ions results in loss of beam particles and heating power. Key parameters in the theory are the value of q/sub 0/ and the injection angle. High frequency broadband magnetic fluctuations have been observed on ISX-B and D-III and a correlation with the deterioration of plasma confinement was reported. During enhanced confinement (H-mode) discharges in divertor plasmas, two new edge instabilities were observed, both localized radially near the separatrix. By assembling results from the different tokamak experiments, it is found that the simple theoretical ideal MHD beta limit has not been exceeded. Whether this represents an ultimate tokamak limit or if beta optimized configurations (Dee- or bean-shaped plasmas) can exceed this limit and perhaps enter a second regime of stability remains to be clarified.« less

Nonlinear Excitation of Acoustic Modes by Large Amplitude Alfvén waves in the Large Plasma Device (LAPD)

NASA Astrophysics Data System (ADS)

Dorfman, S. E.; Carter, T. A.; Pribyl, P.; Tripathi, S.; Van Compernolle, B.; Vincena, S. T.; Sydora, R. D.

2013-12-01

Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in space plasmas. While the linear behavior of these waves has been extensively studied [1], non-linear effects are important in many real systems, including the solar corona and solar wind. In particular, a parametric decay process in which a large amplitude Alfvén wave decays into an ion acoustic wave and backward propagating Alfvén wave may play an important role in the coronal heating problem. Specifically, the decay of large-amplitude Alfvén waves propagating outward from the photosphere could lead to heating of the corona by the daughter ion acoustic modes [2]. As direct observational evidence of parametric decay is limited [3], laboratory experiments may play an important role in validating simple theoretical predictions and aiding in the interpretation of space measurements. Recent counter-propagating Alfvén wave experiments in the Large Plasma Device (LAPD) have recorded the first laboratory observation of the Alfvén-acoustic mode coupling at the heart of this parametric decay instability [4]. A resonance in the beat wave response produced by the two launched Alfvén waves is observed and is identified as a damped ion acoustic mode based on the measured dispersion relation. Other properties of the interaction including the spatial profile of the beat mode and response amplitude are also consistent with theoretical predictions for a three-wave interaction driven by a nonlinear ponderomotive force. Strong damping observed after the pump Alfvén waves are turned off is under investigation; a novel ion acoustic wave launcher is under development to launch the mode directly for damping studies. New experiments also aim to identify decay instabilities from a single large-amplitude Alfvén wave. In conjunction with these experiments, gyrokinetic simulation efforts are underway to scope out the relevant parameter space. [1] W. Gekelman, et. al., Phys. Plasmas 18, 055501 (2011). [2] F. Pruneti, F and M. Velli, ESA Spec. Pub. 404, 623 (1997). [3] S. R. Spangler, et. al., Phys. Plasmas 4, 846 (1997). [4] S. Dorfman and T. Carter, Phys. Rev. Lett. 110, 195001 (2013).

Investigation of the coupling of the momentum distribution of a BEC with its collective of modes

NASA Astrophysics Data System (ADS)

Henn, Emanuel; Tavares, Pedro; Fritsch, Amilson; Vivanco, Franklin; Telles, Gustavo; Bagnato, Vanderlei

In our group we have a strong research line on quantum turbulence and the general investigation of Bose-Einstein condensates (BEC) subjected to oscillatory excitations. Inside this research line we investigate first the behavior of the normal modes of the BEC under this excitation and observe a non-linear behavior in the amplitude of the quadrupolar mode. Also, inside this same procedure of investigation we study the momentum distribution of a BEC to understand if it is possible to extract Kolmogorov like excitation spectra which would point to a turbulent state of matter. The condensate is perturbed, and we let it evolve in-trap after which we perform standard time-of- flight absorption imaging. The momentum distribution is extracted and analyzed as a function of the in-trap free evolution time for a 2D projected cloud. We show that the momentum distribution has its features varying periodically with the same frequency as the quadrupolar mode displayed by the atomic gas hinting at a strong coupling of both. The main consequence of that one cannot be assertive about the quantitative features of the extract spectrum of momentum and we can only rely on its qualitative features. Financial Support: FAPESP, CNPq.

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.

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.

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.

Effects of eddy initial conditions on nonlinear forcing of planetary scale waves by amplifying baroclinic eddies

NASA Technical Reports Server (NTRS)

Young, Richard E.

1986-01-01

The previous study of Young and Villere concerning growth of planetary scale waves forced by wave-wave interactions of amplifying intermediate scale baroclinic eddies is extended to investigate effects of different eddy initial conditions. A global, spectral, primitive equation model is used for the calculations. For every set of eddy initial conditions considered, growth rates of planetary modes are considerably greater than growth rates computed from linear instability theory for a fixed zonally independent basic state. However, values of growth rates ranged over a factor of 3 depending on the particular set of eddy initial conditions used. Nonlinear forcing of planetary modes via wave-wave coupling becomes more important than baroclinic growth on the basic state at small values of the intermediate-scale modal amplitudes. The relative importance of direct transfer of kinetic energy from intermediate scales of motion to a planetary mode, compared to baroclinic conversion of available potential energy to kinetic energy within that planetary mode, depends on the individual case. In all cases, however, the transfer of either kinetic or available potential energy to the planetary modes was accomplished principally by wave-wave transfer from intermediate scale eddies, rather than from the zonally averaged state. The zonal wavenumber 2 planetary mode was prominent in all solutions, even in those for which eddy initial conditions were such that a different planetary mode was selectively forced at the start. General characteristics of the structural evolution of the planetary wave components of total heat and momentum flux, and modal structures themselves, were relatively insensitive to variations in eddy initial conditions, even though quantitative details varied from case to case.

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

Coupled resonator optical waveguides based on silicon-on-insulator photonic wires

NASA Astrophysics Data System (ADS)

Xia, Fengnian; Sekaric, Lidija; O'Boyle, Martin; Vlasov, Yurii

2006-07-01

Coupled resonator optical waveguides (CROWs) comprised of up to 16 racetrack resonators based on silicon-on-insulator (SOI) photonic wires were fabricated and characterized. The optical properties of the CROWs were simulated using measured single resonator parameters based on a matrix approach. The group delay property of CROWs was also analyzed. The SOI based CROWs consisting of multiple resonators have extremely small footprints and can find applications in optical filtering, dispersion compensation, and optical buffering. Moreover, such CROW structure is a promising candidate for exploration of low light level nonlinear optics due to its resonant nature and compact mode size (˜0.1μm2) in photonic wire.

Photoinduced currents in metal-barrier-metal junctions

NASA Technical Reports Server (NTRS)

Guedes, M. P.; Gustafson, T. K.; Heiblum, M.; Siu, D. P.; Slayman, C. W.; Whinnery, J. R.; Yasuoka, Y.

1978-01-01

The fabrication and application of metal-barrier-metal tunneling junctions for radiative interactions are discussed. Particular attention is given to the photolithographic fabrication of small area devices and the coupling to such devices via surface plasmon waves which play an important role at infrared and optical frequencies. It has been shown that the junction electron tunneling currents can be strongly coupled to surface plasmon junction modes, and spontaneous and stimulated emission of the latter are possible as well as nonlinear interactions. Finally, results demonstrating the photo-excitation of electrons with subsequent tunneling induced by ultraviolet radiation are presented. It is estimated that quantum efficiencies of the order of 5% and higher are possible in the ultraviolet region.

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

Collins, Liam; Belianinov, Alex; Kalinin, Sergei V.

In this work, we develop a full information capture approach for Magnetic Force Microscopy (MFM), referred to as generalized mode (G-Mode) MFM. G-Mode MFM acquires and stores the full data stream from the photodetector, captured at sampling rates approaching the intrinsic photodiode limit. The data can be subsequently compressed, denoised, and analyzed, without information loss. Here, G-Mode MFM is implemented and compared to the traditional heterodyne-based MFM on model systems, including domain structures in ferromagnetic Yttrium Iron Garnet and the electronically and magnetically inhomogeneous high entropy alloy, CoFeMnNiSn. We investigate the use of information theory to mine the G-Mode MFMmore » data and demonstrate its usefulness for extracting information which may be hidden in traditional MFM modes, including signatures of nonlinearities and mode-coupling phenomena. Finally, we demonstrate detection and separation of magnetic and electrostatic tip-sample interactions from a single G-Mode image, by analyzing the entire frequency response of the cantilever. G-Mode MFM is immediately implementable on any atomic force microscopy platform and as such is expected to be a useful technique for probing spatiotemporal cantilever dynamics and mapping material properties, as well as their mutual interactions.« less

Relativistic weak lensing from a fully non-linear cosmological density field

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

Thomas, D.B.; Bruni, M.; Wands, D., E-mail: thomas.daniel@ucy.ac.cy, E-mail: marco.bruni@port.ac.uk, E-mail: david.wands@port.ac.uk

2015-09-01

In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the post-Friedmann formalism, a post-Newtonian type framework for cosmology, to derive the full weak-lensing deflection angle valid on non-linear scales for any metric theory of gravity. We show that the only contributing term that is quadratic in the first order deflection is the expected Born correction and lens-lens coupling term. We use this deflection angle to analyse the vector and tensor contributions to the E- andmore » B- mode cosmic shear power spectra. In our approach, once the gravitational theory has been specified, the metric components are related to the matter content in a well-defined manner. Specifying General Relativity, we write down a complete set of equations for a GR+ΛCDM universe for computing all of the possible lensing terms from Newtonian N-body simulations. We illustrate this with the vector potential and show that, in a GR+ΛCDM universe, its contribution to the E-mode is negligible with respect to that of the conventional Newtonian scalar potential, even on non-linear scales. Thus, under the standard assumption that Newtonian N-body simulations give a good approximation of the matter dynamics, we show that the standard ray tracing approach gives a good description for a ΛCDM cosmology.« less

Enhanced energy transport owing to nonlinear interface interaction

PubMed Central

Su, Ruixia; Yuan, Zongqiang; Wang, Jun; Zheng, Zhigang

2016-01-01

It is generally expected that the interface coupling leads to the suppression of thermal transport through coupled nanostructures due to the additional interface phonon-phonon scattering. However, recent experiments demonstrated that the interface van der Waals interactions can significantly enhance the thermal transfer of bonding boron nanoribbons compared to a single freestanding nanoribbon. To obtain a more in-depth understanding on the important role of the nonlinear interface coupling in the heat transports, in the present paper, we explore the effect of nonlinearity in the interface interaction on the phonon transport by studying the coupled one-dimensional (1D) Frenkel-Kontorova lattices. It is found that the thermal conductivity increases with increasing interface nonlinear intensity for weak inter-chain nonlinearity. By developing the effective phonon theory of coupled systems, we calculate the dependence of heat conductivity on interfacial nonlinearity in weak inter-chain couplings regime which is qualitatively in good agreement with the result obtained from molecular dynamics simulations. Moreover, we demonstrate that, with increasing interface nonlinear intensity, the system dimensionless nonlinearity strength is reduced, which in turn gives rise to the enhancement of thermal conductivity. Our results pave the way for manipulating the energy transport through coupled nanostructures for future emerging applications. PMID:26787363