Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

NASA Astrophysics Data System (ADS)

Gong, Chun-Lin; Fang, Zhe; Chen, Gang

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

A string of Peregrine rogue waves in the nonlocal nonlinear Schrödinger equation with parity-time symmetric self-induced potential

NASA Astrophysics Data System (ADS)

Gupta, Samit Kumar

2018-03-01

Dynamic wave localization phenomena draw fundamental and technological interests in optics and photonics. Based on the recently proposed (Ablowitz and Musslimani, 2013) continuous nonlocal nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity (PTNLSE), a numerical investigation has been carried out for two first order Peregrine solitons as the initial ansatz. Peregrine soliton, as an exact solution to the PTNLSE, evokes a very potent question: what effects does the interaction of two first order Peregrine solitons have on the overall optical field dynamics. Upon numerical computation, we observe the appearance of Kuznetsov-Ma (KM) soliton trains in the unbroken PT-phase when the initial Peregrine solitons are in phase. In the out of phase condition, it shows repulsive nonlinear waves. Quite interestingly, our study shows that within a specific range of the interval factor in the transverse co-ordinate there exists a string of high intensity well-localized Peregrine rogue waves in the PT unbroken phase. We note that the interval factor as well as the transverse shift parameter play important roles in the nonlinear interaction and evolution dynamics of the optical fields. This could be important in developing fundamental understanding of nonlocal non-Hermitian NLSE systems and dynamic wave localization behaviors.

ARTICLES: Nonlinear interaction of infrared waves on a VO2 surface at a semiconductor-metal phase transition

NASA Astrophysics Data System (ADS)

Berger, N. K.; Zhukov, E. A.; Novokhatskiĭ, V. V.

1984-04-01

The use of a semiconductor-metal phase transition for wavefront reversal of laser radiation was proposed. An investigation was made of nonlinear reflection of CO2 laser radiation at a phase transition in VO2. A three-wave interaction on a VO2 surface was achieved using low-power cw and pulsed CO2 lasers. In the first case, the intensity reflection coefficient was 0.5% for a reference wave intensity of 0.9 W/cm2 and in the second case, it was 42% for a threshold reference wave energy density of 0.6-0.8 mJ/cm2.

Communication: The origin of many-particle signals in nonlinear optical spectroscopy of non-interacting particles

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

Mukamel, Shaul

Nonlinear spectroscopy signals detected by fluorescence from dilute samples of N non-interacting molecules are usually adequately described by simply multiplying the single molecule response by N. We show that signals that scale with higher powers of N are generated by the joint detection of several particles. This can be accomplished by phase sensitive detection such as phase cycling, photo-acoustic modulation, or by Hanbury-Brown Twiss photon coincidence. Such measurements can dissect the ensemble according to the number of excited particles.

Synchronization and Cardio-pulmonary feedback in Sleep Apnea

NASA Astrophysics Data System (ADS)

Xu, Limei; Ivanov, Plamen Ch.; Chen, Zhi; Hu, Kun; Paydarfar, David; Stanley, H. Eugene

2004-03-01

Findings indicate a dynamical coupling between respiratory and cardiac function. However, the nature of this nonlinear interaction remains not well understood. We investigate transient patterns in the cardio-pulmonary interaction under healthy conditions by means of cross-correlation and nonlinear synchronization techniques, and we compare how these patterns change under pathologic conditions such as obstructive sleep apnea --- a periodic cessation of breathing during sleep. We find that during apnea episodes the nonlinear features of cardio-pulmonary interaction change intermittently, and can exhibit variations characterized by different time delays in the phase synchronization between breathing and heartbeat dynamics.

Nonlinear two-dimensional terahertz photon echo and rotational spectroscopy in the gas phase.

PubMed

Lu, Jian; Zhang, Yaqing; Hwang, Harold Y; Ofori-Okai, Benjamin K; Fleischer, Sharly; Nelson, Keith A

2016-10-18

Ultrafast 2D spectroscopy uses correlated multiple light-matter interactions for retrieving dynamic features that may otherwise be hidden under the linear spectrum; its extension to the terahertz regime of the electromagnetic spectrum, where a rich variety of material degrees of freedom reside, remains an experimental challenge. We report a demonstration of ultrafast 2D terahertz spectroscopy of gas-phase molecular rotors at room temperature. Using time-delayed terahertz pulse pairs, we observe photon echoes and other nonlinear signals resulting from molecular dipole orientation induced by multiple terahertz field-dipole interactions. The nonlinear time domain orientation signals are mapped into the frequency domain in 2D rotational spectra that reveal J-state-resolved nonlinear rotational dynamics. The approach enables direct observation of correlated rotational transitions and may reveal rotational coupling and relaxation pathways in the ground electronic and vibrational state.

Spin-orbit optical cross-phase-modulation

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

Brasselet, Etienne

2010-12-15

We show experimentally that optical phase singularities (PSs) can be written and erased, locally and in a controllable manner, into a light beam using the giant Kerr optical nonlinearities of liquid crystals. The method relies on the nonlinear optical spin-orbit coupling experienced by a collimated probe beam when a collinear focused pump beam imprints a radial birefringent pattern into a nematic film. In addition, experimental data are quantitatively described, accounting for the elastic anisotropy of the material and its nonlocal spatial response to the pump light field. Since we show that the optical intensity of a light beam (the 'pump')more » controls the phase of another beam (the 'probe') in a singular fashion (i.e., with the generation of a screw PS) via their interaction in a nonlinear medium that involves spin-orbit coupling, we dubbed such a nonlinear optical process as spin-orbit optical cross-phase-modulation.« less

Some Boussinesq Equations with Saturation

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

Christou, M. A.

2010-11-25

We investigate numerically some Boussinesq type equations with square or cubic and saturated nonlinearity. We examine the propagation, interaction and overtake interaction of soliton solutions. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the square or cubic nonlinearity without saturation. We calculate numerically the phase shift experienced by the solitons upon collision and conclude the impact of saturation.

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.

Microscopic Lagrangian description of warm plasmas. III - Nonlinear wave-particle interaction

NASA Technical Reports Server (NTRS)

Galloway, J. J.; Crawford, F. W.

1977-01-01

The averaged-Lagrangian method is applied to nonlinear wave-particle interactions in an infinite, homogeneous, magnetic-field-free plasma. The specific example of Langmuir waves is considered, and the combined effects of four-wave interactions and wave-particle interactions are treated. It is demonstrated how the latter lead to diffusion in velocity space, and the quasilinear diffusion equation is derived. The analysis is generalized to the random phase approximation. The paper concludes with a summary of the method as applied in Parts 1-3 of the paper.

Nonlinear evolution of Mack modes in a hypersonic boundary layer

NASA Astrophysics Data System (ADS)

Chokani, Ndaona

2005-01-01

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

Second order harmonic guided wave mutual interactions in plate: Vector analysis, numerical simulation, and experimental results

NASA Astrophysics Data System (ADS)

Hasanian, Mostafa; Lissenden, Cliff J.

2017-08-01

The extraordinary sensitivity of nonlinear ultrasonic waves to the early stages of material degradation makes them excellent candidates for nondestructive material characterization. However, distinguishing weak material nonlinearity from instrumentation nonlinearity remains problematic for second harmonic generation approaches. A solution to this problem is to mix waves having different frequencies and to let their mutual interaction generate sum and difference harmonics at frequencies far from those of the instrumentation. Mixing of bulk waves and surface waves has been researched for some time, but mixing of guided waves has not yet been investigated in depth. A unique aspect of guided waves is their dispersive nature, which means we need to assure that a wave can propagate at the sum or difference frequency. A wave vector analysis is conducted that enables selection of primary waves traveling in any direction that generate phase matched secondary waves. We have tabulated many sets of primary waves and phase matched sum and difference harmonics. An example wave mode triplet of two counter-propagating collinear shear horizontal waves that interact to generate a symmetric Lamb wave at the sum frequency is simulated using finite element analysis and then laboratory experiments are conducted. The finite element simulation eliminates issues associated with instrumentation nonlinearities and signal-to-noise ratio. A straightforward subtraction method is used in the experiments to identify the material nonlinearity induced mutual interaction and show that the generated Lamb wave propagates on its own and is large enough to measure. Since the Lamb wave has different polarity than the shear horizontal waves the material nonlinearity is clearly identifiable. Thus, the mutual interactions of shear horizontal waves in plates could enable volumetric characterization of material in remote regions from transducers mounted on just one side of the plate.

Quantum state detection and state preparation based on cavity-enhanced nonlinear interaction of atoms with single photon

NASA Astrophysics Data System (ADS)

Hosseini, Mahdi

Our ability to engineer quantum states of light and matter has significantly advanced over the past two decades, resulting in the production of both Gaussian and non-Gaussian optical states. The resulting tailored quantum states enable quantum technologies such as quantum optical communication, quantum sensing as well as quantum photonic computation. The strong nonlinear light-atom interaction is the key to deterministic quantum state preparation and quantum photonic processing. One route to enhancing the usually weak nonlinear light-atom interactions is to approach the regime of cavity quantum electrodynamics (cQED) interaction by means of high finesse optical resonators. I present results from the MIT experiment of large conditional cross-phase modulation between a signal photon, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. I also present a scheme to probabilistically change the amplitude and phase of a signal photon qubit to, in principle, arbitrary values by postselection on a control photon that has interacted with that state. Notably, small changes of the control photon polarization measurement basis by few degrees can substantially change the amplitude and phase of the signal state. Finally, I present our ongoing effort at Purdue to realize similar peculiar quantum phenomena at the single photon level on chip scale photonic systems.

Phase coupling in the cardiorespiratory interaction.

PubMed

Bahraminasab, A; Kenwright, D; Stefanovska, A; Ghasemi, F; McClintock, P V E

2008-01-01

Markovian analysis is applied to derive nonlinear stochastic equations for the reconstruction of heart rate and respiration rate variability data. A model of their 'phase' interactions is obtained for the first time, thereby gaining new insights into the strength and direction of the cardiorespiratory phase coupling. The reconstructed model can reproduce synchronisation phenomena between the cardiac and the respiratory systems, including switches in synchronisation ratio. The technique is equally applicable to the extraction of the multi-dimensional couplings between many interacting subsystems.

Ion hole formation and nonlinear generation of electromagnetic ion cyclotron waves: THEMIS observations

NASA Astrophysics Data System (ADS)

Shoji, Masafumi; Miyoshi, Yoshizumi; Katoh, Yuto; Keika, Kunihiro; Angelopoulos, Vassilis; Kasahara, Satoshi; Asamura, Kazushi; Nakamura, Satoko; Omura, Yoshiharu

2017-09-01

Electromagnetic plasma waves are thought to be responsible for energy exchange between charged particles in space plasmas. Such an energy exchange process is evidenced by phase space holes identified in the ion distribution function and measurements of the dot product of the plasma wave electric field and the ion velocity. We develop a method to identify ion hole formation, taking into consideration the phase differences between the gyromotion of ions and the electromagnetic ion cyclotron (EMIC) waves. Using this method, we identify ion holes in the distribution function and the resulting nonlinear EMIC wave evolution from Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations. These ion holes are key to wave growth and frequency drift by the ion currents through nonlinear wave-particle interactions, which are identified by a computer simulation in this study.

Nonlinear photonic metasurfaces

NASA Astrophysics Data System (ADS)

Li, Guixin; Zhang, Shuang; Zentgraf, Thomas

2017-03-01

Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.

Current interactions from the one-form sector of nonlinear higher-spin equations

NASA Astrophysics Data System (ADS)

Gelfond, O. A.; Vasiliev, M. A.

2018-06-01

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp ⁡ iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.

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.

New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

NASA Astrophysics Data System (ADS)

Vinayagam, P. S.; Radha, R.; Al Khawaja, U.; Ling, Liming

2018-06-01

We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and four wave mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of four wave mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of four wave mixing results in the generation of a new solutions which is spatially and temporally periodic called "Soliton (Breather) lattice".

Few-cycle solitons and supercontinuum generation with cascaded quadratic nonlinearities in unpoled lithium niobate ridge waveguides.

PubMed

Guo, Hairun; Zeng, Xianglong; Zhou, Binbin; Bache, Morten

2014-03-01

Formation and interaction of few-cycle solitons in a lithium niobate ridge waveguide are numerically investigated. The solitons are created through a cascaded phase-mismatched second-harmonic generation process, which induces a dominant self-defocusing Kerr-like nonlinearity on the pump pulse. The inherent material self-focusing Kerr nonlinearity is overcome over a wide wavelength range, and self-defocusing solitons are supported from 1100 to 1900 nm, covering the whole communication band. Single cycle self-compressed solitons and supercontinuum generation spanning 1.3 octaves are observed when pumped with femtosecond nanojoule pulses at 1550 nm. The waveguide is not periodically poled, as quasi-phase-matching would lead to detrimental nonlinear effects impeding few-cycle soliton formation.

Interactions of solitons in Bragg gratings with dispersive reflectivity in a cubic-quintic medium

NASA Astrophysics Data System (ADS)

Dasanayaka, Sahan; Atai, Javid

2011-08-01

Interactions between quiescent solitons in Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity are systematically investigated. In a previous work two disjoint families of solitons were identified in this model. One family can be viewed as the generalization of the Bragg grating solitons in Kerr nonlinearity with dispersive reflectivity (Type 1). On the other hand, the quintic nonlinearity is dominant in the other family (Type 2). For weak to moderate dispersive reflectivity, two in-phase solitons will attract and collide. Possible collision outcomes include merger to form a quiescent soliton, formation of three solitons including a quiescent one, separation after passing through each other once, asymmetric separation after several quasielastic collisions, and soliton destruction. Type 2 solitons are always destroyed by collisions. Solitons develop sidelobes when dispersive reflectivity is strong. In this case, it is found that the outcome of the interactions is strongly dependent on the initial separation of solitons. Solitons with sidelobes will collide only if they are in-phase and their initial separation is below a certain critical value. For larger separations, both in-phase and π-out-of-phase Type 1 and Type 2 solitons may either repel each other or form a temporary bound state that subsequently splits into two separating solitons. Additionally, in the case of Type 2 solitons, for certain initial separations, the bound state disintegrates into a single moving soliton.

Optimal phase measurements with bright- and vacuum-seeded SU(1,1) interferometers

NASA Astrophysics Data System (ADS)

Anderson, Brian E.; Schmittberger, Bonnie L.; Gupta, Prasoon; Jones, Kevin M.; Lett, Paul D.

2017-06-01

The SU(1,1) interferometer can be thought of as a Mach-Zehnder interferometer with its linear beam splitters replaced with parametric nonlinear optical processes. We consider the cases of bright- and vacuum-seeded SU(1,1) interferometers using intensity or homodyne detectors. A simplified truncated scheme with only one nonlinear interaction is introduced, which not only beats conventional intensity detection with a bright seed, but can saturate the phase-sensitivity bound set by the quantum Fisher information. We also show that the truncated scheme achieves a sub-shot-noise phase sensitivity in the vacuum-seeded case, despite the phase-sensing optical beams having no well-defined phase.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence

PubMed Central

2017-01-01

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167576

Entanglement Dynamics of Linear and Nonlinear Interaction of Two Two-Level Atoms with a Quantized Phase-Damped Field in the Dispersive Regime

NASA Astrophysics Data System (ADS)

Tavassoly, M. K.; Daneshmand, R.; Rustaee, N.

2018-06-01

In this paper we study the linear and nonlinear (intensity-dependent) interactions of two two-level atoms with a single-mode quantized field far from resonance, while the phase-damping effect is also taken into account. To find the analytical solution of the atom-field state vector corresponding to the considered model, after deducing the effective Hamiltonian we evaluate the time-dependent elements of the density operator using the master equation approach and superoperator method. Consequently, we are able to study the influences of the special nonlinearity function f (n) = √ {n}, the intensity of the initial coherent state field and the phase-damping parameter on the degree of entanglement of the whole system as well as the field and atom. It is shown that in the presence of damping, by passing time, the amount of entanglement of each subsystem with the rest of system, asymptotically reaches to its stationary and maximum value. Also, the nonlinear interaction does not have any effect on the entanglement of one of the atoms with the rest of system, but it changes the amplitude and time period of entanglement oscillations of the field and the other atom. Moreover, this may cause that, the degree of entanglement which may be low (high) at some moments of time becomes high (low) by entering the intensity-dependent function in the atom-field coupling.

Linear and non-linear interdependence of EEG and HRV frequency bands in human sleep.

PubMed

Chaparro-Vargas, Ramiro; Dissanayaka, P Chamila; Patti, Chanakya Reddy; Schilling, Claudia; Schredl, Michael; Cvetkovic, Dean

2014-01-01

The characterisation of functional interdependencies of the autonomic nervous system (ANS) stands an evergrowing interest to unveil electroencephalographic (EEG) and Heart Rate Variability (HRV) interactions. This paper presents a biosignal processing approach as a supportive computational resource in the estimation of sleep dynamics. The application of linear, non-linear methods and statistical tests upon 10 overnight polysomnographic (PSG) recordings, allowed the computation of wavelet coherence and phase locking values, in order to identify discerning features amongst the clinical healthy subjects. Our findings showed that neuronal oscillations θ, α and σ interact with cardiac power bands at mid-to-high rank of coherence and phase locking, particularly during NREM sleep stages.

Growth and Interaction of Colloid Nuclei

NASA Astrophysics Data System (ADS)

Lam, Michael-Angelo; Khusid, Boris; Meyer, William; Kondic, Lou

2017-11-01

We study evolution of colloid systems under zero-gravity conditions. In particular, we focus on the regime where there is a coexistence between a liquid and a solid state. Under zero gravity, the dominating process in the bulk of the fluid phase and the solid phase is diffusion. At the moving solid/liquid interface, osmotic pressure is balanced by surface tension, as well as balancing fluxes (conservation of mass) with the kinematics of nuclei growth (Wilson-Frenkel law). Due to the highly nonlinear boundary condition at the moving boundary, care has to be taken when performing numerical simulations. In this work, we present a nonlinear model for colloid nuclei growth. Numerical simulations using a finite volume method are compared with asymptotic analysis of the governing equation and experimental results for nuclei growth. Novel component in our numerical simulations is the inclusion of nonlinear (collective) diffusion terms that depend on the chemical potentials of the colloid in the solid and fluid phase. The results include growth and dissolution of a single colloidal nucleus, as well as evolution of multiple interacting nuclei. Supported by NASA Grant No. NNX16AQ79G.

Coupling fluid-structure interaction with phase-field fracture

NASA Astrophysics Data System (ADS)

Wick, Thomas

2016-12-01

In this work, a concept for coupling fluid-structure interaction with brittle fracture in elasticity is proposed. The fluid-structure interaction problem is modeled in terms of the arbitrary Lagrangian-Eulerian technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase-field approach is re-formulated in Lagrangian coordinates to combine it with fluid-structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented Lagrangian iteration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the residuals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed.

LINEAR AND NONLINEAR CORRECTIONS IN THE RHIC INTERACTION REGIONS.

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

PILAT,F.; CAMERON,P.; PTITSYN,V.

2002-06-02

A method has been developed to measure operationally the linear and non-linear effects of the interaction region triplets, that gives access to the multipole content through the action kick, by applying closed orbit bumps and analysing tune and orbit shifts. This technique has been extensively tested and used during the RHIC operations in 2001. Measurements were taken at 3 different interaction regions and for different focusing at the interaction point. Non-linear effects up to the dodecapole have been measured as well as the effects of linear, sextupolar and octupolar corrections. An analysis package for the data processing has been developedmore » that through a precise fit of the experimental tune shift data (measured by a phase lock loop technique to better than 10{sup -5} resolution) determines the multipole content of an IR triplet.« less

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

NASA Astrophysics Data System (ADS)

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

2000-01-01

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

Spontaneous collective synchronization in the Kuramoto model with additional non-local interactions

NASA Astrophysics Data System (ADS)

Gupta, Shamik

2017-10-01

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we report on a very rich phase diagram in presence of thermal noise and an additional non-local interaction on a one-dimensional periodic lattice. Remarkably, the phase diagram involves both equilibrium and non-equilibrium phase transitions. In two contrasting limits of the dynamics, we obtain exact analytical results for the phase transitions. These two limits correspond to (i) the absence of thermal noise, when the dynamics reduces to that of a non-linear dynamical system, and (ii) the oscillators having the same natural frequency, when the dynamics becomes that of a statistical system in contact with a heat bath and relaxing to a statistical equilibrium state. In the former case, our exact analysis is based on the use of the so-called Ott-Antonsen ansatz to derive a reduced set of nonlinear partial differential equations for the macroscopic evolution of the system. Our results for the case of statistical equilibrium are on the other hand obtained by extending the well-known transfer matrix approach for nearest-neighbor Ising model to consider non-local interactions. The work offers a case study of exact analysis in many-body interacting systems. The results obtained underline the crucial role of additional non-local interactions in either destroying or enhancing the possibility of observing synchrony in mean-field systems exhibiting spontaneous synchronization.

Optical wave turbulence and the condensation of light

NASA Astrophysics Data System (ADS)

Bortolozzo, Umberto; Laurie, Jason; Nazarenko, Sergey; Residori, Stefania

2009-11-01

In an optical experiment, we report a wave turbulence regime that, starting with weakly nonlinear waves with randomized phases, shows an inverse cascade of photons towards the lowest wavenumbers. We show that the cascade is induced by a six-wave resonant interaction process and is characterized by increasing nonlinearity. At low wavenumbers the nonlinearity becomes strong and leads to modulational instability developing into solitons, whose number is decreasing further along the beam.

Detection and description of non-linear interdependence in normal multichannel human EEG data.

PubMed

Breakspear, M; Terry, J R

2002-05-01

This study examines human scalp electroencephalographic (EEG) data for evidence of non-linear interdependence between posterior channels. The spectral and phase properties of those epochs of EEG exhibiting non-linear interdependence are studied. Scalp EEG data was collected from 40 healthy subjects. A technique for the detection of non-linear interdependence was applied to 2.048 s segments of posterior bipolar electrode data. Amplitude-adjusted phase-randomized surrogate data was used to statistically determine which EEG epochs exhibited non-linear interdependence. Statistically significant evidence of non-linear interactions were evident in 2.9% (eyes open) to 4.8% (eyes closed) of the epochs. In the eyes-open recordings, these epochs exhibited a peak in the spectral and cross-spectral density functions at about 10 Hz. Two types of EEG epochs are evident in the eyes-closed recordings; one type exhibits a peak in the spectral density and cross-spectrum at 8 Hz. The other type has increased spectral and cross-spectral power across faster frequencies. Epochs identified as exhibiting non-linear interdependence display a tendency towards phase interdependencies across and between a broad range of frequencies. Non-linear interdependence is detectable in a small number of multichannel EEG epochs, and makes a contribution to the alpha rhythm. Non-linear interdependence produces spatially distributed activity that exhibits phase synchronization between oscillations present at different frequencies. The possible physiological significance of these findings are discussed with reference to the dynamical properties of neural systems and the role of synchronous activity in the neocortex.

Phase Matching in Presence of Feedback: Higher Order Terms and Enhancement of Nonlinear Interactions

DTIC Science & Technology

2003-12-01

Papers submitted for publication: M. Centini, G. D’Aguanno, L. Sciscione, C. Sibilia, M. Bertolotti, M. Scalora , M. Bloemer: “Phase matching in the...M. Centini, G. D’Aguanno, L. Sciscione, C. Sibilia, M. Bertolotti, M. Scalora , M. Bloemer: “Phase matching in the presence of feedback: High order

X-ray light curves of active galactic nuclei are phase incoherent

NASA Technical Reports Server (NTRS)

Krolik, Julian; Done, Chris; Madejski, Grzegorz

1993-01-01

We compute the Fourier phase spectra for the light curves of five low-luminosity active galactic nuclei observed by EXOSAT. There is no statistically significant phase coherence in any of them. This statement is equivalent, subject to a technical caveat, to a demonstration that their fluctuation statistics are Gaussian. Models in which the X-ray output is controlled wholly by a unitary process undergoing a nonlinear limit cycle are therefore ruled out, while models with either a large number of randomly excited independent oscillation modes or nonlinearly interacting spatially dependent oscillations are favored. We also demonstrate how the degree of phase coherence in light curve fluctuations influences the application of causality bounds on internal length scales.

Phase-Controlled Bistability of a Dark Soliton Train in a Polariton Fluid.

PubMed

Goblot, V; Nguyen, H S; Carusotto, I; Galopin, E; Lemaître, A; Sagnes, I; Amo, A; Bloch, J

2016-11-18

We use a one-dimensional polariton fluid in a semiconductor microcavity to explore the nonlinear dynamics of counterpropagating interacting Bose fluids. The intrinsically driven-dissipative nature of the polariton fluid allows us to use resonant pumping to impose a phase twist across the fluid. When the polariton-polariton interaction energy becomes comparable to the kinetic energy, linear interference fringes transform into a train of solitons. A novel type of bistable behavior controlled by the phase twist across the fluid is experimentally evidenced.

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

Influence of pump-field scattering on nonclassical-light generation in a photonic-band-gap nonlinear planar waveguide

NASA Astrophysics Data System (ADS)

Peřina, Jan, Jr.; Sibilia, Concita; Tricca, Daniela; Bertolotti, Mario

2005-04-01

Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. The properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic-band-gap structure inside the waveguide. A general quantum model of linear operator amplitude corrections to the amplitude mean values and its numerical analysis provide conditions for efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. The destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band-gap structure inside the waveguide. Also an increase of the signal-to-noise ratio of the incident optical field can be reached in the waveguide.

Engineering quadratic nonlinear photonic crystals for frequency conversion of lasers

NASA Astrophysics Data System (ADS)

Chen, Baoqin; Hong, Lihong; Hu, Chenyang; Zhang, Chao; Liu, Rongjuan; Li, Zhiyuan

2018-03-01

Nonlinear frequency conversion offers an effective way to extend the laser wavelength range. Quadratic nonlinear photonic crystals (NPCs) are artificial materials composed of domain-inversion structures whose sign of nonlinear coefficients are modulated with desire to implement quasi-phase matching (QPM) required for nonlinear frequency conversion. These structures can offer various reciprocal lattice vectors (RLVs) to compensate the phase-mismatching during the quadratic nonlinear optical processes, including second-harmonic generation (SHG), sum-frequency generation and the cascaded third-harmonic generation (THG). The modulation pattern of the nonlinear coefficients is flexible, which can be one-dimensional or two-dimensional (2D), be periodic, quasi-periodic, aperiodic, chirped, or super-periodic. As a result, these NPCs offer very flexible QPM scheme to satisfy various nonlinear optics and laser frequency conversion problems via design of the modulation patterns and RLV spectra. In particular, we introduce the electric poling technique for fabricating QPM structures, a simple effective nonlinear coefficient model for efficiently and precisely evaluating the performance of QPM structures, the concept of super-QPM and super-periodically poled lithium niobate for finely tuning nonlinear optical interactions, the design of 2D ellipse QPM NPC structures enabling continuous tunability of SHG in a broad bandwidth by simply changing the transport direction of pump light, and chirped QPM structures that exhibit broadband RLVs and allow for simultaneous radiation of broadband SHG, THG, HHG and thus coherent white laser from a single crystal. All these technical, theoretical, and physical studies on QPM NPCs can help to gain a deeper insight on the mechanisms, approaches, and routes for flexibly controlling the interaction of lasers with various QPM NPCs for high-efficiency frequency conversion and creation of novel lasers.

Phase space trajectories and Lyapunov exponents in the dynamics of an alpha-helical protein lattice with intra- and inter-spine interactions

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

Angelin Jeba, K.; Latha, M. M., E-mail: lathaisaac@yahoo.com; Jain, Sudhir R.

2015-11-15

The nonlinear dynamics of intra- and inter-spine interaction models of alpha-helical proteins is investigated by proposing a Hamiltonian using the first quantized operators. Hamilton's equations of motion are derived, and the dynamics is studied by constructing the trajectories and phase space plots in both cases. The phase space plots display a chaotic behaviour in the dynamics, which opens questions about the relationship between the chaos and exciton-exciton and exciton-phonon interactions. This is verified by plotting the Lyapunov characteristic exponent curves.

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

Sharma, Arvind, E-mail: arvindsharma230771@gmail.com; Nagar, A. K., E-mail: ajaya.nagar@gmail.com

We investigate the interaction of optical vector soliton with a symmetric thin-film gallium-silica waveguide structure using the equivalent particle theory. The relevant nonlinear Schrodinger equation has been solved by the method of phase plane analysis. The analysis shows beam break up into transmitted, reflected and nonlinear surface waves at the interface. The stability properties of the solitons so formed have been discussed.

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.

2000-03-01

We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.

Several localized waves induced by linear interference between a nonlinear plane wave and bright solitons

NASA Astrophysics Data System (ADS)

Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.

Why do large and small scales couple in a turbulent boundary layer?

NASA Astrophysics Data System (ADS)

Bandyopadhyay, Promode R.

2011-11-01

Correlation measurement, which is not definitive, suggests that large and small scales in a turbulent boundary layer (TBL) couple. A TBL is modeled as a jungle of interacting nonlinear oscillators to explore the origin of the coupling. These oscillators have the inherent property of self-sustainability, disturbance rejection, and of self-referential phase reset whereby several oscillators can phase align (or have constant phase difference between them) when an ``external'' impulse is applied. Consequently, these properties of a TBL are accounted for: self-sustainability, return of the wake component after a disturbance is removed, and the formation of the 18o large structures, which are composed of a sequential train of hairpin vortices. The nonlinear ordinary differential equations of the oscillators are solved using an analog circuit for rapid solution. The post-bifurcation limit cycles are determined. A small scale and a large scale are akin to two different oscillators. The state variables from the two disparate interacting oscillators are shown to couple and the small scales appear at certain regions of the phase of the large scale. The coupling is a consequence of the nonlinear oscillatory behavior. Although state planes exist where the disparate scales appear de-superposed, all scales in a TBL are in fact coupled and they cannot be monochromatically isolated.

Linear time-varying models can reveal non-linear interactions of biomolecular regulatory networks using multiple time-series data.

PubMed

Kim, Jongrae; Bates, Declan G; Postlethwaite, Ian; Heslop-Harrison, Pat; Cho, Kwang-Hyun

2008-05-15

Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. The software used in this article is available from http://sbie.kaist.ac.kr/software

Stability and phase transition of localized modes in Bose–Einstein condensates with both two- and three-body interactions

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

Bai, Xiao-Dong; Ai, Qing; Zhang, Mei

We investigate the stability and phase transition of localized modes in Bose–Einstein Condensates (BECs) in an optical lattice with the discrete nonlinear Schrödinger model by considering both two- and three-body interactions. We find that there are three types of localized modes, bright discrete breather (DB), discrete kink (DK), and multi-breather (MUB). Moreover, both two- and three-body on-site repulsive interactions can stabilize DB, while on-site attractive three-body interactions destabilize it. There is a critical value for the three-body interaction with which both DK and MUB become the most stable ones. We give analytically the energy thresholds for the destabilization of localizedmore » states and find that they are unstable (stable) when the total energy of the system is higher (lower) than the thresholds. The stability and dynamics characters of DB and MUB are general for extended lattice systems. Our result is useful for the blocking, filtering, and transfer of the norm in nonlinear lattices for BECs with both two- and three-body interactions.« less

The Effects of Hydrogen Band EMIC Waves on Ring Current H+ Ions

NASA Astrophysics Data System (ADS)

Wang, Zhiqiang; Zhai, Hao; Gao, Zhuxiu

2017-12-01

Hydrogen band electromagnetic ion cyclotron (EMIC) waves have received much attention recently because they are found to frequently span larger spatial areas than the other band EMIC waves. Using test particle simulations, we study the nonlinear effects of hydrogen band EMIC waves on ring current H+ ions. A dimensionless parameter R is used to characterize the competition between wave-induced and adiabatic motions. The results indicate that there are three regimes of wave-particle interactions for typical 35 keV H+ ions at L = 5: diffusive (quasi-linear) behavior when αeq ≤ 35° (R ≥ 2.45), the nonlinear phase trapping when 35° < αeq < 50° (0.75 < R < 2.45), and both the nonlinear phase bunching and phase trapping when αeq ≥ 50° (R ≤ 0.75). The phase trapping can transport H+ ions toward large pitch angle, while the phase bunching has the opposite effect. The phase-trapped H+ ions can be significantly accelerated (from 35 keV to over 500 keV) in about 4 min and thus contribute to the formation of high energy components of ring current ions. The results suggest that the effect of hydrogen band EMIC waves is not ignorable in the nonlinear acceleration and resonance scattering of ring current H+ ions.

Nonlinear magnetoelectric effect and magnetostriction in piezoelectric CsCuCl{sub 3} in paramagnetic and antiferromagnetic states

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

Kharkovskiy, A. I., E-mail: akharkovskiy@inbox.ru; L.F. Vereshchagin Institute for High Pressure Physics RAS, 142190 Troitsk, Moscow; Shaldin, Yu. V.

2016-01-07

The direct nonlinear magnetoelectric (ME) effect and the magnetostriction of piezoelectric CsCuCl{sub 3} single crystals were comprehensively studied over a wide temperature range in stationary magnetic fields of up to 14 T. The direct nonlinear ME effect measurements were also performed in pulsed magnetic fields up to 31 T, at liquid helium temperature in the antiferromagnetic (AF) state for the crystallographic direction in which effect has the maximum value. The nonlinear ME effect was quadratic in the paramagnetic state for the whole range of magnetic fields. In the AF state the phase transition between different configurations of spins manifested itself as plateau-likemore » peculiarity on the nonlinear ME effect. The nonlinear ME effect was saturated by the phase transition to the spin-saturated paramagnetic state. Two contributions to the nonlinear ME effects in CsCuCl{sub 3} were extracted from the experimental data: the intrinsic ME effect originated from the magnetoelectric interactions, and the extrinsic one, which resulted from a magnetostriction-induced piezoelectric effect.« less

Interaction between Liénard and Ikeda dynamics in a nonlinear electro-optical oscillator with delayed bandpass feedback.

PubMed

Marquez, Bicky A; Larger, Laurent; Brunner, Daniel; Chembo, Yanne K; Jacquot, Maxime

2016-12-01

We report on experimental and theoretical analysis of the complex dynamics generated by a nonlinear time-delayed electro-optic bandpass oscillator. We investigate the interaction between the slow- and fast-scale dynamics of autonomous oscillations in the breather regime. We analyze in detail the coupling between the fast-scale behavior associated to a characteristic low-pass Ikeda behavior and the slow-scale dynamics associated to a Liénard limit-cycle. Finally, we show that when projected onto a two-dimensional phase space, the attractors corresponding to periodic and chaotic breathers display a spiral-like pattern, which strongly depends on the shape of the nonlinear function.

Generation and multi-octave shaping of mid-infrared intense single-cycle pulses

NASA Astrophysics Data System (ADS)

Krogen, Peter; Suchowski, Haim; Liang, Houkun; Flemens, Noah; Hong, Kyung-Han; Kärtner, Franz X.; Moses, Jeffrey

2017-03-01

The generation of intense mid-infrared (mid-IR) optical pulses with customizable shape and spectra spanning a multiple-octave range of vibrational frequencies is an elusive technological capability. While some recent approaches to mid-IR supercontinuum generation—such as filamentation, multicolour four-wave-mixing and optical rectification—have successfully generated broad spectra, no process has been identified for achieving complex pulse shaping at the generation step. The adiabatic frequency converter allows for a one-to-one transfer of spectral phase through nonlinear frequency conversion over a larger-than-octave-spanning range and with an overall linear phase transfer function. Here, we show that we can convert shaped near-infrared (near-IR) pulses to shaped, energetic, multi-octave-spanning mid-IR pulses lasting only 1.2 optical cycles, and extendable to the sub-cycle regime. We expect this capability to enable a new class of precisely controlled nonlinear interactions in the mid-IR spectral range, from nonlinear vibrational spectroscopy to strong light-matter interactions and single-shot remote sensing.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence.

PubMed

Duvvuri, Subrahmanyam; McKeon, Beverley

2017-03-13

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Parabolized Stability Equations analysis of nonlinear interactions with forced eigenmodes to control subsonic jet instabilities

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

Itasse, Maxime, E-mail: Maxime.Itasse@onera.fr; Brazier, Jean-Philippe, E-mail: Jean-Philippe.Brazier@onera.fr; Léon, Olivier, E-mail: Olivier.Leon@onera.fr

2015-08-15

Nonlinear evolution of disturbances in an axisymmetric, high subsonic, high Reynolds number hot jet with forced eigenmodes is studied using the Parabolized Stability Equations (PSE) approach to understand how modes interact with one another. Both frequency and azimuthal harmonic interactions are analyzed by setting up one or two modes at higher initial amplitudes and various phases. While single mode excitation leads to harmonic growth and jet noise amplification, controlling the evolution of a specific mode has been made possible by forcing two modes (m{sub 1}, n{sub 1}), (m{sub 2}, n{sub 2}), such that the difference in azimuth and in frequencymore » matches the desired “target” mode (m{sub 1} − m{sub 2}, n{sub 1} − n{sub 2}). A careful setup of the initial amplitudes and phases of the forced modes, defined as the “killer” modes, has allowed the minimizing of the initially dominant instability in the near pressure field, as well as its estimated radiated noise with a 15 dB loss. Although an increase of the overall sound pressure has been found in the range of azimuth and frequency analyzed, the present paper reveals the possibility to make the initially dominant instability ineffective acoustically using nonlinear interactions with forced eigenmodes.« less

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1987-01-01

It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities.

Transmutation of skyrmions to half-solitons driven by the nonlinear optical spin Hall effect.

PubMed

Flayac, H; Solnyshkov, D D; Shelykh, I A; Malpuech, G

2013-01-04

We show that the spin domains, generated in the linear optical spin Hall effect by the analog of spin-orbit interaction for exciton polaritons, are associated with the formation of a Skyrmion lattice. In the nonlinear regime, the spin anisotropy of the polariton-polariton interactions results in a spatial compression of the domains and in a transmutation of the Skyrmions into oblique half-solitons. This phase transition is associated with both the focusing of the spin currents and the emergence of a strongly anisotropic emission pattern.

Continuous theory of active matter systems with metric-free interactions.

PubMed

Peshkov, Anton; Ngo, Sandrine; Bertin, Eric; Chaté, Hugues; Ginelli, Francesco

2012-08-31

We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones-a situation advocated recently to be relevant for bird flocks, fish schools, and crowds-we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that the density-independent collision rate per particle characteristic of topological interactions suppresses the linear instability of the homogeneous ordered phase and the nonlinear density segregation generically present near threshold in metric models, in agreement with microscopic simulations.

Non-linear coherent mode interactions and the control of shear layers

NASA Technical Reports Server (NTRS)

Nikitopoulos, D. E.; Liu, J. T. C.

1990-01-01

A nonlinear integral formulation, based on local linear stability considerations, is used to study the collective interactions between discrete wave-modes associated with large-scale structures and the mean flow in a developing shear layer. Aspects of shear layer control are examined in light of the sensitivity of these interactions to the initial frequency parameter, modal energy contents and modal phases. Manipulation of the large-scale structure is argued to be an effective means of controlling the flow, including the small-scale turbulence dominated region far downstream. Cases of fundamental, 1st and 2nd subharmonic forcing are discussed in conjunction with relevant experiments.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

NASA Astrophysics Data System (ADS)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

Investigating the interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance

NASA Technical Reports Server (NTRS)

Van Dongen, Hans P A.; Dinges, David F.

2003-01-01

The two-process model of sleep regulation has been applied successfully to describe, predict, and understand sleep-wake regulation in a variety of experimental protocols such as sleep deprivation and forced desynchrony. A non-linear interaction between the homeostatic and circadian processes was reported when the model was applied to describe alertness and performance data obtained during forced desynchrony. This non-linear interaction could also be due to intrinsic non-linearity in the metrics used to measure alertness and performance, however. Distinguishing these possibilities would be of theoretical interest, but could also have important implications for the design and interpretation of experiments placing sleep at different circadian phases or varying the duration of sleep and/or wakefulness. Although to date no resolution to this controversy has been found, here we show that the issue can be addressed with existing data sets. The interaction between the homeostatic and circadian processes of sleep-wake regulation was investigated using neurobehavioural performance data from a laboratory experiment involving total sleep deprivation. The results provided evidence of an actual non-linear interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance.

Nonlinear nature of composite structure induced by the interaction of nonplanar solitons in a nonextensive plasma

NASA Astrophysics Data System (ADS)

Han, Jiu-Ning; Luo, Jun-Hua; Liu, Zhen-Lai; Shi, Jun; Xiang, Gen-Xiang; Li, Jun-Xiu

2015-06-01

The nonlinear properties of composite structure induced by the head-on collision of electron-acoustic solitons in a general plasma composed of cold fluid electrons, hot nonextensive distributed electron, and stationary ions are studied. We have made a detailed investigation on the time-evolution process of this merged wave structure. It is found that the structure survives during some time interval, and there are obviously different for the properties of the composite structures which are induced in cylindrical and spherical geometries. Moreover, it is shown that there are both positive and negative phase shifts for each colliding soliton after the interaction. For fixed plasma parameters, the soliton received the largest phase shift in spherical geometry, followed by the cylindrical and one-dimensional planar geometries.

NOLM-based all-optical 40 Gbit/s format conversion through sum-frequency generation (SFG) in a PPLN waveguide

NASA Astrophysics Data System (ADS)

Wang, Jian; Sun, Junqiang

2005-11-01

A novel all-optical format conversion scheme from NRZ to RZ based on sum-frequency generation (SFG) in a periodically poled LiNbO 3 (PPLN) waveguide is proposed, using a nonlinear optical loop mirror (NOLM). The conversion mechanism relies on the combination of attenuation and nonlinear phase shift induced on the clockwise signal field during the SFG process. The SFG between pump, and co- and counter- propagating signals in the PPLN waveguide are numerically studied, showing that counter-propagating SFG can be ignored when quasi-phase matching (QPM) for SFG during co-propagating interaction. The nonlinear phase shift induced on the clockwise signal field is analyzed in detail, showing that it is more effective to yield large values for nonlinear phase shift when appropriately phase mismatched for the SFG process. Two tuning schemes are proposed depend on whether the sum-frequency wavelength is variable or fixed. It is found that the latter has a rather wide 3dB signal conversion bandwidth approximately 154nm. Finally, the influence of reversible process of SFG is discussed and the optimum arrangement of pump and signal peak powers is theoretically demonstrated. The result shows that proper power arrangement, pump width, and waveguide length are necessary for achieving a good conversion effect.

Modeling of Nonlinear Optical Response in Gaseous Media and Its Comparison with Experiment

NASA Astrophysics Data System (ADS)

Xia, Yi

This thesis demonstrates the model and application of nonlinear optical response with Metastable Electronic State Approach (MESA) in ultrashort laser propagation and verifies accuracy of MESA through extensive comparison with experimental data. The MESA is developed from quantum mechanics to describe the nonlinear off-resonant optical response together with strong-field ionization in gaseous medium. The conventional light-matter interaction models are based on a piece-wise approach where Kerr effect and multi-photon ionization are treated as independent nonlinear responses. In contrast, MESA is self-consistent as the response from freed electrons and bound electrons are microscopically linked. It also can be easily coupled to the Unidirectional Pulse Propagation Equations (UPPE) for large scale simulation of experiments. This work tests the implementation of MESA model in simulation of nonlinear phase transients of ultrashort pulse propagation in a gaseous medium. The phase transient has been measured through Single-Shot Supercontinuum Spectral Interferometry. This technique can achieve high temporal resolution (10 fs) and spatial resolution (5 mum). Our comparison between simulation and experiment gives a quantitive test of MESA model including post-adiabatic corrections. This is the first time such a comparison was achieved for a theory suitable for large scale numerical simulation of modern nonlinear-optics experiments. In more than one respect, ours is a first-of-a-kind achievement. In particular, • Large amount of data are compared. We compare the data of nonlinear response induced by different pump intensity in Ar and Nitrogen. The data sets are three dimensions including two transverse spacial dimensions and one axial temporal dimension which reflect the whole structure of nonlinear response including the interplay between Kerr and plasma-induced effects. The resolutions of spatial and temporal dimension are about a few micrometer and several femtosecond. • The regime of light-matter interaction investigated here is between the strong and perturbative, where the pulse intensity can induce nonlinear refractive index change and partial ionization of dielectric medium. Obviously, such regimes are difficult to study both experimentally and theoretically. • MESA is a quantum based model, but it retains the same computation complexity as conventional light-matter interaction model. MESA contains the response from both bound and continuum states in a single self-consistent "Package". So, it is fair to say that this experiment-theory comparison sets a new standard for nonlinear light-matter interaction models and their verification in the area of extreme nonlinear optics.

Numerical assessment of factors affecting nonlinear internal waves in the South China Sea

NASA Astrophysics Data System (ADS)

Li, Qiang

2014-02-01

Nonlinear internal waves in the South China Sea exhibit diverse characteristics, which are associated with the complex conditions in Luzon Strait, such as the double ridge topography, the Earth’s rotation, variations in stratification and the background current induced by the Kuroshio. These effects are individually assessed using the MITgcm. The performance of the model is first validated through comparison with field observations. Because of in-phased ray interaction, the western ridge in Luzon Strait intensifies the semidiurnal internal tides generated from the eastern ridge, thus reinforcing the formation of nonlinear internal waves. However, the ray interaction for K1 forcing becomes anti-phased so that the K1 internal tide generation is reduced by the western ridge. Not only does the rotational dispersion suppress internal tide generation, it also inhibits nonlinear steepening and consequent internal solitary wave formation. As a joint effect, the double ridges and the rotational dispersion result in a paradoxical phenomenon: diurnal barotropic tidal forcing is dominant in Luzon Strait, but semidiurnal internal tides prevail in the deep basin of the South China Sea. The seasonal variation of the Kuroshio is consistent with the seasonal appearance of nonlinear internal waves in the South China Sea. The model results show that the westward inflow due to the Kuroshio intrusion reduces the amplitude of internal tides in the South China Sea, causing the weakening or absence of internal solitary waves. Winter stratification cannot account for the significant reduction of nonlinear internal waves, because the amplitude growth of internal tides due to increased thermocline tilting counteracts the reduced nonlinearity caused by thermocline deepening.

Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Jia, Hui-Xian; Shan, Dong-Ming

2017-10-01

In this article, a fifth-order nonlinear Schrödinger equation, which can be used to characterise the solitons in the optical fibre and inhomogeneous Heisenberg ferromagnetic spin system, has been investigated. Akhmediev breather, Kuzentsov soliton, and generalised soliton have all been attained via the Darbox transformation. Propagation and interaction for three-type breathers have been studied: the types of breather are determined by the module and complex angle of parameter ξ; interaction between Akhmediev breather and generalised soliton displays a phase shift, whereas the others do not. Modulation instability of the generalised solitons have been analysed: a small perturbation can develop into a rogue wave, which is consistent with the results of rogue wave solutions.

Safety effects of exclusive and concurrent signal phasing for pedestrian crossing.

PubMed

Zhang, Yaohua; Mamun, Sha A; Ivan, John N; Ravishanker, Nalini; Haque, Khademul

2015-10-01

This paper describes the estimation of pedestrian crash count and vehicle interaction severity prediction models for a sample of signalized intersections in Connecticut with either concurrent or exclusive pedestrian phasing. With concurrent phasing, pedestrians cross at the same time as motor vehicle traffic in the same direction receives a green phase, while with exclusive phasing, pedestrians cross during their own phase when all motor vehicle traffic on all approaches is stopped. Pedestrians crossing at each intersection were observed and classified according to the severity of interactions with motor vehicles. Observation intersections were selected to represent both types of signal phasing while controlling for other physical characteristics. In the nonlinear mixed models for interaction severity, pedestrians crossing on the walk signal at an exclusive signal experienced lower interaction severity compared to those crossing on the green light with concurrent phasing; however, pedestrians crossing on a green light where an exclusive phase was available experienced higher interaction severity. Intersections with concurrent phasing have fewer total pedestrian crashes than those with exclusive phasing but more crashes at higher severity levels. It is recommended that exclusive pedestrian phasing only be used at locations where pedestrians are more likely to comply. Copyright © 2015. Published by Elsevier Ltd.

Transition Theory and Experimental Comparisons on (I) Amplification into Streets and (II) a Strongly Nonlinear Break-up Criterion

NASA Astrophysics Data System (ADS)

Smith, F. T.; Bowles, R. I.

1992-10-01

The two stages I, II are studied by using recent nonlinear theory and then compared with the experiments of Nishioka et al. (1979) on the transition of plane Poiseuille flow. The first stage I starts at low amplitude from warped input, which is deformed through weakly nonlinear interaction into a blow-up in amplitude and phase accompanied by spanwise focusing into streets. This leads into the strongly nonlinear stage II. It holds for a broad range of interactive boundary layers and related flows, to all of which the nonlinear break-up criterion applies. The experimental comparisons on I, II for channel flow overall show encouraging quantitative agreement, supporting recent comparisons (in the boundary-layer setting) of the description of stage I in Stewart & Smith (1992) with the experiments of Klebanoff & Tidstrom (1959) and of the break-up criterion of Smith (1988a) with the computations of Peridier et al. (1991 a, b).

Hollow Gaussian beam generation through nonlinear interaction of photons with orbital angular momentum

PubMed Central

Chaitanya, N. Apurv; Jabir, M. V.; Banerji, J.; Samanta, G. K.

2016-01-01

Hollow Gaussian beams (HGB) are a special class of doughnut shaped beams that do not carry orbital angular momentum (OAM). Such beams have a wide range of applications in many fields including atomic optics, bio-photonics, atmospheric science, and plasma physics. Till date, these beams have been generated using linear optical elements. Here, we show a new way of generating HGBs by three-wave mixing in a nonlinear crystal. Based on nonlinear interaction of photons having OAM and conservation of OAM in nonlinear processes, we experimentally generated ultrafast HGBs of order as high as 6 and power >180 mW at 355 nm. This generic concept can be extended to any wavelength, timescales (continuous-wave and ultrafast) and any orders. We show that the removal of azimuthal phase of vortices does not produce Gaussian beam. We also propose a new and only method to characterize the order of the HGBs. PMID:27581625

Linear and weakly nonlinear aspects of free shear layer instability, roll-up, subharmonic interaction and wall influence

NASA Technical Reports Server (NTRS)

Cain, A. B.; Thompson, M. W.

1986-01-01

The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.

Localized states and their stability in an anharmonic medium with a nonlinear defect

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

Gerasimchuk, I. V., E-mail: igor.gera@gmail.com

2015-10-15

A comprehensive analysis of soliton states localized near a plane defect (a defect layer) possessing nonlinear properties is carried out within a quasiclassical approach for different signs of nonlinearity of the medium and different characters of interaction of elementary excitations of the medium with the defect. A quantum interpretation is given to these nonlinear localized modes as a bound state of a large number of elementary excitations. The domains of existence of such states are determined, and their properties are analyzed as a function of the character of interaction of elementary excitations between each other and with the defect. Amore » full analysis of the stability of all the localized states with respect to small perturbations of amplitude and phase is carried out analytically, and the frequency of small oscillations of the state localized on the defect is determined.« less

Complex behavior in chains of nonlinear oscillators.

PubMed

Alonso, Leandro M

2017-06-01

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

The Parkinsonian Subthalamic Network: Measures of Power, Linear, and Non-linear Synchronization and their Relationship to L-DOPA Treatment and OFF State Motor Severity.

PubMed

West, Timothy; Farmer, Simon; Berthouze, Luc; Jha, Ashwani; Beudel, Martijn; Foltynie, Thomas; Limousin, Patricia; Zrinzo, Ludvic; Brown, Peter; Litvak, Vladimir

2016-01-01

In this paper we investigated the dopaminergic modulation of neuronal interactions occurring in the subthalamic nucleus (STN) during Parkinson's disease (PD). We utilized linear measures of local and long range synchrony such as power and coherence, as well as Detrended Fluctuation Analysis for Phase Synchrony (DFA-PS)- a recently developed non-linear method that computes the extent of long tailed autocorrelations present in the phase interactions between two coupled signals. Through analysis of local field potentials (LFPs) taken from the STN we seek to determine changes in the neurodynamics that may underpin the pathophysiology of PD in a group of 12 patients who had undergone surgery for deep brain stimulation. We demonstrate up modulation of alpha-theta (5-12 Hz) band power in response to L-DOPA treatment, whilst low beta band power (15-20 Hz) band-power is suppressed. We also find evidence for significant local connectivity within the region surrounding STN although there was evidence for its modulation via administration of L-DOPA. Further to this we present evidence for a positive correlation between the phase ordering of bilateral STN interactions and the severity of bradykinetic and rigidity symptoms in PD. Although, the ability of non-linear measures to predict clinical state did not exceed standard measures such as beta power, these measures may help identify the connections which play a role in pathological dynamics.

Optical polarization based logic functions (XOR or XNOR) with nonlinear Gallium nitride nanoslab.

PubMed

Bovino, F A; Larciprete, M C; Giardina, M; Belardini, A; Centini, M; Sibilia, C; Bertolotti, M; Passaseo, A; Tasco, V

2009-10-26

We present a scheme of XOR/XNOR logic gate, based on non phase-matched noncollinear second harmonic generation from a medium of suitable crystalline symmetry, Gallium nitride. The polarization of the noncollinear generated beam is a function of the polarization of both pump beams, thus we experimentally investigated all possible polarization combinations, evidencing that only some of them are allowed and that the nonlinear interaction of optical signals behaves as a polarization based XOR. The experimental results show the peculiarity of the nonlinear optical response associated with noncollinear excitation, and are explained using the expression for the effective second order optical nonlinearity in noncollinear scheme.

Phase space information in a non-linear quantum system containing a Kerr-like medium through Su(1, 1)-algebraic treatment

NASA Astrophysics Data System (ADS)

Mohamed, Abdel-Baset A.

2018-05-01

Analytical description for a Su(2)-quantum system interacting with a damped Su(1, 1)-cavity, which is filled with a non-linear Kerr medium, is presented. The dynamics of non-classicality of Su(1, 1)-state is investigated via the negative part of the Wigner function. We show that the negative part depends on the unitary interaction and the Kerr-like medium and it can be disappeared by increasing the dissipation rate and the detuning parameter. The phase space information of the Husimi function and its Wehrl density is very sensitive not only to the coupling to the environment and the unitary interaction but also to the detuning as well as to the Kerr-like medium. The phase space information may be completely erased by increasing the coupling to the environment. The coherence loss of the Su(2)-state is investigated via the Husimi Wehrl entropy. If the effects of the detuning parameter or/and of the Kerr-like medium are combined with the damping effect, the damping effect of the coupling to the environment may be weaken, and the Wehrl entropy is delayed to reach its steady-state value. At the steady-state value, the phase space information and the coherence are quickly lost.

Solitonic and chaotic behaviors of a (3+1)-dimensional nonlinear Schrödinger equation in a magnetized electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Zhen, Hui-Ling; Tian, Bo; Xie, Xi-Yang; Chai, Jun

2015-05-01

In a magnetized e-p-i plasma with two-electron temperatures, the (3+1)-dimensional nonlinear Schrödinger equation for the ion-acoustic envelope solitons is hereby investigated. Bright and dark soliton solutions are both obtained. It is found that the soliton amplitude is inversely related to P, Q and R, with P, Q and R respectively as the coefficients of the dispersive term, nonlinear term and combined effect of the transverse perturbation and magnetic field. Head-on interactions are displayed, and with Q and R decreasing, can be transferred into the overtaking ones. Bright bound-state solitons are obtained, and the interaction period decreases with Q increasing. Both the head-on and overtaking interactions between the two dark solitons are displayed, and such a head-on interaction can be transformed into the overtaking one with R increasing. Upon the introduction of the external perturbation, the developed and weak chaos are observed. Phase projections and power spectra are presented. Difference between the two chaotic motions roots in the inequality between the nonlinear and perturbed terms. Developed chaos can be weakened with Q decreasing, or with the frequency of external perturbation increasing.

The cardiorespiratory interaction: a nonlinear stochastic model and its synchronization properties

NASA Astrophysics Data System (ADS)

Bahraminasab, A.; Kenwright, D.; Stefanovska, A.; McClintock, P. V. E.

2007-06-01

We address the problem of interactions between the phase of cardiac and respiration oscillatory components. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows us to derive nonlinear stochastic equations for the reconstruction of the cardiorespiratory signals. The properties of these equations provide interesting new insights into the strength and direction of coupling which enable us to divide the couplings to two parts: deterministic and stochastic. It is shown that the synchronization behaviors of the reconstructed signals are statistically identical with original one.

An iterative fullwave simulation approach to multiple scattering in media with randomly distributed microbubbles

NASA Astrophysics Data System (ADS)

Joshi, Aditya; Lindsey, Brooks D.; Dayton, Paul A.; Pinton, Gianmarco; Muller, Marie

2017-05-01

Ultrasound contrast agents (UCA), such as microbubbles, enhance the scattering properties of blood, which is otherwise hypoechoic. The multiple scattering interactions of the acoustic field with UCA are poorly understood due to the complexity of the multiple scattering theories and the nonlinear microbubble response. The majority of bubble models describe the behavior of UCA as single, isolated microbubbles suspended in infinite medium. Multiple scattering models such as the independent scattering approximation can approximate phase velocity and attenuation for low scatterer volume fractions. However, all current models and simulation approaches only describe multiple scattering and nonlinear bubble dynamics separately. Here we present an approach that combines two existing models: (1) a full-wave model that describes nonlinear propagation and scattering interactions in a heterogeneous attenuating medium and (2) a Paul-Sarkar model that describes the nonlinear interactions between an acoustic field and microbubbles. These two models were solved numerically and combined with an iterative approach. The convergence of this combined model was explored in silico for 0.5 × 106 microbubbles ml-1, 1% and 2% bubble concentration by volume. The backscattering predicted by our modeling approach was verified experimentally with water tank measurements performed with a 128-element linear array transducer. An excellent agreement in terms of the fundamental and harmonic acoustic fields is shown. Additionally, our model correctly predicts the phase velocity and attenuation measured using through transmission and predicted by the independent scattering approximation.

Resonant Triad in Boundary-Layer Stability. Part 2; Composite Solution and Comparison with Observations

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Nonlinear dynamics, chaos and complex cardiac arrhythmias

NASA Technical Reports Server (NTRS)

Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.

1987-01-01

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

All-optical simultaneous multichannel quadrature phase shift keying signal regeneration based on phase-sensitive amplification

NASA Astrophysics Data System (ADS)

Wang, Hongxiang; Wang, Qi; Bai, Lin; Ji, Yuefeng

2018-01-01

A scheme is proposed to realize the all-optical phase regeneration of four-channel quadrature phase shift keying (QPSK) signal based on phase-sensitive amplification. By utilizing conjugate pump and common pump in a highly nonlinear optical fiber, degenerate four-wave mixing process is observed, and QPSK signals are regenerated. The number of waves is reduced to decrease the cross talk caused by undesired nonlinear interaction during the coherent superposition process. In addition, to avoid the effect of overlapping frequency, frequency spans between pumps and signals are set to be nonintegral multiples. Optical signal-to-noise ratio improvement is validated by bit error rate measurements. Compared with single-channel regeneration, multichannel regeneration brings 0.4-dB OSNR penalty when the value of BER is 10-3, which shows the cross talk in regeneration process is negligible.

Postquench prethermalization in a disordered quantum fluid of light

NASA Astrophysics Data System (ADS)

Larré, Pierre-Élie; Delande, Dominique; Cherroret, Nicolas

2018-04-01

We study the coherence of a disordered and interacting quantum light field after propagation along a nonlinear optical fiber. Disorder is generated by a cross-phase modulation with a randomized auxiliary classical light field, while interactions are induced by self-phase modulation. When penetrating the fiber from free space, the incoming quantum light undergoes a disorder and interaction quench. By calculating the coherence function of the transmitted quantum light, we show that the decoherence induced by the quench spreads in a light-cone fashion in the nonequilibrium many-body quantum system, leaving the latter prethermalize with peculiar features originating from disorder.

Influence of the four-photon parametric processes and cross-phase modulation on the relative motion of optical filaments

NASA Astrophysics Data System (ADS)

Kovachev, L. M.; Georgieva, D. A.; Dakova, A. M.

2015-10-01

We investigate two types of nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing {{P}\\text{cr}} . In the first case we study energy exchange between filaments. The model describes this process through a degenerate four-photon parametric mixing (FPPM) scheme and requests initial phase difference between the waves. When there is no initial phase difference between the pulses, the FPPM process does not work. In this case the second type of interaction is obtained as merging between two, three or four filaments in a single filament with higher power. It is found that in the second case the interflow between the filaments has the potential for interaction due to cross-phase modulation (CPM).

Stability, diffusion and interactions of nonlinear excitations in a many body system

NASA Astrophysics Data System (ADS)

Coste, Christophe; Jean, Michel Saint; Dessup, Tommy

2017-04-01

When repelling particles are confined in a quasi-one-dimensional trap by a transverse potential, a configurational phase transition happens. All particles are aligned along the trap axis at large confinement, but below a critical transverse confinement they adopt a staggered row configuration (zigzag phase). This zigzag transition is a subcritical pitchfork bifurcation in extended systems and in systems with cyclic boundary conditions in the longitudinal direction. Among many evidences, phase coexistence is exhibited by localized nonlinear patterns made of a zigzag phase embedded in otherwise aligned particles. We give the normal form at the bifurcation and we show that these patterns can be described as solitary wave envelopes that we call bubbles. They are stable in a large temperature range and can diffuse as quasi-particles, with a diffusion coefficient that may be deduced from the normal form. The potential energy of a bubble is found to be lower than that of the homogeneous bifurcated phase, which explains their stability. We observe also metastable states, that are pairs of solitary wave envelopes which spontaneously evolve toward a stable single bubble. We evidence a strong effect of the discreteness of the underlying particles system and introduce the concept of topological frustration of a bubble pair. A configuration is frustrated when the particles between the two bubbles are not organized in a modulated staggered row. For a nonfrustrated (NF) bubble pair configuration, the bubbles interaction is attractive so that the bubbles come closer and eventually merge as a single bubble. In contrast, the bubbles interaction is found to be repulsive for a frustrated (F) configuration. We describe a model of interacting solitary wave that provides all qualitative characteristics of the interaction force: it is attractive for NF-systems, repulsive for F-systems, and decreases exponentially with the bubbles distance.

Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching media.

PubMed

Phillips, C R; Mayer, B W; Gallmann, L; Keller, U

2016-07-11

Advances in the amplification and manipulation of ultrashort laser pulses have led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine these separate functionalities (pulse amplification, frequency transfer, and pulse shaping) into a single monolithic device that is bandwidth- and power-scalable. The approach is based on two-dimensional (2D) patterning of quasi-phase-matching (QPM) gratings combined with optical parametric interactions involving spatially dispersed laser pulses. Our proof of principle experiment demonstrates this technique via mid-infrared optical parametric chirped pulse amplification of few-cycle pulses. Additionally, we present a detailed theoretical and numerical analysis of such 2D-QPM devices and how they can be designed.

Rate and timing cues associated with the cochlear amplifier: level discrimination based on monaural cross-frequency coincidence detection.

PubMed

Heinz, M G; Colburn, H S; Carney, L H

2001-10-01

The perceptual significance of the cochlear amplifier was evaluated by predicting level-discrimination performance based on stochastic auditory-nerve (AN) activity. Performance was calculated for three models of processing: the optimal all-information processor (based on discharge times), the optimal rate-place processor (based on discharge counts), and a monaural coincidence-based processor that uses a non-optimal combination of rate and temporal information. An analytical AN model included compressive magnitude and level-dependent-phase responses associated with the cochlear amplifier, and high-, medium-, and low-spontaneous-rate (SR) fibers with characteristic frequencies (CFs) spanning the AN population. The relative contributions of nonlinear magnitude and nonlinear phase responses to level encoding were compared by using four versions of the model, which included and excluded the nonlinear gain and phase responses in all possible combinations. Nonlinear basilar-membrane (BM) phase responses are robustly encoded in near-CF AN fibers at low frequencies. Strongly compressive BM responses at high frequencies near CF interact with the high thresholds of low-SR AN fibers to produce large dynamic ranges. Coincidence performance based on a narrow range of AN CFs was robust across a wide dynamic range at both low and high frequencies, and matched human performance levels. Coincidence performance based on all CFs demonstrated the "near-miss" to Weber's law at low frequencies and the high-frequency "mid-level bump." Monaural coincidence detection is a physiologically realistic mechanism that is extremely general in that it can utilize AN information (average-rate, synchrony, and nonlinear-phase cues) from all SR groups.

Vertical melting of a stack of membranes

NASA Astrophysics Data System (ADS)

Borelli, M. E. S.; Kleinert, H.; Schakel, A. M. J.

2001-02-01

A stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is studied. At low temperatures, the system forms a lamellar phase. At a critical temperature, the stack disorders vertically in a melting-like transition.

Nonlinear simulation of the fishbone instability

NASA Astrophysics Data System (ADS)

Idouakass, Malik; Faganello, Matteo; Berk, Herbert; Garbet, Xavier; Benkadda, Sadruddin; PIIM Team; IFS Team; IRFM Team

2014-10-01

We propose to extend the Odblom-Breizman precessional fishbone model to account for both the MagnetoHydroDynamic (MHD) nonlinearity at the q = 1 surface and the nonlinear response of the energetic particles contained within the q = 1 surface. This electromagnetic mode, whose excitation, damping and frequency chirping are determined by the self-consistent interaction between an energetic trapped particle population and the bulk plasma evolution, can induce effective transport and losses for the energetic particles, being them alpha-particles in next-future fusion devices or heated particles in present Tokamaks. The model is reduced to its simplest form, assuming a reduced MHD description for the bulk plasma and a two-dimensional phase-space evolution (gyro and bounce averaged) for deeply trapped energetic particles. Numerical simulations have been performed in order to characterize the mode chirping and saturation, in particular looking at the interplay between the development of phase-space structures and the system dissipation associated to the MHD non-linearities at the resonance locations.

Control of terahertz nonlinear transmission with electrically gated graphene metadevices.

PubMed

Choi, Hyun Joo; Baek, In Hyung; Kang, Bong Joo; Kim, Hyeon-Don; Oh, Sang Soon; Hamm, Joachim M; Pusch, Andreas; Park, Jagang; Lee, Kanghee; Son, Jaehyeon; Jeong, Young U K; Hess, Ortwin; Rotermund, Fabian; Min, Bumki

2017-02-20

Graphene, which is a two-dimensional crystal of carbon atoms arranged in a hexagonal lattice, has attracted a great amount of attention due to its outstanding mechanical, thermal and electronic properties. Moreover, graphene shows an exceptionally strong tunable light-matter interaction that depends on the Fermi level - a function of chemical doping and external gate voltage - and the electromagnetic resonance provided by intentionally engineered structures. In the optical regime, the nonlinearities of graphene originated from the Pauli blocking have already been exploited for mode-locking device applications in ultrafast laser technology, whereas nonlinearities in the terahertz regime, which arise from a reduction in conductivity due to carrier heating, have only recently been confirmed experimentally. Here, we investigated two key factors for controlling nonlinear interactions of graphene with an intense terahertz field. The induced transparencies of graphene can be controlled effectively by engineering meta-atoms and/or changing the number of charge carriers through electrical gating. Additionally, nonlinear phase changes of the transmitted terahertz field can be observed by introducing the resonances of the meta-atoms.

Spatially Nonlinear Interdependence of Alpha-Oscillatory Neural Networks under Chan Meditation

PubMed Central

Chang, Chih-Hao

2013-01-01

This paper reports the results of our investigation of the effects of Chan meditation on brain electrophysiological behaviors from the viewpoint of spatially nonlinear interdependence among regional neural networks. Particular emphasis is laid on the alpha-dominated EEG (electroencephalograph). Continuous-time wavelet transform was adopted to detect the epochs containing substantial alpha activities. Nonlinear interdependence quantified by similarity index S(X∣Y), the influence of source signal Y on sink signal X, was applied to the nonlinear dynamical model in phase space reconstructed from multichannel EEG. Experimental group involved ten experienced Chan-Meditation practitioners, while control group included ten healthy subjects within the same age range, yet, without any meditation experience. Nonlinear interdependence among various cortical regions was explored for five local neural-network regions, frontal, posterior, right-temporal, left-temporal, and central regions. In the experimental group, the inter-regional interaction was evaluated for the brain dynamics under three different stages, at rest (stage R, pre-meditation background recording), in Chan meditation (stage M), and the unique Chakra-focusing practice (stage C). Experimental group exhibits stronger interactions among various local neural networks at stages M and C compared with those at stage R. The intergroup comparison demonstrates that Chan-meditation brain possesses better cortical inter-regional interactions than the resting brain of control group. PMID:24489583

Non-linear glasses and metaglasses for photonics, a review: Part II. Kerr nonlinearity and metaglasses of positive and negative refraction

NASA Astrophysics Data System (ADS)

Romaniuk, Ryszard S.

2008-01-01

This is the second part of a paper on nonlinear properties of optical glasses and metaglasses. A subject of the paper is a review of the basic properties of several families of high optical quality glasses for photonics. The emphasis is put on nonlinear properties of these glasses, including nonlinearities of higher order. Nonlinear effects were debated and systematized. Interactions between optical wave of high power density with glass were described. All parameters of the glass increasing the optical nonlinearities were categorized. Optical nonlinearities in glasses were grouped into the following categories: time and frequency domain, amplitude and phase, resonant and non-resonant, elastic and inelastic, lossy and lossless, reversible and irreversible, instant and slow, adiabatic and non-adiabatic, with virtual versus real excitation of glass, destroying and non-destroying, etc. Nonlinear effects in glasses are based on the following effects: optical, thermal, mechanical and/or acoustic, electrical, magnetic, density and refraction modulation, chemical, etc.

Some optical properties of KTP, LiIO3, and LiNbO3

NASA Technical Reports Server (NTRS)

Gettemy, Donald J.; Harker, William C.; Lindholm, Glenn; Barnes, Norman P.

1988-01-01

Measurements of the absorption coefficient for KTP, LiIO3, and LiNbO3 are discussed. The variation of the refractive index with temperature has been measured for KTP and LiIO3. It is necessary to know both the absorption coefficient beta and the variation in the indexes of refraction with temperature change dn/dT to determine the average power limit of a nonlinear interaction. With the dn/dT information, it is also possible to estimate the temperature half width of any nonlinear interaction by calculating the variation of the phase-matching condition with temperature.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Film thickness measurement based on nonlinear phase analysis using a Linnik microscopic white-light spectral interferometer.

PubMed

Guo, Tong; Chen, Zhuo; Li, Minghui; Wu, Juhong; Fu, Xing; Hu, Xiaotang

2018-04-20

Based on white-light spectral interferometry and the Linnik microscopic interference configuration, the nonlinear phase components of the spectral interferometric signal were analyzed for film thickness measurement. The spectral interferometric signal was obtained using a Linnik microscopic white-light spectral interferometer, which includes the nonlinear phase components associated with the effective thickness, the nonlinear phase error caused by the double-objective lens, and the nonlinear phase of the thin film itself. To determine the influence of the effective thickness, a wavelength-correction method was proposed that converts the effective thickness into a constant value; the nonlinear phase caused by the effective thickness can then be determined and subtracted from the total nonlinear phase. A method for the extraction of the nonlinear phase error caused by the double-objective lens was also proposed. Accurate thickness measurement of a thin film can be achieved by fitting the nonlinear phase of the thin film after removal of the nonlinear phase caused by the effective thickness and by the nonlinear phase error caused by the double-objective lens. The experimental results demonstrated that both the wavelength-correction method and the extraction method for the nonlinear phase error caused by the double-objective lens improve the accuracy of film thickness measurements.

Hydrodynamic optical soliton tunneling

NASA Astrophysics Data System (ADS)

Sprenger, P.; Hoefer, M. A.; El, G. A.

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

Hydrodynamic optical soliton tunneling.

PubMed

Sprenger, P; Hoefer, M A; El, G A

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.

The generation of a zonal-wind oscillation by nonlinear interactions of internal gravity waves

NASA Astrophysics Data System (ADS)

Campbell, Lucy

2003-11-01

Nonlinear interactions of internal gravity waves give rise to numerous large-scale phenomena that are observed in the atmosphere, for example the quasi-biennial oscillation (QBO). This is an oscillation in zonal wind direction which is observed in the equatorial stratosphere; it is characterized by alternating regimes of easterly and westerly shear that descend with time. In the past few decades, a number of theories have been developed to explain the mechanism by which the QBO is generated. These theories are all based on ``quasi-linear'' representations of wave-mean-flow interactions. In this presentation, a fully nonlinear numerical simulation of the QBO is described. A spectrum of gravity waves over a range of phase speeds is forced at the lower boundary of the computational domain and propagates upwards in a density-stratified shear flow. As a result of the absorption and reflection of the waves at their critical levels, regions of large shear develop in the background flow and propagate downwards with time.

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

NASA Astrophysics Data System (ADS)

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

2013-01-01

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

A nonlinear analysis of the terahertz serpentine waveguide traveling-wave amplifier

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

Li, Ke, E-mail: like.3714@163.com; Cao, Miaomiao, E-mail: mona486@yeah.net; Institute of Electronics, University of Chinese Academy of Sciences, Beijing 100190

A nonlinear model for the numerical simulation of terahertz serpentine waveguide traveling-wave tube (SW-TWT) is described. In this model, the electromagnetic wave transmission in the SW is represented as an infinite set of space harmonics to interact with an electron beam. Analytical expressions for axial electric fields in axisymmetric interaction gaps of SW-TWTs are derived and compared with the results from CST simulation. The continuous beam is treated as discrete macro-particles with different initial phases. The beam-tunnel field equations, space-charge field equations, and motion equations are combined to solve the beam-wave interaction. The influence of backward wave and relativistic effectmore » is also considered in the series of equations. The nonlinear model is used to design a 340 GHz SW-TWT. Several favorable comparisons of model predictions with results from a 3-D Particle-in-cell simulation code CHIPIC are presented, in which the output power versus beam voltage and interaction periods are illustrated. The relative error of the predicted output power is less than 15% in the 3 dB bandwidth and the relative error of the saturated length is less than 8%.The results show that the 1-D nonlinear analysis model is appropriate to solve the terahertz SW-TWT operation characteristics.« less

Giant asymmetric self-phase modulation in superconductor thin films

NASA Astrophysics Data System (ADS)

Robson, Charles W.; Biancalana, Fabio

2018-04-01

Self-phase modulation (SPM) of light pulses is found to occur strongly, at low incident intensities, in the coupling of light with superconductors. We develop a theory from a synthesis of the time-dependent Ginzburg-Landau (TDGL) equation and basic electrodynamics which shows the strongly non-linear phase accumulated in the interaction. Unusually, the SPM of the pulse in this system is found to be highly asymmetric, producing a strongly redshifted spectrum when interacting with a superconducting thin film, and it develops in just a few nanometers of propagation. In this paper we present theoretical results and simulations in the THz regime, for both hyperbolic secant and supergaussian-shaped pulses.

Cyclotron Acceleration of Relativistic Electrons through Landau Resonance with Obliquely Propagating Whistler Mode Chorus Emissions

NASA Astrophysics Data System (ADS)

Omura, Y.; Hsieh, Y. K.; Foster, J. C.; Erickson, P. J.; Kletzing, C.; Baker, D. N.

2017-12-01

A recent test particle simulation of obliquely propagating whistler mode wave-particle interaction [Hsieh and Omura, 2017] shows that the perpendicular wave electric field can play a significant role in trapping and accelerating relativistic electrons through Landau resonance. A further theoretical and numerical investigation verifies that there occurs nonlinear wave trapping of relativistic electrons by the nonlinear Lorentz force of the perpendicular wave magnetic field. An electron moving with a parallel velocity equal to the parallel phase velocity of an obliquely propagating wave basically see a stationary wave phase. Since the electron position is displaced from its gyrocenter by a distance ρ*sin(φ), where ρ is the gyroradius and φ is the gyrophase, the wave phase is modulated with the gyromotion, and the stationary wave fields as seen by the electron are expanded as series of Bessel functions Jn with phase variations n*φ. The J1 components of the wave electric and magnetic fields rotate in the right-hand direction with the gyrofrequency, and they can be in resonance with the electron undergoing the gyromotion, resulting in effective electron acceleration and pitch angle scattering. We have performed a subpacket analysis of chorus waveforms observed by the Van Allen Probes [Foster et al., 2017], and calculated the energy gain by the cyclotron acceleration through Landau resonance. We compare the efficiencies of accelerations by cyclotron and Landau resonances in typical events of rapid electron acceleration observed by the Van Allen Probes.References:[1] Hsieh, Y.-K., and Y. Omura (2017), Nonlinear dynamics of electrons interacting with oblique whistler mode chorus in the magnetosphere, J. Geophys. Res. Space Physics, 122, 675-694, doi:10.1002/2016JA023255.[2] Foster, J. C., P. J. Erickson, Y. Omura, D. N. Baker, C. A. Kletzing, and S. G. Claudepierre (2017), Van Allen Probes observations of prompt MeV radiation belt electron acceleration in nonlinear interactions with VLF chorus, J. Geophys. Res. Space Physics, 122, 324-339, doi:10.1002/2016JA023429.

The Effect of Acoustic Forcing on Instabilities and Breakdown in Swept-Wing Flow over a Backward-Facing Step

NASA Technical Reports Server (NTRS)

Eppink, Jenna L.; Shishkov, Olga; Wlezien, Richard W.; King, Rudolph A.; Choudhari, Meelan

2016-01-01

Instability interaction and breakdown were experimentally investigated in the flow over a swept backward-facing step. Acoustic forcing was used to excite the Tollmien-Schlichting (TS) instability and to acquire phase-locked results. The phase-averaged results illustrate the complex nature of the interaction between the TS and stationary cross flow instabilities. The weak stationary cross flow disturbance causes a distortion of the TS wavefront. The breakdown process is characterized by large positive and negative spikes in velocity. The positive spikes occur near the same time and location as the positive part of the TS wave. Higher-order spectral analysis was used to further investigate the nonlinear interactions between the TS instability and the traveling cross flow disturbances. The results reveal that a likely cause for the generation of the spikes corresponds to nonlinear interactions between the TS, traveling cross flow, and stationary cross flow disturbances. The spikes begin at low amplitudes of the unsteady and steady disturbances (2-4% U (sub e) (i.e. boundary layer edge velocity)) but can achieve very large amplitudes (20-30 percent U (sub e) (i.e. boundary layer edge velocity)) that initiate an early, though highly intermittent, breakdown to turbulence.

Collinear and vector interaction of light waves in nonlinear optical crystals KTiOPO4("KTP"), Ba2NaNb5O15 ("banana")

NASA Astrophysics Data System (ADS)

Deinekina, N. A.; Korosteleva, I. A.; Kravchenko, O. V.; Faleev, D. S.

2016-11-01

Esents the research results of biaxial crystals with mm2 symmetry class. These crystals were used for determining regularities of nonlinear conversion of broadband optical emission on the basis of collinear and vector light waves interactions of different nature. The quantities of the basis nonlinear optical characteristics of "KTP" (KTiOPO4) and "banana" (Ba2NaNb5O15) crystals were calculated in case of synchronous conversion of broadband emission from the area of 0.8 - 2.8 micron to the visible spectrum of 0.4 - 0.7 micron. The nonlinear optical characteristics of "KTP" crystals are defined by their geometrical structure, the mode of interaction of light waves, and the infra-red spectrum width, that was experimentally confirmed on "KTP" crystal. The quality characteristics β were calculated for the "KTP" crystal. For "banana" crystal the angle of phase synchronism θc changes insignificantly when the observation plane is changed. It can be explained by the fact that the biaxiality of crystal is not strongly expressed, because of the basis refraction indices the conditions nz<=ny≈nx are performed.

Nonlinear terahertz coherent excitation of vibrational modes of liquids.

PubMed

Allodi, Marco A; Finneran, Ian A; Blake, Geoffrey A

2015-12-21

We report the first coherent excitation of intramolecular vibrational modes via the nonlinear interaction of a TeraHertz (THz) light field with molecular liquids. A terahertz-terahertz-Raman pulse sequence prepares the coherences with a broadband, high-energy, (sub)picosecond terahertz pulse, that are then measured in a terahertz Kerr effect spectrometer via phase-sensitive, heterodyne detection with an optical pulse. The spectrometer reported here has broader terahertz frequency coverage, and an increased sensitivity relative to previously reported terahertz Kerr effect experiments. Vibrational coherences are observed in liquid diiodomethane at 3.66 THz (122 cm(-1)), and in carbon tetrachloride at 6.50 THz (217 cm(-1)), in exact agreement with literature values of those intramolecular modes. This work opens the door to 2D spectroscopies, nonlinear in terahertz field, that can study the dynamics of condensed-phase molecular systems, as well as coherent control at terahertz frequencies.

Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks.

PubMed

Gao, Zhongke; Jin, Ningde

2009-06-01

The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K -mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.

Quantum Noise Reduction with Pulsed Light in Optical Fibers.

NASA Astrophysics Data System (ADS)

Bergman, Keren

Optical fibers offer considerable advantages over bulk nonlinear media for the generation of squeezed states. This thesis reports on experimental investigations of reducing quantum noise by means of squeezing in nonlinear fiber optic interferometers. Fibers have low insertion loss which allows for long interaction lengths. High field intensities are easily achieved in the small cores of single mode fibers. Additionally, the nonlinear process employed is self phase modulation or the Kerr effect, whose broad band nature requires no phase matching and can be exploited with ultra-short pulses of high peak intensity. All these advantageous features of fibers result in easily obtained large nonlinear phase shifts and subsequently large squeezing parameters. By the self phase modulation process a correlation is produced between the phase and amplitude fluctuations of the optical field. The attenuated or squeezed quadrature has a lower noise level than the initial level associated with the coherent state field before propagation. The resulting reduced quantum noise quadrature can be utilized to improve the sensitivity of a phase measuring instrument such as an interferometer. Because the Kerr nonlinearity is a degenerate self pumping process, the squeezed noise is at the same frequency as the pump field. Classical pump noise can therefore interfere with the desired measurement of the quantum noise reduction. The most severe noise process is the phase noise caused by thermally induced index modulation of the fiber. This noise termed Guided Acoustic Wave Brillouin Scattering, or GAWBS, by previous researchers is studied and analyzed. Experiments performed to overcome GAWBS successfully with several schemes are described. An experimental demonstration of an interferometric measurement with better sensitivity than the standard quantum limit is described. The results lead to new understandings into the limitations of quantum noise reduction that can be achieved in the laboratory. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media

PubMed Central

Shen, Ming; Gao, Jinsong; Ge, Lijuan

2015-01-01

We investigate the spatially optical solitons shedding from Airy beams and anomalous interactions of Airy beams in nonlocal nonlinear media by means of direct numerical simulations. Numerical results show that nonlocality has profound effects on the propagation dynamics of the solitons shedding from the Airy beam. It is also shown that the strong nonlocality can support periodic intensity distribution of Airy beams with opposite bending directions. Nonlocality also provides a long-range attractive force between Airy beams, leading to the formation of stable bound states of both in-phase and out-of-phase breathing Airy solitons which always repel in local media. PMID:25900878

Incoherent population mixing contributions to phase-modulation two-dimensional coherent excitation spectra

NASA Astrophysics Data System (ADS)

Grégoire, Pascal; Srimath Kandada, Ajay Ram; Vella, Eleonora; Tao, Chen; Leonelli, Richard; Silva, Carlos

2017-09-01

We present theoretical and experimental results showing the effects of incoherent population mixing on two-dimensional (2D) coherent excitation spectra that are measured via a time-integrated population and phase-sensitive detection. The technique uses four collinear ultrashort pulses and phase modulation to acquire two-dimensional spectra by isolating specific nonlinear contributions to the photoluminescence or photocurrent excitation signal. We demonstrate that an incoherent contribution to the measured line shape, arising from nonlinear population dynamics over the entire photoexcitation lifetime, generates a similar line shape to the expected 2D coherent spectra in condensed-phase systems. In those systems, photoexcitations are mobile such that inter-particle interactions are important on any time scale, including those long compared with the 2D coherent experiment. Measurements on a semicrystalline polymeric semiconductor film at low temperatures show that, in some conditions in which multi-exciton interactions are suppressed, the technique predominantly detects coherent signals and can be used, in our example, to extract homogeneous line widths. The same method used on a lead-halide perovskite photovoltaic cell shows that incoherent population mixing of mobile photocarriers can dominate the measured signal since carrier-carrier bimolecular scattering is active even at low excitation densities, which hides the coherent contribution to the spectral line shape. In this example, the intensity dependence of the signal matches the theoretical predictions over more than two orders of magnitude, confirming the incoherent nature of the signal. While these effects are typically not significant in dilute solution environments, we demonstrate the necessity to characterize, in condensed-phase materials systems, the extent of nonlinear population dynamics of photoexcitations (excitons, charge carriers, etc.) in the execution of this powerful population-detected coherent spectroscopy technique.

Employment, Production and Consumption model: Patterns of phase transitions

NASA Astrophysics Data System (ADS)

Lavička, H.; Lin, L.; Novotný, J.

2010-04-01

We have simulated the model of Employment, Production and Consumption (EPC) using Monte Carlo. The EPC model is an agent based model that mimics very basic rules of industrial economy. From the perspective of physics, the nature of the interactions in the EPC model represents multi-agent interactions where the relations among agents follow the key laws for circulation of capital and money. Monte Carlo simulations of the stochastic model reveal phase transition in the model economy. The two phases are the phase with full unemployment and the phase with nearly full employment. The economy switches between these two states suddenly as a reaction to a slight variation in the exogenous parameter, thus the system exhibits strong non-linear behavior as a response to the change of the exogenous parameters.

Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System.

PubMed

Sarkar, Sujit

2017-05-12

An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).

Phases of a stack of membranes in a large number of dimensions of configuration space

NASA Astrophysics Data System (ADS)

Borelli, M. E.; Kleinert, H.

2001-05-01

The phase diagram of a stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is calculated exactly in a large number of dimensions of configuration space. At low temperatures, the system forms a lamellar phase with spontaneously broken translational symmetry in the vertical direction. At a critical temperature, the stack disorders vertically in a meltinglike transition. The critical temperature is determined as a function of the interlayer separation l.

Non-linear unsteady wing theory, part 1. Quasi two-dimensional behavior: Airfoils and slender wings

NASA Technical Reports Server (NTRS)

Mccune, J. E.

1987-01-01

The initial phases of a study of the large-amplitude unsteady aerodynamics of wings in severe maneuver are reported. The research centers on vortex flows, their initiation at wing surfaces, their subsequent convection, and interaction dynamically with wings and control surfaces. The focus is on 2D and quasi-2D aspects of the problem and features the development of an exact nonlinear unsteady airfoil theory as well as an approach to the crossflow problem for slender wing applications including leading-edge separation. The effective use of interactive on-line computing in quantifying and visualizing the nonsteady effects of severe maneuver is demonstrated. Interactive computational work is now possible, in which a maneuver can be initiated and its effects observed and analyzed immediately.

PREFACE: The 6th International Symposium on Measurement Techniques for Multiphase Flows

NASA Astrophysics Data System (ADS)

Okamoto, Koji; Murai, Yuichi

2009-02-01

Research on multi-phase flows is very important for industrial applications, including power stations, vehicles, engines, food processing, and so on. Also, from the environmental viewpoint, multi-phase flows need to be investigated to overcome global warming. Multi-phase flows originally have non-linear features because they are multi-phased. The interaction between the phases plays a very interesting role in the flows. The non-linear interaction causes the multi-phase flows to be very difficult to understand phenomena. The International Symposium on Measurement Techniques for Multi-phase Flows (ISMTMF) is a unique symposium. The target of the symposium is to exchange the state-of-the-art knowledge on the measurement techniques for non-linear multi-phase flows. Measurement technique is the key technology to understanding non-linear phenomena. The ISMTMF began in 1995 in Nanjing, China. The symposium has continuously been held every two or three years. The ISMTMF-2008 was held in Okinawa, Japan as the 6th symposium of ISMTMF on 15-17 December 2008. Okinawa has a long history as the Ryukyus Kingdom. China and Japan have had cultural and economic exchanges through Okinawa for more than 1000 years. Please enjoy Okinawa and experience its history to enhance our international communication. The present symposium was attended by 124 participants, the program included 107 contributions with 5 plenary lectures, 2 keynote lectures, and 100 oral regular paper presentations. The topics include, besides the ordinary measurement techniques for multiphase flows, acoustic and electric sensors, bubbles and microbubbles, computed tomography, gas-liquid interface, laser-imaging and PIV, oil/coal/drop and spray, solid and powder, spectral and multi-physics. This volume includes the presented papers at ISMTMF-2008. In addition to this volume, ten selected papers will be published in a special issue of Measurement Science and Technology. We would like to express special thanks to all the participants and the contributors to the symposium, and also to the supporting organizations; The Japanese Society for Multiphase Flow, The Chinese Society for Measurement, National Natural Science Foundation of China, The Chinese Academy of Science, and University of the Ryukyus, Okinawa, Japan. Koji Okamoto Chair of 6th ISMTMF and proceedings editor The University of Tokyo, Japan Yuichi Murai Proceedings co-editor Hokkaido University, Japan

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

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

Speck, Thomas; Menzel, Andreas M.; Bialké, Julian

2015-06-14

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation ontomore » that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.« less

Impact of nonlinear effective interactions on group field theory quantum gravity condensates

NASA Astrophysics Data System (ADS)

Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar

2016-09-01

We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.

Spatial and temporal ultrafast imaging and control of terahertz wavepackets

NASA Astrophysics Data System (ADS)

Koehl, Richard Michael

Some polar optical phonons couple strongly to far- infrared electromagnetic radiation and move at light-like speeds through dielectric media. These phonon-polaritons retain both ionic and electromagnetic character. One of the fruitful implications of this mixing is that vibrational and electronic nonlinearities in ferroelectric and other highly anharmonic media interact with traveling electromagnetic waves spanning several frequency regimes, permitting nonlinear wave mixing at infrared and optical frequencies. Nonlinear optical mixing techniques are well-developed because optical light is easy to produce, but the lack of similar far- infrared sources has stymied similar efforts at terahertz frequencies. Nonlinear interactions in this frequency regime provide information about vibrational potential energy surfaces and are very strong when the lattice vibration is associated with a phase transition. In this thesis, I review methods based on a well known nonlinear optical technique, impulsive stimulated Raman scattering (ISRS), to monitor the progress of coherent phonon polaritons in a highly nonlinear ferroelectric, lithium tantalate. I also advance multiple-pulse ISRS optical techniques to attempt to elucidate information about the ferroelectric's vibrational potential energy surface, and I discuss significant recent progress that has been made in the development of ultrafast optical tools to generate far-infrared radiation through ISRS at specified times and spatial locations and control the interactions of coherent phonon-polariton wavepackets. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Characterization of plasma wake excitation and particle trapping in the nonlinear bubble regime

NASA Astrophysics Data System (ADS)

Benedetti, Carlo; Schroeder, Carl; Esarey, Eric; Leemans, Wim

2010-11-01

We investigate the excitation of nonlinear wake (bubble) formation by an ultra-short (kpL ˜2), intense (e Alaser/mc^2 > 2) laser pulse interacting with an underdense plasma. A detailed analysis of particle orbits in the wakefield is performed by using reduced analytical models and numerical simulations performed with the 2D cylindrical, envelope, ponderomotive, hybrid PIC/fluid code INF&RNO, recently developed at LBNL. In particular we study the requirements for injection and/or trapping of background plasma electrons in the nonlinear wake. Characterization of the phase-space properties of the injected particle bunch will also be discussed.

A quantum-classical theory with nonlinear and stochastic dynamics

NASA Astrophysics Data System (ADS)

Burić, N.; Popović, D. B.; Radonjić, M.; Prvanović, S.

2014-12-01

The method of constrained dynamical systems on the quantum-classical phase space is utilized to develop a theory of quantum-classical hybrid systems. Effects of the classical degrees of freedom on the quantum part are modeled using an appropriate constraint, and the interaction also includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement.

Application of a Phase-resolving, Directional Nonlinear Spectral Wave Model

NASA Astrophysics Data System (ADS)

Davis, J. R.; Sheremet, A.; Tian, M.; Hanson, J. L.

2014-12-01

We describe several applications of a phase-resolving, directional nonlinear spectral wave model. The model describes a 2D surface gravity wave field approaching a mildly sloping beach with parallel depth contours at an arbitrary angle accounting for nonlinear, quadratic triad interactions. The model is hyperbolic, with the initial wave spectrum specified in deep water. Complex amplitudes are generated based on the random phase approximation. The numerical implementation includes unidirectional propagation as a special case. In directional mode, it solves the system of equations in the frequency-alongshore wave number space. Recent enhancements of the model include the incorporation of dissipation caused by breaking and propagation over a viscous mud layer and the calculation of wave induced setup. Applications presented include: a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation, a study of the evolution of a single directional triad, and several preliminary comparisons to wave spectra collected at the USACE-FRF in Duck, NC which show encouraging results although further validation with a wider range of beach slopes and wave conditions is needed.

Energetic mid-IR femtosecond pulse generation by self-defocusing soliton-induced dispersive waves in a bulk quadratic nonlinear crystal.

PubMed

Zhou, Binbin; Guo, Hairun; Bache, Morten

2015-03-09

Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO(3) cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm(-1)) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR.

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.

Toy models and stylized realities

NASA Astrophysics Data System (ADS)

Marsili, M.

2007-01-01

I discuss the role of toy models as theoretical tools for understanding complex systems of interacting agents. I review some concrete examples, in order to illustrate how this approach is able to capture, though in an admittedly stylized way, the interactions and non-linearities which are responsible for the rich phenomenology observed in reality. This allows one to interpret the system's behavior in terms of phase transitions and critical phenomena.

Predicting haemodynamic networks using electrophysiology: The role of non-linear and cross-frequency interactions

PubMed Central

Tewarie, P.; Bright, M.G.; Hillebrand, A.; Robson, S.E.; Gascoyne, L.E.; Morris, P.G.; Meier, J.; Van Mieghem, P.; Brookes, M.J.

2016-01-01

Understanding the electrophysiological basis of resting state networks (RSNs) in the human brain is a critical step towards elucidating how inter-areal connectivity supports healthy brain function. In recent years, the relationship between RSNs (typically measured using haemodynamic signals) and electrophysiology has been explored using functional Magnetic Resonance Imaging (fMRI) and magnetoencephalography (MEG). Significant progress has been made, with similar spatial structure observable in both modalities. However, there is a pressing need to understand this relationship beyond simple visual similarity of RSN patterns. Here, we introduce a mathematical model to predict fMRI-based RSNs using MEG. Our unique model, based upon a multivariate Taylor series, incorporates both phase and amplitude based MEG connectivity metrics, as well as linear and non-linear interactions within and between neural oscillations measured in multiple frequency bands. We show that including non-linear interactions, multiple frequency bands and cross-frequency terms significantly improves fMRI network prediction. This shows that fMRI connectivity is not only the result of direct electrophysiological connections, but is also driven by the overlap of connectivity profiles between separate regions. Our results indicate that a complete understanding of the electrophysiological basis of RSNs goes beyond simple frequency-specific analysis, and further exploration of non-linear and cross-frequency interactions will shed new light on distributed network connectivity, and its perturbation in pathology. PMID:26827811

Time-dependent behavior in a transport-barrier model for the quasi-single helcity state

NASA Astrophysics Data System (ADS)

Terry, P. W.; Whelan, G. G.

2014-09-01

Time-dependent behavior that follows from a recent theory of the quasi-single-helicity (QSH) state of the reversed field pinch is considered. The theory (Kim and Terry 2012 Phys. Plasmas 19 122304) treats QSH as a core fluctuation structure tied to a tearing mode of the same helicity, and shows that strong magnetic and velocity shears in the structure suppress the nonlinear interaction with other fluctuations. By summing the multiple helicity fluctuation energies over wavenumber, we reduce the theory to a predator-prey model. The suppression of the nonlinear interaction is governed by the single helicity energy, which, for fixed radial structure, controls the magnetic and velocity shearing rates. It is also controlled by plasma current which, in the theory, sets the shearing threshold for suppression. The model shows a limit cycle oscillation in which the system toggles between QSH and multiple helicity states, with the single helicity phase becoming increasingly long-lived relative to the multiple helicity phase as plasma current increases.

Nonlinear collisionless electron cyclotron interaction in the pre-ionisation stage

NASA Astrophysics Data System (ADS)

Farina, D.

2018-06-01

Electron cyclotron (EC) wave-particle interaction is theoretically investigated in the pre-ionisation phase, much before collisions and other mechanisms can play a role. In the very first phase of a plasma discharge with EC-assisted breakdown, the motion of an electron at room temperature in a static magnetic field under the action of a localised microwave beam is nonlinear, and transition to states of larger energy can occur via wave trapping. Within a Hamiltonian adiabatic formalism, the conditions at which the particles gain energy in single beam crossing are derived in a rigorous way, and the energy variation is characterized quantitatively as a function of the wave frequency, harmonic number, polarisation and EC power and beam width. Estimates of interest for applications to tokamak start-up are obtained for the first, second and third cyclotron harmonic. The investigation confirms that electrons can easily gain energies well above the ionisation energy in most conditions at the first two harmonics, while not at the third harmonic, as observed in experiments.

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.

Investigation of the effect of phase nonuniformities and the microwave field distribution on the electronic efficiency of a diffraction-radiation generator

NASA Astrophysics Data System (ADS)

Maksimov, P. P.; Tsvyk, A. I.; Shestopalov, V. P.

1985-10-01

The effect of local phase nonuniformities of the diffraction gratings and the field distribution of the open cavity on the electronic efficiency of a diffraction-radiation generator (DRG) is analyzed numerically on the basis of a self-consistent system of nonlinear stationary equations for the DRG. It is shown that the interaction power and efficiency of a DRG can be increased by the use of an open cavity with a nonuniform diffraction grating and a complex form of microwave field distribution over the interaction space.

Effect of bottom slope on the nonlinear triad interactions in shallow water

NASA Astrophysics Data System (ADS)

Chen, Hongzhou; Tang, Xiaocheng; Zhang, Ri; Gao, Junliang

2018-05-01

This paper aims at investigating the effect of bottom slope to the nonlinear triad interactions for irregular waves propagating in shallow water. The physical experiments are conducted in a wave flume with respect to the transformation of waves propagating on three bottom slopes ( β = 1/15, 1/30, and 1/45). Irregular waves with different type of breaking that are mechanically generated based on JONSWAP spectra are used for the test. The obviously different variations of spectra measured on each bottom reveal a crucial role of slope effect in the energy transfer between harmonics. The wavelet-based bispectrum were used to examine the bottom slope effect on the nonlinear triad interactions. Results show that the different bottom slopes which waves are propagated on will cause a significant discrepancy of triad interactions. Then, the discussions on the summed bicoherence which denote the distribution of phase coupling on each frequency further clarify the effect of bottom slope. Furthermore, the summed of the real and imaginary parts of bispectrum which could reflect the intensity of frequency components participating in the wave skewness and asymmetry were also investigated. Results indicate that the value of these parameters will increase as the bottom slope gets steeper.

Numerical Simulation of Two Phase Flows

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing

2001-01-01

Two phase flows can be found in broad situations in nature, biology, and industry devices and can involve diverse and complex mechanisms. While the physical models may be specific for certain situations, the mathematical formulation and numerical treatment for solving the governing equations can be general. Hence, we will require information concerning each individual phase as needed in a single phase. but also the interactions between them. These interaction terms, however, pose additional numerical challenges because they are beyond the basis that we use to construct modern numerical schemes, namely the hyperbolicity of equations. Moreover, due to disparate differences in time scales, fluid compressibility and nonlinearity become acute, further complicating the numerical procedures. In this paper, we will show the ideas and procedure how the AUSM-family schemes are extended for solving two phase flows problems. Specifically, both phases are assumed in thermodynamic equilibrium, namely, the time scales involved in phase interactions are extremely short in comparison with those in fluid speeds and pressure fluctuations. Details of the numerical formulation and issues involved are discussed and the effectiveness of the method are demonstrated for several industrial examples.

Competition between SFG and two SHGs in broadband type-I QPM

NASA Astrophysics Data System (ADS)

Dang, Weirui; Chen, Yuping; Gong, Mingjun; Chen, Xianfeng

2013-03-01

In this paper, we have studied the characteristics of second-order nonlinear interactions with band-overlapped type-I quasi-phase-matching (QPM) second harmonic generation (SHG) and sum-frequency generation (SFG), and predicted a blue-shift with a band-narrowing of their bands and a sunken response in the SFG curve, which are due to the phase-matching-dependent competition between band-overlapped SHG and SFG processes. This prediction is then verified by the experiment in an 18-mm-long bulk MgO-doped periodically poled lithium niobate crystal (MgO:PPLN) and may provide the candidate solution to output controlling for flexible broadcast wavelength conversion, channel-selective wavelength conversion and all-optical logic gates by cascaded QPM second-order nonlinear processes.

Nonlinear Mixing of Optical Vortices with Fractional Topological Charges in Raman Sideband Generation.

NASA Astrophysics Data System (ADS)

Strohaber, James; Boran, Yakup; Sayrac, Muhammed; Johnson, Lewis; Zhu, Feng; Kolomenskii, Alexandre; Schuessler, Hans

We studied the nonlinear parametric interaction of femtosecond fractionally-charged optical vortices in a Raman-active medium. Propagation of such beams is described using the Kirchhoff-Fresnel integrals by embedding a non-integer 2pi phase step in a Gaussian beam profile. When using fractionally-charged pump or Stokes beams, we observed the production of new topological charge and phase discontinuities in the Raman field. These newly generated fractionally-charged Raman vortex beams were found to follow the same orbital angular momentum algebra derived by for integer vortex beams. This work was funded by the Robert A. Welch Foundation, Grant No. A1546 and the Qatar Foundation under Grants No. NPRP 6-465-1-091.

Phase dynamics of coupled oscillators reconstructed from data

NASA Astrophysics Data System (ADS)

Rosenblum, Michael; Kralemann, Bjoern; Pikovsky, Arkady

2013-03-01

We present a technique for invariant reconstruction of the phase dynamics equations for coupled oscillators from data. The invariant description is achieved by means of a transformation of phase estimates (protophases) obtained from general scalar observables to genuine phases. Staring from the bivariate data, we obtain the coupling functions in terms of these phases. We discuss the importance of the protophase-to-phase transformation for characterization of strength and directionality of interaction. To illustrate the technique we analyse the cardio-respiratory interaction on healthy humans. Our invariant approach is confirmed by high similarity of the coupling functions obtained from different observables of the cardiac system. Next, we generalize the technique to cover the case of small networks of coupled periodic units. We use the partial norms of the reconstructed coupling functions to quantify directed coupling between the oscillators. We illustrate the method by different network motifs for three coupled oscillators. We also discuss nonlinear effects in coupling.

The chimera state in colloidal phase oscillators with hydrodynamic interaction

NASA Astrophysics Data System (ADS)

Hamilton, Evelyn; Bruot, Nicolas; Cicuta, Pietro

2017-12-01

The chimera state is the incongruous situation where coherent and incoherent populations coexist in sets of identical oscillators. Using driven non-linear oscillators interacting purely through hydrodynamic forces at low Reynolds number, previously studied as a simple model of motile cilia supporting waves, we find concurrent incoherent and synchronised subsets in small arrays. The chimeras seen in simulation display a "breathing" aspect, reminiscent of uniformly interacting phase oscillators. In contrast to other systems where chimera has been observed, this system has a well-defined interaction metric, and we know that the emergent dynamics inherit the symmetry of the underlying Oseen tensor eigenmodes. The chimera state can thus be connected to a superposition of eigenstates, whilst considering the mean interaction strength within and across subsystems allows us to make a connection to more generic (and abstract) chimeras in populations of Kuramoto phase oscillators. From this work, we expect the chimera state to emerge in experimental observations of oscillators coupled through hydrodynamic forces.

Subwavelength nonlinear phase control and anomalous phase matching in plasmonic metasurfaces

NASA Astrophysics Data System (ADS)

Almeida, Euclides; Shalem, Guy; Prior, Yehiam

2016-01-01

Metasurfaces, and in particular those containing plasmonic-based metallic elements, constitute an attractive set of materials with a potential for replacing standard bulky optical elements. In recent years, increasing attention has been focused on their nonlinear optical properties, particularly in the context of second and third harmonic generation and beam steering by phase gratings. Here, we harness the full phase control enabled by subwavelength plasmonic elements to demonstrate a unique metasurface phase matching that is required for efficient nonlinear processes. We discuss the difference between scattering by a grating and by subwavelength phase-gradient elements. We show that for such interfaces an anomalous phase-matching condition prevails, which is the nonlinear analogue of the generalized Snell's law. The subwavelength phase control of optical nonlinearities paves the way for the design of ultrathin, flat nonlinear optical elements. We demonstrate nonlinear metasurface lenses, which act both as generators and as manipulators of the frequency-converted signal.

All-optical 40Gbit/s format conversion from NRZ to RZ based on SFG in a PPLN waveguide

NASA Astrophysics Data System (ADS)

Wang, Jian; Sun, Junqiang

2006-01-01

A novel all-optical 40Gbit/s NRZ-to-RZ data format conversion scheme based on sum-frequency generation (SFG) interaction in a periodically poled LiNbO 3 (PPLN) waveguide is presented for the first time, using a Mach-Zehnder interferometer (MZI). The conversion mechanism relies on the combination of attenuation and nonlinear phase shift Φ NL induced on the signal field. The performance of the conversion is numerically evaluated, with the result showing that it is more effective to yield Φ NL when appropriately phase mismatched for SFG process but Φ NL~0 when quasi-phase-matching (QPM). Compared with the cascaded second-order nonlinear interactions (SHG+DFG) with the influence of walk-off effect, a high conversion efficiency and good performance are achieved with peak power 500mw and width 2ps of the pump, which can be used in super high-speed situation (40Gbit/s and above). Finally, the inverse process of SFG and corresponding walk-off effect are analyzed and the optimum arrangement of power is proposed, showing that proper power, pump width, and waveguide length are necessary for achieving a satisfied conversion effect.

Phase-resolved two-dimensional terahertz spectroscopy - a probe of highly nonlinear light-matter interactions

NASA Astrophysics Data System (ADS)

Elsaesser, Thomas

Terahertz (THz) spectroscopy gives insight into low-frequency excitations and charge dynamics in condensed matter. So far, most experiments in a frequency range from 0.5 to 30 THz have focused on the linear THz response to determine linear absorption and disperion spectra, and/or electric conductivities. The generation of ultrashort THz transients with peak electric fields up to megavolts/cm has allowed for addressing nonlinear light-matter interactions and inducing excitations far from equilibrium. The novel method of two-dimensional THz (2D-THz) spectroscopy allows for mapping ultrafast dynamics and couplings of elementary excitations up to arbitrary nonlinear order in the electric field, both under resonant and nonresonant excitation conditions. In particular, different contributions to the overall nonlinear response are separated by dissecting it as a function of excitation and detection frequencies and for different waiting times after excitation. This talk gives an introduction in 2D-THz spectroscopy, including its recent extension to 3-pulse sequences and interaction schemes. To illustrate the potential of the method, recent results on two-phonon coherences and high-order interband excitations in the semiconductor InSb will be presented. Nonlinear THz excitation of two-phonon coherences exploits a resonance enhancement by the large electronic interband dipole of InSb and is, thus, far more efficient than linear excitation via resonant two-phonon absorption. As a second application, the nonlinear softmode response in a crystal consisting of aspirin molecules will be discussed. At moderate THz driving fields, the pronounced correlation of rotational modes of CH3 groups with collective oscillations of π-electrons drives the system into the regime of nonperturbative light-matter interaction. Nonlinear absorption around 1.1 THz leads to a blue-shifted coherent emission at 1.5 THz, revealing a dynamic breakup of the strong electron-phonon correlations.

A photon-photon quantum gate based on a single atom in an optical resonator.

PubMed

Hacker, Bastian; Welte, Stephan; Rempe, Gerhard; Ritter, Stephan

2016-08-11

That two photons pass each other undisturbed in free space is ideal for the faithful transmission of information, but prohibits an interaction between the photons. Such an interaction is, however, required for a plethora of applications in optical quantum information processing. The long-standing challenge here is to realize a deterministic photon-photon gate, that is, a mutually controlled logic operation on the quantum states of the photons. This requires an interaction so strong that each of the two photons can shift the other's phase by π radians. For polarization qubits, this amounts to the conditional flipping of one photon's polarization to an orthogonal state. So far, only probabilistic gates based on linear optics and photon detectors have been realized, because "no known or foreseen material has an optical nonlinearity strong enough to implement this conditional phase shift''. Meanwhile, tremendous progress in the development of quantum-nonlinear systems has opened up new possibilities for single-photon experiments. Platforms range from Rydberg blockade in atomic ensembles to single-atom cavity quantum electrodynamics. Applications such as single-photon switches and transistors, two-photon gateways, nondestructive photon detectors, photon routers and nonlinear phase shifters have been demonstrated, but none of them with the ideal information carriers: optical qubits in discriminable modes. Here we use the strong light-matter coupling provided by a single atom in a high-finesse optical resonator to realize the Duan-Kimble protocol of a universal controlled phase flip (π phase shift) photon-photon quantum gate. We achieve an average gate fidelity of (76.2 ± 3.6) per cent and specifically demonstrate the capability of conditional polarization flipping as well as entanglement generation between independent input photons. This photon-photon quantum gate is a universal quantum logic element, and therefore could perform most existing two-photon operations. The demonstrated feasibility of deterministic protocols for the optical processing of quantum information could lead to new applications in which photons are essential, especially long-distance quantum communication and scalable quantum computing.

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.

Exploration of multiphoton entangled states by using weak nonlinearities

PubMed Central

He, Ying-Qiu; Ding, Dong; Yan, Feng-Li; Gao, Ting

2016-01-01

We propose a fruitful scheme for exploring multiphoton entangled states based on linear optics and weak nonlinearities. Compared with the previous schemes the present method is more feasible because there are only small phase shifts instead of a series of related functions of photon numbers in the process of interaction with Kerr nonlinearities. In the absence of decoherence we analyze the error probabilities induced by homodyne measurement and show that the maximal error probability can be made small enough even when the number of photons is large. This implies that the present scheme is quite tractable and it is possible to produce entangled states involving a large number of photons. PMID:26751044

On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

NASA Astrophysics Data System (ADS)

BOERTJENS, G. J.; VAN HORSSEN, W. T.

2000-08-01

In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

The nonlinear gyroresonance interaction between energetic electrons and coherent VLF waves propagating at an arbitrary angle with respect to the earth's magnetic field

NASA Technical Reports Server (NTRS)

Bell, T. F.

1984-01-01

A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.

A non-linear piezoelectric actuator calibration using N-dimensional Lissajous figure

NASA Astrophysics Data System (ADS)

Albertazzi, A.; Viotti, M. R.; Veiga, C. L. N.; Fantin, A. V.

2016-08-01

Piezoelectric translators (PZTs) are very often used as phase shifters in interferometry. However, they typically present a non-linear behavior and strong hysteresis. The use of an additional resistive or capacitive sensor make possible to linearize the response of the PZT by feedback control. This approach works well, but makes the device more complex and expensive. A less expensive approach uses a non-linear calibration. In this paper, the authors used data from at least five interferograms to form N-dimensional Lissajous figures to establish the actual relationship between the applied voltages and the resulting phase shifts [1]. N-dimensional Lissajous figures are formed when N sinusoidal signals are combined in an N-dimensional space, where one signal is assigned to each axis. It can be verified that the resulting Ndimensional ellipsis lays in a 2D plane. By fitting an ellipsis equation to the resulting 2D ellipsis it is possible to accurately compute the resulting phase value for each interferogram. In this paper, the relationship between the resulting phase shift and the applied voltage is simultaneously established for a set of 12 increments by a fourth degree polynomial. The results in speckle interferometry show that, after two or three interactions, the calibration error is usually smaller than 1°.

Noncollinear wave mixing of attosecond XUV and few-cycle optical laser pulses in gas-phase atoms: Toward multidimensional spectroscopy involving XUV excitations

NASA Astrophysics Data System (ADS)

Cao, Wei; Warrick, Erika R.; Fidler, Ashley; Neumark, Daniel M.; Leone, Stephen R.

2016-11-01

Ultrafast nonlinear spectroscopy, which records transient wave-mixing signals in a medium, is a powerful tool to access microscopic information using light sources in the radio-frequency and optical regimes. The extension of this technique towards the extreme ultraviolet (XUV) or even x-ray regimes holds the promise to uncover rich structural or dynamical information with even higher spatial or temporal resolution. Here, we demonstrate noncollinear wave mixing between weak XUV attosecond pulses and a strong near-infrared (NIR) few-cycle laser pulse in gas phase atoms (one photon of XUV and two photons of NIR). In the noncollinear geometry the attosecond and either one or two NIR pulses interact with argon atoms. Nonlinear XUV signals are generated in a spatially resolved fashion as required by phase matching. Different transition pathways can be identified from these background-free nonlinear signals according to the specific phase-matching conditions. Time-resolved measurements of the spatially gated XUV signals reveal electronic coherences of Rydberg wave packets prepared by a single XUV photon or XUV-NIR two-photon excitation, depending on the applied pulse sequences. These measurements open possible applications of tabletop multidimensional spectroscopy to the study of dynamics associated with valence or core excitation with XUV photons.

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

A numerical and experimental study on the nonlinear evolution of long-crested irregular waves

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

Goullet, Arnaud; Choi, Wooyoung; Division of Ocean Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 305-701

2011-01-15

The spatial evolution of nonlinear long-crested irregular waves characterized by the JONSWAP spectrum is studied numerically using a nonlinear wave model based on a pseudospectral (PS) method and the modified nonlinear Schroedinger (MNLS) equation. In addition, new laboratory experiments with two different spectral bandwidths are carried out and a number of wave probe measurements are made to validate these two wave models. Strongly nonlinear wave groups are observed experimentally and their propagation and interaction are studied in detail. For the comparison with experimental measurements, the two models need to be initialized with care and the initialization procedures are described. Themore » MNLS equation is found to approximate reasonably well for the wave fields with a relatively smaller Benjamin-Feir index, but the phase error increases as the propagation distance increases. The PS model with different orders of nonlinear approximation is solved numerically, and it is shown that the fifth-order model agrees well with our measurements prior to wave breaking for both spectral bandwidths.« less

Resonance controlled transport in phase space

NASA Astrophysics Data System (ADS)

Leoncini, Xavier; Vasiliev, Alexei; Artemyev, Anton

2018-02-01

We consider the mechanism of controlling particle transport in phase space by means of resonances in an adiabatic setting. Using a model problem describing nonlinear wave-particle interaction, we show that captures into resonances can be used to control transport in momentum space as well as in physical space. We design the model system to provide creation of a narrow peak in the distribution function, thus producing effective cooling of a sub-ensemble of the particles.

A geometric theory of waves and its applications to plasma physics.

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

Ruiz, Daniel

Waves play an essential role in many aspects of plasma dynamics. For example, they are indispensable in plasma manipulation and diagnostics. Although the physics of waves is well understood in the context of relatively simple problems, difficulties arise when studying waves that propagate in inhomogeneous or nonlinear media. This thesis presents a new systematic wave theory based on phase-space variational principles. In this dissertation, waves are treated as geometric objects of a variational theory rather than formal solutions of specific PDEs. This approach simplifies calculations, highlights the underlying wave symmetries, and leads to improved modeling of wave dynamics. Specifically, thismore » dissertation presents two important breakthroughs that were obtained in the general theory of waves. The first main contribution of the present dissertation is an extension of the theory of geometrical optics (GO) in order to include polarization effects. Even when diffraction is ignored, the GO ray equations are not entirely accurate. This occurs because GO treats wave rays as classical particles described by their position and momentum coordinates. However, vector waves have another degree of freedom, their polarization. As a result, wave rays can behave as particles with spin and show polarization dynamics, such as polarization precession and polarization-driven bending of ray trajectories. In this thesis, the theory of GO is reformulated as a first-principle Lagrangian wave theory that governs both mentioned polarization phenomena simultaneously. The theory was applied successfully to several systems of interest, such as relativistic spin-$1/2$ particles and radio-frequency waves propagating in magnetized plasmas. The second main contribution of this thesis is the development of a phase-space method to study basic properties of nonlinear wave--wave interactions. Specifically, a general theory is proposed that describes the ponderomotive refraction that a wave can experience when interacting with another wave. It is also shown that phase-space methods can be useful to study problems in the field of wave turbulence, such as the nonlinear interaction of high-frequency waves with large-scale structures. Overall, the results obtained can serve as a basis for future studies on more complex nonlinear wave--wave interactions, such as modulational instabilities in general wave ensembles or wave turbulence.« less

Exotic states of matter with polariton chains

NASA Astrophysics Data System (ADS)

Kalinin, Kirill P.; Lagoudakis, Pavlos G.; Berloff, Natalia G.

2018-04-01

We consider linear periodic chains of exciton-polariton condensates formed by pumping polaritons nonresonantly into a linear network. To the leading order such a sequence of condensates establishes relative phases as to minimize a classical one-dimensional X Y Hamiltonian with nearest and next-to-nearest neighbors. We show that the low-energy states of polaritonic linear chains demonstrate various classical regimes: ferromagnetic, antiferromagnetic, and frustrated spiral phases where quantum or thermal fluctuations are expected to give rise to a spin-liquid state. At the same time nonlinear interactions at higher pumping intensities bring about phase chaos and novel exotic phases.

Asymptotically stable phase synchronization revealed by autoregressive circle maps

NASA Astrophysics Data System (ADS)

Drepper, F. R.

2000-11-01

A specially designed of nonlinear time series analysis is introduced based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit estimation scheme for the potentially underlying autoregressive circle map (next phase map) guarantee the invertibility of reconstructed phase space trajectories to the original coordinates. The resulting Fourier approximated, invertibility enforcing phase space map allows us to detect conditional asymptotic stability of coupled phases. This comparatively general synchronization criterion unites two existing generalizations of the old concept and can successfully be applied, e.g., to phases obtained from electrocardiogram and airflow recordings characterizing cardiorespiratory interaction.

Cross-phase modulation spectral shifting: nonlinear phase contrast in a pump-probe microscope

PubMed Central

Wilson, Jesse W.; Samineni, Prathyush; Warren, Warren S.; Fischer, Martin C.

2012-01-01

Microscopy with nonlinear phase contrast is achieved by a simple modification to a nonlinear pump-probe microscope. The technique measures cross-phase modulation by detecting a pump-induced spectral shift in the probe pulse. Images with nonlinear phase contrast are acquired both in transparent and absorptive media. In paraffin-embedded biopsy sections, cross-phase modulation complements the chemically-specific pump-probe images with structural context. PMID:22567580

Radiation resistance of nonlinear crystals at a wavelength of 9.55 {mu}m

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

Andreev, Yu M; Voevodin, V G; Badikov, Valerii V

2001-12-31

The results of radiation resistance measurements for twelve nonlinear crystals are presented. The crystals include the well-known nonlinear CdGeAs{sub 2}, ZnGeP{sub 2}, AgGaSe{sub 2}, GaSe, AgGaS{sub 2}, and Ag{sub 3}AsS{sub 3} crystals operating in the middle IR range, new mixed AgGaGeS{sub 4} and Cd{sub 0.35}Hg{sub 0.65}Ga{sub 2}S{sub 4} crystals, two-phase (orange and yellow) HgGa{sub 2}S{sub 4} crystal, and the doped GaSe:In crystal. The mixed crystals and the two-phase HgGa{sub 2}S{sub 4} crystal are transparent in the range from 0.4 - 0.5 to 11.5 - 14.5 {mu}m. The measurements were performed using a pulsed single-mode highly stability TEA CO{sub 2} lasermore » with an output pulse duration of {approx}30 ns. The damage thresholds of new nonlinear AgGaGeS{sub 4} and Cd {sub 0.35}Hg{sub 0.65}Ga{sub 2}S{sub 4} crystals and of the HgGa{sub 2}S{sub 4} crystal (the orange and yellow phases) were found to be 1.5 - 2.2 times higher than for the crystals operating in the middle IR range. (interaction of laser radiation with matter. laser plasma)« less

Orbit-based analysis of nonlinear energetic ion dynamics in tokamaks. II. Mechanisms for rapid chirping and convective amplification

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

Bierwage, Andreas; Shinohara, Kouji

2016-04-15

The nonlinear interactions between shear Alfvén modes and tangentially injected beam ions in the 150–400 keV range are studied numerically in realistic geometry for a JT-60U tokamak scenario. In Paper I, which was reported in the companion paper, the recently developed orbit-based resonance analysis method was used to track the resonant frequency of fast ions during their nonlinear evolution subject to large magnetic and electric drifts. Here, that method is applied to map the wave-particle power transfer from the canonical guiding center phase space into the frequency-radius plane, where it can be directly compared with the evolution of the fluctuation spectramore » of fast-ion-driven modes. Using this technique, we study the nonlinear dynamics of strongly driven shear Alfvén modes with low toroidal mode numbers n = 1 and n = 3. In the n = 3 case, both chirping and convective amplification can be attributed to the mode following the resonant frequency of the radially displaced particles, i.e., the usual one-dimensional phase locking process. In the n = 1 case, a new chirping mechanism is found, which involves multiple dimensions, namely, wave-particle trapping in the radial direction and phase mixing across velocity coordinates.« less

Contribution of non-resonant wave-wave interactions in the dynamics of long-crested sea wave fields

NASA Astrophysics Data System (ADS)

Benoit, Michel

2017-04-01

Gravity waves fields at the surface of the oceans evolve under the combined effects of several physical mechanisms, of which nonlinear wave-wave interactions play a dominant role. These interactions transfer energy between components within the energy spectrum and allow in particular to explain the shape of the distribution of wave energy according to the frequencies and directions of propagation. In the oceanic domain (deep water conditions), dominant interactions are third-order resonant interactions, between quadruplets (or quartets) of wave components, and the evolution of the wave spectrum is governed by a kinetic equation, established by Hasselmann (1962) and Zakharov (1968). The kinetic equation has a number of interesting properties, including the existence of self-similar solutions and cascades to small and large wavelengths of waves, which can be studied in the framework of the wave (or weak) turbulence theory (e.g. Badulin et al., 2005). With the aim to obtain more complete and precise modelling of sea states dynamics, we investigate here the possibility and consequences of taking into account the non-resonant interactions -quasi-resonant in practice- among 4 waves. A mathematical formalism has recently been proposed to account for these non-resonant interactions in a statistical framework by Annenkov & Shrira (2006) (Generalized Kinetic Equation, GKE) and Gramstad & Stiassnie (2013) (Phase Averaged Equation, PAE). In order to isolate the non-resonant contributions, we limit ourselves here to monodirectional (i.e. long-crested) wave trains, since in this case the 4-wave resonant interactions vanish. The (stochastic) modelling approaches proposed by Annenkov & Shrira (2006) and Gramstad & Stiassnie (2013) are compared to phase-resolving (deterministic) simulations based on a fully nonlinear potential approach (using a high-order spectral method, HOS). We study and compare the evolution dynamics of the wave spectrum at different time scales (i.e. over durations ranging from a few wave periods to 1000 periods), with the aim of highlighting the capabilities and limitations of the GKE-PAE models. Different situations are considered by varying the relative water depth, the initial steepness of the wave field, and the shape of the initial wave spectrum, including arbitrary forms. References: Annenkov S.Y., Shrira V.I. (2006) Role of non-resonant interactions in the evolution of nonlinear random water wave fields. J. Fluid Mech., 561, 181-207. Badulin S.I., Pushkarev A.N., Resio D., Zakharov V.E. (2005) Self-similarity of wind-driven seas. Nonlin. Proc. Geophys., 12, 891-946. Gramstad O., Stiassnie M. (2013) Phase-averaged equation for water waves. J. Fluid Mech., 718, 280- 303. Hasselmann K. (1962) On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech., 12, 481-500. Zakharov V.E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. App. Mech. Tech. Phys., 9(2), 190-194.

Conditional phase-shift enhancement through dynamical Rydberg blockade

NASA Astrophysics Data System (ADS)

Wu, Jin-Hui; Artoni, M.; Cataliotti, F.; La Rocca, G. C.

2017-12-01

Large cross-phase shifts per photon can be attained through an all-optical polarization control of dipole blockade in Rydberg atoms. A pair of weak circularly polarized signal and control light pulses experience a giant nonlinear cross-interaction through the conditional excitation of a Rydberg state. Conditional cross-phase modulations on the order of π-radians may be attained under specific symmetric EIT quasi-resonant driving conditions at large degrees of transparency. We also suggest the possibility of extending our scheme to work at very low intensities and within a few-blockade-radii regions.

Study of parameter of nonlinearity in 2-chloroethanol with 2-dimethylethanolamine/2-diethylethanolamine at different temperatures

NASA Astrophysics Data System (ADS)

Awasthi, Anjali; Awasthi, Aashees

2017-06-01

The acoustic non-linearity parameter (B/A) for binary mixtures of 2-chloroethanol with 2-dimethylethanolamine (2-DMAE) and 2-diethylethanolamine (2-DEAE) are evaluated using Tong Dong, Beyer and Beyer-Tong Dong coefficients at varying concentrations and temperatures ranging from 293.15 to 313.15 K. The nonlinearity parameter is used to calculate various molecular properties such as internal pressure, cohesive energy density, Van der waals' constant, distance of closest approach, diffusion coefficient and rotational correlation time. Additionally, the intermediate quantities like temperature and pressure derivatives of sound velocity and phase shift parameter as a function of temperature are also deduced. The extent of intermolecular interactions, anharmonicity and structural configuration of the binaries under investigation are discussed in terms of excess non-linearity parameter (B/A)E.

On the interaction of small-scale linear waves with nonlinear solitary waves

NASA Astrophysics Data System (ADS)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow interaction in a fully nonlinear framework.

Experimental investigation of gravity wave turbulence and of non-linear four wave interactions..

NASA Astrophysics Data System (ADS)

Berhanu, Michael

2017-04-01

Using the large basins of the Ecole Centrale de Nantes (France), non-linear interactions of gravity surface waves are experimentally investigated. In a first part we study statistical properties of a random wave field regarding the insights from the Wave Turbulence Theory. In particular freely decaying gravity wave turbulence is generated in a closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonl-inear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, non-linear and dissipative time scales to test the time scale separation. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated. In a second part, resonant interactions of oblique surface gravity waves in a large basin are studied. We generate two oblique waves crossing at an acute angle. These mother waves mutually interact and give birth to a resonant wave whose properties (growth rate, resonant response curve and phase locking) are fully characterized. All our experimental results are found in good quantitative agreement with four-wave interaction theory. L. Deike, B. Miquel, P. Gutiérrez, T. Jamin, B. Semin, M. Berhanu, E. Falcon and F. Bonnefoy, Role of the basin boundary conditions in gravity wave turbulence, Journal of Fluid Mechanics 781, 196 (2015) F. Bonnefoy, F. Haudin, G. Michel, B. Semin, T. Humbert, S. Aumaître, M. Berhanu and E. Falcon, Observation of resonant interactions among surface gravity waves, Journal of Fluid Mechanics (Rapids) 805, R3 (2016)

Guided wave methods and apparatus for nonlinear frequency generation

DOEpatents

Durfee, III, Charles G.; Rundquist, Andrew; Kapteyn, Henry C.; Murnane, Margaret M.

2000-01-01

Methods and apparatus are disclosed for the nonlinear generation of sum and difference frequencies of electromagnetic radiation propagating in a nonlinear material. A waveguide having a waveguide cavity contains the nonlinear material. Phase matching of the nonlinear generation is obtained by adjusting a waveguide propagation constant, the refractive index of the nonlinear material, or the waveguide mode in which the radiation propagates. Phase matching can be achieved even in isotropic nonlinear materials. A short-wavelength radiation source uses phase-matched nonlinear generation in a waveguide to produce high harmonics of a pulsed laser.

Nonlinear optical effects of opening a gap in graphene

NASA Astrophysics Data System (ADS)

Carvalho, David N.; Biancalana, Fabio; Marini, Andrea

2018-05-01

Graphene possesses remarkable electronic, optical, and mechanical properties that have taken the research of two-dimensional relativistic condensed matter systems to prolific levels. However, the understanding of how its nonlinear optical properties are affected by relativisticlike effects has been broadly uncharted. It has been recently shown that highly nontrivial currents can be generated in free-standing samples, notably leading to the generation of even harmonics. Since graphene monolayers are centrosymmetric media, for which such harmonic generation at normal incidence is deemed inaccessible, this light-driven phenomenon is both startling and promising. More realistically, graphene samples are often deposited on a dielectric substrate, leading to additional intricate interactions. Here, we present a treatment to study this instance by gapping the spectrum and we show this leads to the appearance of a Berry phase in the carrier dynamics. We analyze the role of such a phase in the generated nonlinear current and conclude that it suppresses odd-harmonic generation. The pump energy can be tuned to the energy gap to yield interference among odd harmonics mediated by interband transitions, allowing even harmonics to be generated. Our results and general methodology pave the way for understanding the role of gap opening in the nonlinear optics of two-dimensional lattices.

Suppression of Phase Mixing in Drift-Kinetic Plasma Turbulence

NASA Astrophysics Data System (ADS)

Parker, J. T.; Dellar, P. J.; Schekochihin, A. A.; Highcock, E. G.

2017-12-01

The solar wind and interstellar medium are examples of strongly magnetised, weakly collisional, astrophysical plasmas. Their turbulent fluctuations are strongly anisotropic, with small amplitudes, and frequencies much lower than the Larmor frequency. This regime is described by gyrokinetic theory, a reduced five-dimensional kinetic system describing averages over Larmor orbits. A turbulent plasma may transfer free energy, a measure of fluctuation amplitudes, from injection at large scales, typically by an instability, to dissipation at small physical scales like a turbulent fluid. Alternatively, a turbulent plasma may form fine scale structures in velocity space via phase-mixing, the mechanism that leads to Landau damping in linear plasma theory. Macroscopic plasma properties like heat and momentum transport are affected by both mechanisms. While each is understood in isolation, their interaction is not. We study this interaction using a Hankel-Hermite velocity space representation of gyrokinetic theory. The Hankel transform interacts neatly with the Bessel functions that arise from averaging over Larmor orbits, so the perpendicular velocity space is decoupled for linearized problems. The Hermite transform expresses phase mixing as nearest-neighbor coupling between parallel velocity space scales represented by Hermite mode numbers. We use this representation to study transfer mechanisms in drift-kinetic plasma turbulence, the long wavelength limit of gyrokinetic theory. We show that phase space is divided into two regions, with one transfer mechanism dominating in each. Most energy is contained in the region where the fluid-like nonlinear cascade dominates. Moreover, in that region the nonlinear cascade interferes with phase mixing by exciting an "anti phase mixing" transfer of free energy from small to large velocity space scales. This cancels out the usual phase mixing, and renders the overall behavior fluid-like. These results profoundly change our understanding of free energy flow in drift-kinetic turbulence, and, moreover, explain previously observed spectra.

Theory and design of nonlinear metamaterials

NASA Astrophysics Data System (ADS)

Rose, Alec Daniel

If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers and oscillators. By applying this set of tools and knowledge to microwave metamaterials, I experimentally confirm several novel nonlinear phenomena. Most notably, I construct a backward wave nonlinear medium from varactor-loaded split ring resonators loaded in a rectangular waveguide, capable of generating second-harmonic opposite to conventional nonlinear materials with a conversion efficiency as high as 1.5%. In addition, I confirm nonlinear magnetoelectric coupling in two dual gap varactor-loaded split ring resonator metamaterials through measurement of the amplitude and phase of the second-harmonic generated in the forward and backward directions from a thin slab. I then use the presence of simultaneous nonlinearities in such metamaterials to observe nonlinear interference, manifest as unidirectional difference frequency generation with contrasts of 6 and 12 dB in the forward and backward directions, respectively. Finally, I apply these principles and intuition to several plasmonic platforms with the goal of achieving similar enhancements and configurations at optical frequencies. Using the example of fluorescence enhancement in optical patch antennas, I develop a semi-classical numerical model for the calculation of field-induced enhancements to both excitation and spontaneous emission rates of an embedded fluorophore, showing qualitative agreement with experimental results, with enhancement factors of more than 30,000. Throughout these series of works, I emphasize the indispensability of effective design and retrieval tools in understanding and optimizing both metamaterials and plasmonic systems. Ultimately, when weighed against the disadvantages in fabrication and optical losses, the results presented here provide a context for the application of nonlinear metamaterials within three distinct areas where a competitive advantage over conventional materials might be obtained: fundamental science demonstrations, linear and nonlinear anisotropy engineering, and extremely compact resonant all-optical devices.

Study of nonlinear interaction between bunched beam and intermediate cavities in a relativistic klystron amplifier

NASA Astrophysics Data System (ADS)

Wu, Y.; Xu, Z.; Li, Z. H.; Tang, C. X.

2012-07-01

In intermediate cavities of a relativistic klystron amplifier (RKA) driven by intense relativistic electron beam, the equivalent circuit model, which is widely adopted to investigate the interaction between bunched beam and the intermediate cavity in a conventional klystron design, is invalid due to the high gap voltage and the nonlinear beam loading in a RKA. According to Maxwell equations and Lorentz equation, the self-consistent equations for beam-wave interaction in the intermediate cavity are introduced to study the nonlinear interaction between bunched beam and the intermediate cavity in a RKA. Based on the equations, the effects of modulation depth and modulation frequency of the beam on the gap voltage amplitude and its phase are obtained. It is shown that the gap voltage is significantly lower than that estimated by the equivalent circuit model when the beam modulation is high. And the bandwidth becomes wider as the beam modulation depth increases. An S-band high gain relativistic klystron amplifier is designed based on the result. And the corresponding experiment is carried out on the linear transformer driver accelerator. The peak output power has achieved 1.2 GW with an efficiency of 28.6% and a gain of 46 dB in the corresponding experiment.

A Linear Model of Phase-Dependent Power Correlations in Neuronal Oscillations

PubMed Central

Eriksson, David; Vicente, Raul; Schmidt, Kerstin

2011-01-01

Recently, it has been suggested that effective interactions between two neuronal populations are supported by the phase difference between the oscillations in these two populations, a hypothesis referred to as “communication through coherence” (CTC). Experimental work quantified effective interactions by means of the power correlations between the two populations, where power was calculated on the local field potential and/or multi-unit activity. Here, we present a linear model of interacting oscillators that accounts for the phase dependency of the power correlation between the two populations and that can be used as a reference for detecting non-linearities such as gain control. In the experimental analysis, trials were sorted according to the coupled phase difference of the oscillators while the putative interaction between oscillations was taking place. Taking advantage of the modeling, we further studied the dependency of the power correlation on the uncoupled phase difference, connection strength, and topology. Since the uncoupled phase difference, i.e., the phase relation before the effective interaction, is the causal variable in the CTC hypothesis we also describe how power correlations depend on that variable. For uni-directional connectivity we observe that the width of the uncoupled phase dependency is broader than for the coupled phase. Furthermore, the analytical results show that the characteristics of the phase dependency change when a bidirectional connection is assumed. The width of the phase dependency indicates which oscillation frequencies are optimal for a given connection delay distribution. We propose that a certain width enables a stimulus-contrast dependent extent of effective long-range lateral connections. PMID:21808618

Nonlinear Metasurface for Simultaneous Control of Spin and Orbital Angular Momentum in Second Harmonic Generation.

PubMed

Li, Guixin; Wu, Lin; Li, King F; Chen, Shumei; Schlickriede, Christian; Xu, Zhengji; Huang, Siya; Li, Wendi; Liu, Yanjun; Pun, Edwin Y B; Zentgraf, Thomas; Cheah, Kok W; Luo, Yu; Zhang, Shuang

2017-12-13

The spin and orbital angular momentum (SAM and OAM) of light is providing a new gateway toward high capacity and robust optical communications. While the generation of light with angular momentum is well studied in linear optics, its further integration into nonlinear optical devices will open new avenues for increasing the capacity of optical communications through additional information channels at new frequencies. However, it has been challenging to manipulate the both SAM and OAM of nonlinear signals in harmonic generation processes with conventional nonlinear materials. Here, we report the generation of spin-controlled OAM of light in harmonic generations by using ultrathin photonic metasurfaces. The spin manipulation of OAM mode of harmonic waves is experimentally verified by using second harmonic generation (SHG) from gold meta-atom with 3-fold rotational symmetry. By introducing nonlinear phase singularity into the metasurface devices, we successfully generate and measure the topological charges of spin-controlled OAM mode of SHG through an on-chip metasurface interferometer. The nonlinear photonic metasurface proposed in this work not only opens new avenues for manipulating the OAM of nonlinear optical signals but also benefits the understanding of the nonlinear spin-orbit interaction of light in nanoscale devices.

Numerical investigation of frequency spectrum in the Hasegawa-Wakatani model

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

Kim, Juhyung; Terry, P. W.

2013-10-15

The wavenumber-frequency spectrum of the two-dimensional Hasegawa-Wakatani model is investigated in the hydrodynamic, intermediate, and adiabatic regimes. A nonlinear frequency and a line width related to energy transfer properties provide a measure of the average frequency and spectral broadening, respectively. In the adiabatic regime, narrow spectra, typical of wave turbulence, are observed with a nonlinear frequency shift in the electron drift direction. In the hydrodynamic regime, broad spectra with almost zero nonlinear frequencies are observed. Nonlinear frequency shifts are shown to be related to nonlinear energy transfer by vorticity advection through the high frequency region of the spectrum. In themore » intermediate regime, the nonlinear frequency shift for density fluctuations is observed to be weaker than that of electrostatic potential fluctuations. The weaker frequency shift of the density fluctuations is due to nonlinear density advection, which favors energy transfer in the low frequency range. Both the nonlinear frequency and the spectral width increase with poloidal wavenumber k{sub y}. In addition, in the adiabatic regime where the nonlinear interactions manifest themselves in the nonlinear frequency shift, the cross-phase between the density and potential fluctuations is observed to match a linear relation, but only if the linear response of the linearly stable eigenmode branch is included. Implications of these numerical observations are discussed.« less

Emergent universe with wormholes in massive gravity

NASA Astrophysics Data System (ADS)

Paul, B. C.; Majumdar, A. S.

2018-03-01

An emergent universe (EU) scenario is proposed to obtain a universe free from big-bang singularity. In this framework the present universe emerged from a static Einstein universe phase in the infinite past. A flat EU scenario is found to exist in Einstein’s gravity with a non-linear equation of state (EoS). It has been shown subsequently that a physically realistic EU model can be obtained considering cosmic fluid composed of interacting fluids with a non-linear equation of state. It results a viable cosmological model accommodating both early inflation and present accelerating phases. In the present paper, the origin of an initial static Einstein universe needed in the EU model is explored in a massive gravity theory which subsequently emerged to be a dynamically evolving universe. A new gravitational instanton solution in a flat universe is obtained in the massive gravity theory which is a dynamical wormhole that might play an important role in realizing the origin of the initial state of the emergent universe. The emergence of a Lorentzian universe from a Euclidean gravity is understood by a Wick rotation τ = i t . A universe with radiation at the beginning finally transits into the present observed universe with a non-linear EoS as the interactions among the fluids set in. Thus a viable flat EU scenario where the universe stretches back into time infinitely, with no big bang is permitted in a massive gravity.

Interacting dark energy: Dynamical system analysis

NASA Astrophysics Data System (ADS)

Golchin, Hanif; Jamali, Sara; Ebrahimi, Esmaeil

We investigate the impacts of interaction between dark matter (DM) and dark energy (DE) in the context of two DE models, holographic (HDE) and ghost dark energy (GDE). In fact, using the dynamical system analysis, we obtain the cosmological consequence of several interactions, considering all relevant component of universe, i.e. matter (dark and luminous), radiation and DE. Studying the phase space for all interactions in detail, we show the existence of unstable matter-dominated and stable DE-dominated phases. We also show that linear interactions suffer from the absence of standard radiation-dominated epoch. Interestingly, this failure resolved by adding the nonlinear interactions to the models. We find an upper bound for the value of the coupling constant of the interaction between DM and DE as b < 0.57in the case of holographic model, and b < 0.61 in the case of GDE model, to result in a cosmological viable matter-dominated epoch. More specifically, this bound is vital to satisfy instability and deceleration of matter-dominated epoch.

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.

Flat nonlinear optics: metasurfaces for efficient frequency mixing

NASA Astrophysics Data System (ADS)

Nookala, Nishant; Lee, Jongwon; Liu, Yingnan; Bishop, Wells; Tymchenko, Mykhailo; Gomez-Diaz, J. Sebastian; Demmerle, Frederic; Boehm, Gerhard; Amann, Markus-Christian; Wolf, Omri; Brener, Igal; Alu, Andrea; Belkin, Mikhail A.

2017-02-01

Gradient metasurfaces, or ultrathin optical components with engineered transverse impedance gradients along the surface, are able to locally control the phase and amplitude of the scattered fields over subwavelength scales, enabling a broad range of linear components in a flat, integrable platform1-4. On the contrary, due to the weakness of their nonlinear optical responses, conventional nonlinear optical components are inherently bulky, with stringent requirements associated with phase matching and poor control over the phase and amplitude of the generated beam. Nonlinear metasurfaces have been recently proposed to enable frequency conversion in thin films without phase-matching constraints and subwavelength control of the local nonlinear phase5-8. However, the associated optical nonlinearities are far too small to produce significant nonlinear conversion efficiency and compete with conventional nonlinear components for pump intensities below the materials damage threshold. Here, we report multi-quantum-well based gradient nonlinear metasurfaces with second-order nonlinear susceptibility over 106 pm/V for second harmonic generation at a fundamental pump wavelength of 10 μm, 5-6 orders of magnitude larger than traditional crystals. Further, we demonstrate the efficacy of this approach to designing metasurfaces optimized for frequency conversion over a large range of wavelengths, by reporting multi-quantum-well and metasurface structures optimized for a pump wavelength of 6.7 μm. Finally, we demonstrate how the phase of this nonlinearly generated light can be locally controlled well below the diffraction limit using the Pancharatnam-Berry phase approach5,7,9, opening a new paradigm for ultrathin, flat nonlinear optical components.

Laser Imaging of Airborne Acoustic Emission by Nonlinear Defects

NASA Astrophysics Data System (ADS)

Solodov, Igor; Döring, Daniel; Busse, Gerd

2008-06-01

Strongly nonlinear vibrations of near-surface fractured defects driven by an elastic wave radiate acoustic energy into adjacent air in a wide frequency range. The variations of pressure in the emitted airborne waves change the refractive index of air thus providing an acoustooptic interaction with a collimated laser beam. Such an air-coupled vibrometry (ACV) is proposed for detecting and imaging of acoustic radiation of nonlinear spectral components by cracked defects. The photoelastic relation in air is used to derive induced phase modulation of laser light in the heterodyne interferometer setup. The sensitivity of the scanning ACV to different spatial components of the acoustic radiation is analyzed. The animated airborne emission patterns are visualized for the higher harmonic and frequency mixing fields radiated by planar defects. The results confirm a high localization of the nonlinear acoustic emission around the defects and complicated directivity patterns appreciably different from those observed for fundamental frequencies.

Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model

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

Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br; Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de

2015-04-15

We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the fullmore » synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.« less

Multimodal Pressure-Flow Analysis: Application of Hilbert Huang Transform in Cerebral Blood Flow Regulation

NASA Astrophysics Data System (ADS)

Lo, Men-Tzung; Hu, Kun; Liu, Yanhui; Peng, C.-K.; Novak, Vera

2008-12-01

Quantification of nonlinear interactions between two nonstationary signals presents a computational challenge in different research fields, especially for assessments of physiological systems. Traditional approaches that are based on theories of stationary signals cannot resolve nonstationarity-related issues and, thus, cannot reliably assess nonlinear interactions in physiological systems. In this review we discuss a new technique called multimodal pressure flow (MMPF) method that utilizes Hilbert-Huang transformation to quantify interaction between nonstationary cerebral blood flow velocity (BFV) and blood pressure (BP) for the assessment of dynamic cerebral autoregulation (CA). CA is an important mechanism responsible for controlling cerebral blood flow in responses to fluctuations in systemic BP within a few heart-beats. The MMPF analysis decomposes BP and BFV signals into multiple empirical modes adaptively so that the fluctuations caused by a specific physiologic process can be represented in a corresponding empirical mode. Using this technique, we showed that dynamic CA can be characterized by specific phase delays between the decomposed BP and BFV oscillations, and that the phase shifts are significantly reduced in hypertensive, diabetics and stroke subjects with impaired CA. Additionally, the new technique can reliably assess CA using both induced BP/BFV oscillations during clinical tests and spontaneous BP/BFV fluctuations during resting conditions.

Quadratic spatial soliton interactions

NASA Astrophysics Data System (ADS)

Jankovic, Ladislav

Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30 degrees rotation, was measured in the experiments performed. The parameters relevant for characterizing soliton collision processes were also studied in detail. Measurements were performed for various collision angles (from 0.2 to 4 degrees), phase mismatch, relative phase between the solitons and the distance to the collision point within the sample (which affects soliton formation). Both the individual and combined effects of these collision variables were investigated. Based on the research conducted, several all-optical switching scenarios were proposed.

Nonlinear absorption of short intense laser pulse in multispecies plasma

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

Kargarian, A.; Hajisharifi, K.; Mehdian, H.

In the present paper, the detailed investigation concerning the effect of inclusion of heavy negative ions into the finite background plasma on the laser absorption has been carried out by employing particle-in-cell simulation method. For this purpose, in this configuration, the laser energy absorption relying on the nonlinear phenomena such as phase-mixing, wave-breaking, and scattering has been studied in the Raman-Brillouin regime. It is shown that the inclusion of heavy negative ions suppresses the scattering while increases the phase-mixing time. Moreover, it is illustrated that this inclusion can increase the laser absorption in finite plasma environment, after saturation. The obtainedmore » results are expected to be relevant to the experiments on the mass spectrometry with laser desorption techniques as well as on the laser-plasma interaction with application to particles acceleration.« less

Experimental implementation of phase locking in a nonlinear interferometer

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

Wang, Hailong; Jing, Jietai, E-mail: jtjing@phy.ecnu.edu.cn; Marino, A. M.

2015-09-21

Based upon two cascade four-wave mixing processes in two identical hot rubidium vapor cells, a nonlinear interferometer has been experimentally realized [Jing et al., Appl. Phys. Lett. 99, 011110 (2011); Hudelist et al., Nat. Commun. 5, 3049 (2014)]. It has a higher degree of phase sensitivity than a traditional linear interferometer and has many potential applications in quantum metrology. Phase locking of the nonlinear interferometer is needed before it can find its way into applications. In this letter, we investigate the experimental implementation of phase locking of the relative phase between the three beams at different frequencies involved in suchmore » a nonlinear interferometer. We have utilized two different methods, namely, beat note locking and coherent modulation locking. We find that coherent modulation locking can achieve much better phase stability than beat note locking in our system. Our results pave the way for real applications of a nonlinear interferometer in precision measurement and quantum manipulation, for example, phase control in phase-sensitive N-wave mixing process, N-port nonlinear interferometer and quantum-enhanced real-time phase tracking.« less

Nonlinear THz absorption and cyclotron resonance in InSb

NASA Astrophysics Data System (ADS)

Heffernan, Kate; Yu, Shukai; Talbayev, Diyar

The emergence of coherent high-field terahertz (THz) sources in the past decade has allowed the exploration of nonlinear light-matter interaction at THz frequencies. Nonlinear THz response of free electrons in semiconductors has received a great deal of attention. Such nonlinear phenomena as saturable absorption and self-phase modulation have been reported. InSb is a narrow-gap (bandgap 0.17 eV) semiconductor with a very low electron effective mass and high electron mobility. Previous high-field THz work on InSb reported the observation of ultrafast electron cascades via impact ionization. We study the transmission of an intense THz electric field pulse by an InSb wafer at different incident THz amplitudes and 10 K temperature. Contrary to previous reports, we observe an increased transmission at higher THz field. Our observation appears similar to the saturable THz absorption reported in other semiconductors. Along with the increased absorption, we observe a strong modulation of the THz phase at high incident fields, most likely due to the self-phase modulation of the THz pulse. We also study the dependence of the cyclotron resonance on the incident THz field amplitude. The cyclotron resonance exhibits a lower strength and frequency at the higher incident THz field. The work at Tulane was supported by the Louisiana Board of Regents through the Board of Regents Support Fund Contract No. LEQSF(2012-15)-RD-A-23 and through the Pilot Funding for New Research (PFund) Contract No. LEQSF-EPS(2014)-PFUND-378.

Microwave phase conjugation using artificial nonlinear microwave surfaces

NASA Astrophysics Data System (ADS)

Chang, Yian

1997-09-01

A new technique is developed and demonstrated to simulate nonlinear materials in the microwave and millimeter wave regime. Such materials are required to extend nonlinear optical techniques into longer wavelength areas. Using an array of antenna coupled mixers as an artificial nonlinear surface, we have demonstrated two-dimensional free space microwave phase conjugation at 10 GHz. The basic concept is to replace the weak nonlinearity of electron distribution in a crystal with the strong nonlinear V-I response of a P-N junction. This demnstration uses a three-wave mixing method with the effective nonlinear susceptibility χ(2) provided by an artificial nonlinear surface. The pump signal at 2ω (20 GHz) can be injected to the mixing elements electrically or optically. Electrical injection was first used to prove the concept of artificial nonlinear surfaces. However, due to the loss and size of microwave components, electrical injection is not practical for an array of artificial nonlinear surfaces, as would be needed in a three-dimensional free space phase conjugation setup. Therefore optical injection was implemented to carry the 2ω microwave pump signal in phase to all mixing elements. In both cases, two-dimensional free space phase conjugation was observed by directly measuring the electric field amplitude and phase distribution. The electric field wavefronts exhibited retro-directivity and auto- correction characteristics of phase conjugation. This demonstration surface also shows a power gain of 10 dB, which is desired for potential communication applications.

Purely hydrodynamic ordering of rotating disks at a finite Reynolds number.

PubMed

Goto, Yusuke; Tanaka, Hajime

2015-01-28

Self-organization of moving objects in hydrodynamic environments has recently attracted considerable attention in connection to natural phenomena and living systems. However, the underlying physical mechanism is much less clear due to the intrinsically nonequilibrium nature, compared with self-organization of thermal systems. Hydrodynamic interactions are believed to play a crucial role in such phenomena. To elucidate the fundamental physical nature of many-body hydrodynamic interactions at a finite Reynolds number, here we study a system of co-rotating hard disks in a two-dimensional viscous fluid at zero temperature. Despite the absence of thermal noise, this system exhibits rich phase behaviours, including a fluid state with diffusive dynamics, a cluster state, a hexatic state, a glassy state, a plastic crystal state and phase demixing. We reveal that these behaviours are induced by the off-axis and many-body nature of nonlinear hydrodynamic interactions and the finite time required for propagating the interactions by momentum diffusion.

Diagnosis of Magnetic Structures and Intermittency in Space Plasma Turbulence using the Method of Surrogate Data

NASA Technical Reports Server (NTRS)

Sahraoui, Fouad; Goldstein, Melvyn

2008-01-01

Several observations in space plasmas have reported the presence of coherent structures at different plasma scales. Structure formation is believed to be a direct consequence of nonlinear interactions between the plasma modes, which depend strongly on phase synchronization of those modes. Despite this important role of the phases in turbulence, very limited work has been however devoted to study the phases as a potential tracers of nonlinearities in comparison with the wealth of literature on power spectra of turbulence where phases are totally missed. We present a method based on surrogate data to systematically detect coherent structures in turbulent signals. The new method has been applied successfully to magnetosheath turbulence (Sahraoui, Phys. Rev. E, 2008, in press), where the relationship between the identified phase coherence and intermittency (classically identified as non Gaussian tails of the PDFs) as well as the energy cascade has been studied. Here we review the main results obtained in that study and show further applications to small scale solar wind turbulence. Implications of the results on theoretical modelling of space turbulence (applicability of weak/wave turbulence, its validity limits and its connection to intermittency) will be discussed.

Ontology of Earth's nonlinear dynamic complex systems

NASA Astrophysics Data System (ADS)

Babaie, Hassan; Davarpanah, Armita

2017-04-01

As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.

Simultaneous polarization-insensitive phase-space trans-multiplexing and wavelength multicasting via cross-phase modulation in a photonic crystal fiber at 10 GBd

NASA Astrophysics Data System (ADS)

Cannon, Brice M.

This thesis investigates the all-optical combination of amplitude and phase modulated signals into one unified multi-level phase modulated signal, utilizing the Kerr nonlinearity of cross-phase modulation (XPM). Predominantly, the first experimental demonstration of simultaneous polarization-insensitive phase-transmultiplexing and multicasting (PI-PTMM) will be discussed. The PI-PTMM operation combines the data of a single 10-Gbaud carrier-suppressed return-to-zero (CSRZ) on-off keyed (OOK) pump signal and 4x10-Gbaud return-to-zero (RZ) binary phase-shift keyed (BPSK) probe signals to generate 4x10-GBd RZ-quadrature phase-shift keyed (QPSK) signals utilizing a highly nonlinear, birefringent photonic crystal fiber (PCF). Since XPM is a highly polarization dependent nonlinearity, a polarization sensitivity reduction technique was used to alleviate the fluctuations due to the remotely generated signals' unpredictable states of polarization (SOP). The measured amplified spontaneous emission (ASE) limited receiver sensitivity optical signal-to-noise ratio (OSNR) penalty of the PI-PTMM signal relative to the field-programmable gate array (FPGA) pre-coded RZ-DQPSK baseline at a forward-error correction (FEC) limit of 10-3 BER was ≈ 0.3 dB. In addition, the OSNR of the remotely generated CSRZ-OOK signal could be degraded to ≈ 29 dB/0.1nm, before the bit error rate (BER) performance of the PI-PTMM operation began to exponentially degrade. A 138-km dispersion-managed recirculating loop system with a 100-GHz, 13-channel mixed-format dense-wavelength-division multiplexed (DWDM) transmitter was constructed to investigate the effect of metro/long-haul transmission impairments. The PI-PTMM DQPSK and the FPGA pre-coded RZ-DQPSK baseline signals were transmitted 1,900 km and 2,400 km in the nonlinearity-limited transmission regime before reaching the 10-3 BER FEC limit. The relative reduction in transmission distance for the PI-PTMM signal was due to the additional transmitter impairments in the PCF that interact negatively with the transmission fiber.

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

PubMed

Chen, Yong; Yan, Zhenya

2016-03-22

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

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

PubMed Central

Chen, Yong; Yan, Zhenya

2016-01-01

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

Achieving nonlinear optical modulation via four-wave mixing in a four-level atomic system

NASA Astrophysics Data System (ADS)

Li, Hai-Chao; Ge, Guo-Qin; Zubairy, M. Suhail

2018-05-01

We propose an accessible scheme for implementing tunable nonlinear optical amplification and attenuation via a synergetic mechanism of four-wave mixing (FWM) and optical interference in a four-level ladder-type atomic system. By constructing a cyclic atom-field interaction, we show that two reverse FWM processes can coexist via optical transitions in different branches. In the suitable input-field conditions, strong interference effects between the input fields and the generated FWM fields can be induced and result in large amplification and deep attenuation of the output fields. Moreover, such an optical modulation from enhancement to suppression can be controlled by tuning the relative phase. The quantum system can be served as a switchable optical modulator with potential applications in quantum nonlinear optics.

Isoscalar-vector interaction and hybrid quark core in massive neutron stars

NASA Astrophysics Data System (ADS)

Shao, G. Y.; Colonna, M.; Di Toro, M.; Liu, Y. X.; Liu, B.

2013-05-01

The hadron-quark phase transition in the core of massive neutron stars is studied with a newly constructed two-phase model. For nuclear matter, a nonlinear Walecka type model with general nucleon-meson and meson-meson couplings, recently calibrated by Steiner, Hemper and Fischer, is taken. For quark matter, a modified Polyakov-Nambu—Jona-Lasinio model, which gives consistent results with lattice QCD data, is used. Most importantly, we introduce an isoscalar-vector interaction in the description of quark matter, and we study its influence on the hadron-quark phase transition in the interior of massive neutron stars. With the constraints of neutron star observations, our calculation shows that the isoscalar-vector interaction between quarks is indispensable if massive hybrids star exist in the universe, and its strength determines the onset density of quark matter, as well as the mass-radius relations of hybrid stars. Furthermore, as a connection with heavy-ion-collision experiments we give some discussions about the strength of isoscalar-vector interaction and its effect on the signals of hadron-quark phase transition in heavy-ion collisions, in the energy range of the NICA at JINR-Dubna and FAIR at GSI-Darmstadt facilities.

Phase transition of light in cavity QED lattices.

PubMed

Schiró, M; Bordyuh, M; Oztop, B; Türeci, H E

2012-08-03

Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.

Chorus Waves Modulation of Langmuir Waves in the Radiation Belts

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

Li, Jinxing; Bortnik, Jacob; An, Xin

Using high-resolution waveforms measured by the Van Allen Probes, we report a novel observation in the radiation belts. Namely, we show that multiband, discrete, rising-tone whistler-mode chorus emissions exhibit a one-to-one correlation with Langmuir wave bursts. Moreover, the periodic Langmuir wave bursts are generally observed at the phase location where the chorus wave E || component is oriented opposite to its propagation direction. The electron measurements show a beam in phase space density at the particle velocity that matches the parallel phase velocity of the chorus waves. Based on this evidence, we conclude that the chorus waves accelerate the suprathermalmore » electrons via Landau resonance, and generate a localized electron beam in phase space density. Consequently, the Langmuir waves are excited locally and are modulated by the chorus wave phase. As a result, this microscale interaction between chorus waves and high frequency electrostatic waves provides a new insight into the nonlinear wave-particle interaction process.« less

Chorus Waves Modulation of Langmuir Waves in the Radiation Belts

DOE PAGES

Li, Jinxing; Bortnik, Jacob; An, Xin; ...

2017-11-20

Using high-resolution waveforms measured by the Van Allen Probes, we report a novel observation in the radiation belts. Namely, we show that multiband, discrete, rising-tone whistler-mode chorus emissions exhibit a one-to-one correlation with Langmuir wave bursts. Moreover, the periodic Langmuir wave bursts are generally observed at the phase location where the chorus wave E || component is oriented opposite to its propagation direction. The electron measurements show a beam in phase space density at the particle velocity that matches the parallel phase velocity of the chorus waves. Based on this evidence, we conclude that the chorus waves accelerate the suprathermalmore » electrons via Landau resonance, and generate a localized electron beam in phase space density. Consequently, the Langmuir waves are excited locally and are modulated by the chorus wave phase. As a result, this microscale interaction between chorus waves and high frequency electrostatic waves provides a new insight into the nonlinear wave-particle interaction process.« less

A Resonator for Low-Threshold Frequency Conversion

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction

NASA Technical Reports Server (NTRS)

Parker, B. Eugene, Jr.; Cellucci, Richard L.; Abbott, Dean W.; Barron, Roger L.; Jordan, Paul R., III; Poor, H. Vincent

1993-01-01

The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.

Soliton excitations and interactions for the three-coupled fourth-order nonlinear Schrödinger equations in the alpha helical proteins

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Tian, Bo; Wang, Yu-Feng; Zhen, Hui-Ling

2015-06-01

Three-coupled fourth-order nonlinear Schrödinger equations describe the dynamics of alpha helical proteins with the interspine coupling at the higher order. Through symbolic computation and binary Bell-polynomial approach, bilinear forms and N-soliton solutions for such equations are constructed. Key point lies in the introduction of auxiliary functions in the Bell-polynomial expression. Asymptotic analysis is applied to investigate the elastic interaction between the two solitons: two solitons keep their original amplitudes, energies and velocities invariant after the interaction except for the phase shifts. Soliton amplitudes are related to the energy distributed in the solitons of the three spines. Overtaking interaction, head-on interaction and bound-state solitons of two solitons are given. Bound states of three bright solitons arise when all of them propagate in parallel. Elastic interaction between the bound-state solitons and one bright soliton is shown. Increase of the lattice parameter can lead to the increase of the soliton velocity, that is, the interaction period becomes shorter. The solitons propagating along the neighbouring spines are found to interact elastically. Those solitons, exhibited in this paper, might be viewed as a possible carrier of bio-energy transport in the protein molecules.

A method searching for optimum fractional order and its application in self-phase modulation induced nonlinear phase noise estimation in coherent optical fiber transmission systems

NASA Astrophysics Data System (ADS)

Huang, Chuan; Guo, Peng; Yang, Aiying; Qiao, Yaojun

2018-07-01

In single channel systems, the nonlinear phase noise only comes from the channel itself through self-phase modulation (SPM). In this paper, a fast-nonlinear effect estimation method is proposed based on fractional Fourier transformation (FrFT). The nonlinear phase noise caused by Self-phase modulation effect is accurately estimated for single model 10Gbaud OOK and RZ-QPSK signals with the fiber length range of 0-200 km and the launch power range of 1-10 mW. The pulse windowing is adopted to search the optimum fractional order for the OOK and RZ-QPSK signals. Since the nonlinear phase shift caused by the SPM effect is very small, the accurate optimum fractional order of the signal cannot be found based on the traditional method. In this paper, a new method magnifying the phase shift is proposed to get the accurate optimum order and thus the nonlinear phase shift is calculated. The simulation results agree with the theoretical analysis and the method is applicable to signals whose pulse type has the similar characteristics with Gaussian pulse.

Coherent structures in interacting vortex rings

NASA Astrophysics Data System (ADS)

Deng, Jian; Xue, Jingyu; Mao, Xuerui; Caulfield, C. P.

2017-02-01

We investigate experimentally the nonlinear structures that develop from interacting vortex rings induced by a sinusoidally oscillating ellipsoidal disk in fluid at rest. We vary the scaled amplitude or Keulegan-Carpenter number 0.3

A fluid-structure interaction model of soft robotics using an active strain approach

NASA Astrophysics Data System (ADS)

Hess, Andrew; Lin, Zhaowu; Gao, Tong

2017-11-01

Soft robotic swimmers exhibit rich dynamics that stem from the non-linear interplay of the fluid and immersed soft elastic body. Due to the difficulty of handling the nonlinear two-way coupling of hydrodynamic flow and deforming elastic body, studies of flexible swimmers often employ either one-way coupling strategies with imposed motions of the solid body or some simplified elasticity models. To explore the nonlinear dynamics of soft robots powered by smart soft materials, we develop a computational model to deal with the two-way fluid/elastic structure interactions using the fictitious domain method. To mimic the dynamic response of the functional soft material under external actuations, we assume the solid phase to be neo-Hookean, and employ an active strain approach to incorporate actuation, which is based on the multiplicative decomposition of the deformation gradient tensor. We demonstrate the capability of our algorithm by performing a series of numerical explorations that manipulate an elastic structure with finite thickness, starting from simple rectangular or circular plates to soft robot prototypes such as stingrays and jellyfish.

Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering

NASA Astrophysics Data System (ADS)

Maiden, M. D.; Bookman, L. D.; Hoefer, M. A.

2014-05-01

The interaction behaviors of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particle-like, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet.

Topological charge algebra of optical vortices in nonlinear interactions.

PubMed

Zhdanova, Alexandra A; Shutova, Mariia; Bahari, Aysan; Zhi, Miaochan; Sokolov, Alexei V

2015-12-28

We investigate the transfer of orbital angular momentum among multiple beams involved in a coherent Raman interaction. We use a liquid crystal light modulator to shape pump and Stokes beams into optical vortices with various integer values of topological charge, and cross them in a Raman-active crystal to produce multiple Stokes and anti-Stokes sidebands. We measure the resultant vortex charges using a tilted-lens technique. We verify that in every case the generated beams' topological charges obey a simple relationship, resulting from angular momentum conservation for created and annihilated photons, or equivalently, from phase-matching considerations for multiple interacting beams.

Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging

NASA Astrophysics Data System (ADS)

Szigeti, S. S.; Hush, M. R.; Carvalho, A. R. R.; Hope, J. J.

2010-10-01

The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.80.013614 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-field (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.

Feedback control of an interacting Bose-Einstein condensate using phase-contrast imaging

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

Szigeti, S. S.; Hush, M. R.; Carvalho, A. R. R.

2010-10-15

The linewidth of an atom laser is limited by density fluctuations in the Bose-Einstein condensate (BEC) from which the atom laser beam is outcoupled. In this paper we show that a stable spatial mode for an interacting BEC can be generated using a realistic control scheme that includes the effects of the measurement backaction. This model extends the feedback theory, based on a phase-contrast imaging setup, presented by Szigeti, Hush, Carvalho, and Hope [Phys. Rev. A 80, 013614 (2009)]. In particular, it is applicable to a BEC with large interatomic interactions and solves the problem of inadequacy of the mean-fieldmore » (coherent state) approximation by utilizing a fixed number state approximation. Our numerical analysis shows the control to be more effective for a condensate with a large nonlinearity.« less

Analysis of wheezes using wavelet higher order spectral features.

PubMed

Taplidou, Styliani A; Hadjileontiadis, Leontios J

2010-07-01

Wheezes are musical breath sounds, which usually imply an existing pulmonary obstruction, such as asthma and chronic obstructive pulmonary disease (COPD). Although many studies have addressed the problem of wheeze detection, a limited number of scientific works has focused in the analysis of wheeze characteristics, and in particular, their time-varying nonlinear characteristics. In this study, an effort is made to reveal and statistically analyze the nonlinear characteristics of wheezes and their evolution over time, as they are reflected in the quadratic phase coupling of their harmonics. To this end, the continuous wavelet transform (CWT) is used in combination with third-order spectra to define the analysis domain, where the nonlinear interactions of the harmonics of wheezes and their time variations are revealed by incorporating instantaneous wavelet bispectrum and bicoherence, which provide with the instantaneous biamplitude and biphase curves. Based on this nonlinear information pool, a set of 23 features is proposed for the nonlinear analysis of wheezes. Two complementary perspectives, i.e., general and detailed, related to average performance and to localities, respectively, were used in the construction of the feature set, in order to embed trends and local behaviors, respectively, seen in the nonlinear interaction of the harmonic elements of wheezes over time. The proposed feature set was evaluated on a dataset of wheezes, acquired from adult patients with diagnosed asthma and COPD from a lung sound database. The statistical evaluation of the feature set revealed discrimination ability between the two pathologies for all data subgroupings. In particular, when the total breathing cycle was examined, all 23 features, but one, showed statistically significant difference between the COPD and asthma pathologies, whereas for the subgroupings of inspiratory and expiratory phases, 18 out of 23 and 22 out of 23 features exhibited discrimination power, respectively. This paves the way for the use of the wavelet higher order spectral features as an input vector to an efficient classifier. Apparently, this would integrate the intrinsic characteristics of wheezes within computerized diagnostic tools toward their more efficient evaluation.

Electromechanical modelling and design for phase control of locked modes in the DIII-D tokamak

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

Olofsson, K. E. J.; Choi, W.; Humphreys, D. A.

A basic nonlinear electromechanical model is developed for the interaction between a pre-existing near-saturated tearing-mode, a conducting wall, active coils internal to the wall, and active coils external to the wall. The tearing-mode is represented by a perturbed helical surface current and its island has a small but finite moment of inertia. The model is shown to have several properties that are qualitatively consistent with the experimental observations of mode-wall and mode-coil interactions. The main purpose of the model is to guide the design of a phase control system for locked modes (LMs) in tokamaks. Such a phase controller maymore » become an important component in integrated disruption avoidance systems. A realistic feedback controller for the LM phase is designed and tested for the electromechanical model. The results indicate that a simple fixed-gain controller can perform phase control of LMs with a range of sizes, and at arbitrary misalignment relative to a realistically dimensioned background error field. Finally, the basic model is expected to be a useful minimal dynamical system representation also for other aspects of mode-wall-coil interactions.« less

Electromechanical modelling and design for phase control of locked modes in the DIII-D tokamak

DOE PAGES

Olofsson, K. E. J.; Choi, W.; Humphreys, D. A.; ...

2016-02-05

A basic nonlinear electromechanical model is developed for the interaction between a pre-existing near-saturated tearing-mode, a conducting wall, active coils internal to the wall, and active coils external to the wall. The tearing-mode is represented by a perturbed helical surface current and its island has a small but finite moment of inertia. The model is shown to have several properties that are qualitatively consistent with the experimental observations of mode-wall and mode-coil interactions. The main purpose of the model is to guide the design of a phase control system for locked modes (LMs) in tokamaks. Such a phase controller maymore » become an important component in integrated disruption avoidance systems. A realistic feedback controller for the LM phase is designed and tested for the electromechanical model. The results indicate that a simple fixed-gain controller can perform phase control of LMs with a range of sizes, and at arbitrary misalignment relative to a realistically dimensioned background error field. Finally, the basic model is expected to be a useful minimal dynamical system representation also for other aspects of mode-wall-coil interactions.« less

Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficient

NASA Astrophysics Data System (ADS)

Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.

2017-09-01

We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.

2 + 1 dimensional de Sitter universe emerging from the gauge structure of a nonlinear quantum system.

PubMed

Kam, Chon-Fai; Liu, Ren-Bao

2017-08-29

Berry phases and gauge structures are fundamental quantum phenomena. In linear quantum mechanics the gauge field in parameter space presents monopole singularities where the energy levels become degenerate. In nonlinear quantum mechanics, which is an effective theory of interacting quantum systems, there can be phase transitions and hence critical surfaces in the parameter space. We find that these critical surfaces result in a new type of gauge field singularity, namely, a conic singularity that resembles the big bang of a 2 + 1 dimensional de Sitter universe, with the fundamental frequency of Bogoliubov excitations acting as the cosmic scale, and mode softening at the critical surface, where the fundamental frequency vanishes, causing a causal singularity. Such conic singularity may be observed in various systems such as Bose-Einstein condensates and molecular magnets. This finding offers a new approach to quantum simulation of fundamental physics.

KEEN Wave Simulations: Comparing various PIC to various fixed grid Vlasov to Phase-Space Adaptive Sparse Tiling & Effective Lagrangian (PASTEL) Techniques

NASA Astrophysics Data System (ADS)

Afeyan, Bedros; Larson, David; Shadwick, Bradley; Sydora, Richard

2017-10-01

We compare various ways of solving the Vlasov-Poisson and Vlasov-Maxwell equations on rather demanding nonlinear kinetic phenomena associated with KEEN and KEEPN waves. KEEN stands for Kinetic, Electrostatic, Electron Nonlinear, and KEEPN, for electron-positron or pair plasmas analogs. Because these self-organized phase space structures are not steady-state, or single mode, or fluid or low order moment equation limited, typical techniques with low resolution or too much noise will distort the answer too much, too soon, and fail. This will be shown via Penrose criteria triggers for instability at the formation stage as well as particle orbit statistics in fully formed KEEN waves and KEEN-KEEN and KEEN-EPW interacting states. We will argue that PASTEL is a viable alternative to traditional methods with reasonable chances of success in higher dimensions. Work supported by a Grant from AFOSR PEEP.

Oblique Interaction of Dust-ion Acoustic Solitons with Superthermal Electrons in a Magnetized Plasma

NASA Astrophysics Data System (ADS)

Parveen, Shahida; Mahmood, Shahzad; Adnan, Muhammad; Qamar, Anisa

2018-01-01

The oblique interaction between two dust-ion acoustic (DIA) solitons travelling in the opposite direction, in a collisionless magnetized plasma composed of dynamic ions, static dust (positive/negative) charged particles and interialess kappa distributed electrons is investigated. By employing extended Poincaré-Lighthill-Kuo (PLK) method, Korteweg-de Vries (KdV) equations are derived for the right and left moving low amplitude DIA solitons. Their trajectories and corresponding phase shifts before and after their interaction are also obtained. It is found that in negatively charged dusty plasma above the critical dust charged to ion density ratio the positive polarity pulse is formed, while below the critical dust charged density ratio the negative polarity pulse of DIA soliton exist. However it is found that only positive polarity pulse of DIA solitons exist for the positively charged dust particles case in a magnetized nonthermal plasma. The nonlinearity coefficient in the KdV equation vanishes for the negatively charged dusty plasma case for a particular set of parameters. Therefore, at critical plasma density composition for negatively charged dust particles case, the modified Korteweg-de Vries (mKdV) equations having cubic nonlinearity coefficient of the DIA solitons, and their corresponding phase shifts are derived for the left and right moving solitons. The effects of the system parameters including the obliqueness of solitons propagation with respect to magnetic field direction, superthermality of electrons and concentration of positively/negatively static dust charged particles on the phase shifts of the colliding solitons are also discussed and presented numerically. The results are applicable to space magnetized dusty plasma regimes.

Nonlinear shallow ocean-wave soliton interactions on flat beaches.

PubMed

Ablowitz, Mark J; Baldwin, Douglas E

2012-09-01

Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.

A new class of non-topological solitons

NASA Technical Reports Server (NTRS)

Frieman, Joshua A.; Lynn, Bryan W.

1989-01-01

A class of non-topological solitons was constructed in renormalizable scalar field theories with nonlinear self-interactions. For large charge Q, the soliton mass increases linearly with Q, i.e., the soliton mass density is approximately independent of charge. Such objects could be naturally produced in a phase transition in the early universe or in the decay of superconducting cosmic strings.

Helmholtz dark solitons.

PubMed

Chamorro-Posada, P; McDonald, G S

2003-05-15

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

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.

Electron transport near the Mott transition in n-GaAs and n-GaN

NASA Astrophysics Data System (ADS)

Romanets, P. N.; Sachenko, A. V.

2016-01-01

In this paper, we study the temperature dependence of the conductivity and the Hall coefficient near the metal-insulator phase transition. A theoretical investigation is performed within the effective mass approximation. The variational method is used to calculate the eigenvalues and eigenfunctions of the impurity states. Unlike previous studies, we have included nonlinear corrections to the screened impurity potential, because the Thomas-Fermi approximation is incorrect for the insulator phase. It is also shown that near the phase transition the exchange interaction is essential. The obtained temperature dependencies explain several experimental measurements in gallium arsenide (GaAs) and gallium nitride (GaN).

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

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Nonlinear Talbot effect of rogue waves.

PubMed

Zhang, Yiqi; Belić, Milivoj R; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng

2014-03-01

Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.

Tide-surge interaction along the east coast of the Leizhou Peninsula, South China Sea

NASA Astrophysics Data System (ADS)

Zhang, Heng; Cheng, Weicong; Qiu, Xixi; Feng, Xiangbo; Gong, Wenping

2017-06-01

A triply-nested two-dimensional (2D) ocean circulation model along with observed sea level records are used to study tide-surge interaction along the east coast of the Leizhou Peninsula (LP) which is characterized by extensive mudflats, large tidal ranges and a complex coastline. The dependency of surge maxima on the water level and the phase of tide are respectively investigated using two statistical approaches. Results show that tide-surge interaction along the east coast of the LP is significant, where surges peak 3-6 h before or after the nearest high water. The triply-nested 2D ocean circulation model is used to quantify tide-surge interaction in this region and to investigate its physical cause. The largest amplitudes of tide-surge interaction are found in the shallow water region of the Leizhou Bay, with values up to 1 m during typhoon events. Numerical experiments reveal that nonlinear bottom friction is the main contributor to tide-surge interaction, while the contribution of the nonlinear advective effect can be neglected. The shallow water effect enhances the role of nonlinear bottom friction in determining tide-surge modulation, leaving the surge peaks usually occur on the rising or falling tide. It is also found that the relative contribution of local wind and remote wind is different depending on the storm track and storm intensity, which would finally affect the temporal and spatial distribution of tide-surge interaction during typhoon events. These findings confirm the importance of coupling storm surges and tides for the prediction of storm surge events in regions which are characterized by shallow water depths and large tidal ranges.

All-optical regenerator of multi-channel signals.

PubMed

Li, Lu; Patki, Pallavi G; Kwon, Young B; Stelmakh, Veronika; Campbell, Brandon D; Annamalai, Muthiah; Lakoba, Taras I; Vasilyev, Michael

2017-10-12

One of the main reasons why nonlinear-optical signal processing (regeneration, logic, etc.) has not yet become a practical alternative to electronic processing is that the all-optical elements with nonlinear input-output relationship have remained inherently single-channel devices (just like their electronic counterparts) and, hence, cannot fully utilise the parallel processing potential of optical fibres and amplifiers. The nonlinear input-output transfer function requires strong optical nonlinearity, e.g. self-phase modulation, which, for fundamental reasons, is always accompanied by cross-phase modulation and four-wave mixing. In processing multiple wavelength-division-multiplexing channels, large cross-phase modulation and four-wave mixing crosstalks among the channels destroy signal quality. Here we describe a solution to this problem: an optical signal processor employing a group-delay-managed nonlinear medium where strong self-phase modulation is achieved without such nonlinear crosstalk. We demonstrate, for the first time to our knowledge, simultaneous all-optical regeneration of up to 16 wavelength-division-multiplexing channels by one device. This multi-channel concept can be extended to other nonlinear-optical processing schemes.Nonlinear optical processing devices are not yet fully practical as they are single channel. Here the authors demonstrate all-optical regeneration of up to 16 channels by one device, employing a group-delay-managed nonlinear medium where strong self-phase modulation is achieved without nonlinear inter-channel crosstalk.

Quantitative theory of driven nonlinear brain dynamics.

PubMed

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

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

Wang, Lei; Kruk, Sergey; Koshelev, Kirill

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

PubMed

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

2018-06-13

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

Nonlinear Wavefront Control with All-Dielectric Metasurfaces

DOE PAGES

Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

2018-05-11

Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

Quantum annealing with all-to-all connected nonlinear oscillators

PubMed Central

Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L.; Blais, Alexandre

2017-01-01

Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine. PMID:28593952

Measurement of infrared optical constants with visible photons

NASA Astrophysics Data System (ADS)

Paterova, Anna; Yang, Hongzhi; An, Chengwu; Kalashnikov, Dmitry; Krivitsky, Leonid

2018-04-01

We demonstrate a new scheme for infrared spectroscopy with visible light sources and detectors. The technique relies on the nonlinear interference of correlated photons, produced via spontaneous parametric down conversion in a nonlinear crystal. Visible and infrared photons are split into two paths and the infrared photons interact with the sample under study. The photons are reflected back to the crystal, resembling a conventional Michelson interferometer. Interference of the visible photons is observed and it is dependent on the phases of all three interacting photons: pump, visible and infrared. The transmission coefficient and the refractive index of the sample in the infrared range can be inferred from the interference pattern of visible photons. The method does not require the use of potentially expensive and inefficient infrared detectors and sources, it can be applied to a broad variety of samples, and it does not require a priori knowledge of sample properties in the visible range.

Generation of localized patterns in anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion via a variational approach

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Tchakoutio Nguetcho, Aurélien S.

2018-05-01

We use the time-dependent variational method to examine the formation of localized patterns in dynamically unstable anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion. The governing equation is an extended nonlinear Schrödinger equation known for modified Frankel-Kontorova models of atomic lattices and here derived from an extended Bose-Hubbard model of bosonic lattices with local three-body interactions. In presence of modulated waves, we derive and investigate the ordinary differential equations for the time evolution of the amplitude and phase of dynamical perturbation. Through an effective potential, we find the modulationally unstable domains of the lattice and discuss the effect of the fourth-order dispersion in the dynamics. Direct numerical simulations are performed to support our analytical results, and a good agreement is found. Various types of localized patterns, including breathers and solitonic chirped-like pulses, form in the system as a result of interplay between the cubic-quintic nonlinearities and the second- and fourth-order dispersions.

Impairment assessment of orthogonal frequency division multiplexing over dispersion-managed links in backbone and backhaul networks

NASA Astrophysics Data System (ADS)

Tamilarasan, Ilavarasan; Saminathan, Brindha; Murugappan, Meenakshi

2016-04-01

The past decade has seen the phenomenal usage of orthogonal frequency division multiplexing (OFDM) in the wired as well as wireless communication domains, and it is also proposed in the literature as a future proof technique for the implementation of flexible resource allocation in cognitive optical networks. Fiber impairment assessment and adaptive compensation becomes critical in such implementations. A comprehensive analytical model for impairments in OFDM-based fiber links is developed. The proposed model includes the combined impact of laser phase fluctuations, fiber dispersion, self phase modulation, cross phase modulation, four-wave mixing, the nonlinear phase noise due to the interaction of amplified spontaneous emission with fiber nonlinearities, and the photodetector noises. The bit error rate expression for the proposed model is derived based on error vector magnitude estimation. The performance analysis of the proposed model is presented and compared for dispersion compensated and uncompensated backbone/backhaul links. The results suggest that OFDM would perform better for uncompensated links than the compensated links due to the negligible FWM effects and there is a need for flexible compensation. The proposed model can be employed in cognitive optical networks for accurate assessment of fiber-related impairments.

Temperature-triggered reversible dielectric and nonlinear optical switch based on the one-dimensional organic-inorganic hybrid phase transition compound [C6H11NH3]2CdCl4.

PubMed

Liao, Wei-Qiang; Ye, Heng-Yun; Fu, Da-Wei; Li, Peng-Fei; Chen, Li-Zhuang; Zhang, Yi

2014-10-20

The one-dimensional organic-inorganic hybrid compound bis(cyclohexylammonium) tetrachlorocadmate(II) (1), in which the adjacent infinite [CdCl4]n(-) chains are connected to each other though Cd···Cl weak interactions to form perovskite-type layers of corner-sharing CdCl6 octahedra separated by cyclohexylammonium cation bilayers, was synthesized. It undergoes two successive structural phase transitions, at 215 and 367 K, which were confirmed by systematic characterizations including differential scanning calorimetry (DSC) measurements, variable-temperature structural analyses, and dielectric and second harmonic generation (SHG) measurements. A precise structural analysis discloses that the phase transition at 215 K is induced by the disorder-order transition of cyclohexylammonium cations, while the phase transition at 367 K derives from changes in the relative location of Cd atoms. Emphatically, both the dielectric constant and SHG intensity of 1 show a striking change between low and high states at around 367 K, which reveals that 1 might be considered as a potential dielectric and nonlinear optical (NLO) switch with high-temperature response characterization, excellent reversibility, and obvious change of states.

Deterministic entanglement generation from driving through quantum phase transitions.

PubMed

Luo, Xin-Yu; Zou, Yi-Quan; Wu, Ling-Na; Liu, Qi; Han, Ming-Fei; Tey, Meng Khoon; You, Li

2017-02-10

Many-body entanglement is often created through the system evolution, aided by nonlinear interactions between the constituting particles. These very dynamics, however, can also lead to fluctuations and degradation of the entanglement if the interactions cannot be controlled. Here, we demonstrate near-deterministic generation of an entangled twin-Fock condensate of ~11,000 atoms by driving a arubidium-87 Bose-Einstein condensate undergoing spin mixing through two consecutive quantum phase transitions (QPTs). We directly observe number squeezing of 10.7 ± 0.6 decibels and normalized collective spin length of 0.99 ± 0.01. Together, these observations allow us to infer an entanglement-enhanced phase sensitivity of ~6 decibels beyond the standard quantum limit and an entanglement breadth of ~910 atoms. Our work highlights the power of generating large-scale useful entanglement by taking advantage of the different entanglement landscapes separated by QPTs. Copyright © 2017, American Association for the Advancement of Science.

Photonic Switching Devices Using Light Bullets

NASA Technical Reports Server (NTRS)

Goorjian, Peter M. (Inventor)

1999-01-01

A unique ultra-fast, all-optical switching device or switch is made with readily available, relatively inexpensive, highly nonlinear optical materials. which includes highly nonlinear optical glasses, semiconductor crystals and/or multiple quantum well semiconductor materials. At the specified wavelengths. these optical materials have a sufficiently negative group velocity dispersion and high nonlinear index of refraction to support stable light bullets. The light bullets counter-propagate through, and interact within the waveguide to selectively change each others' directions of propagation into predetermined channels. In one embodiment, the switch utilizes a rectangularly planar slab waveguide. and further includes two central channels and a plurality of lateral channels for guiding the light bullets into and out of the waveguide. An advantage of the present all-optical switching device lies in its practical use of light bullets, thus preventing the degeneration of the pulses due to dispersion and diffraction at the front and back of the pulses. Another advantage of the switching device is the relative insensitivity of the collision process to the time difference in which the counter-propagating pulses enter the waveguide. since. contrary to conventional co-propagating spatial solitons, the relative phase of the colliding pulses does not affect the interaction of these pulses. Yet another feature of the present all-optical switching device is the selection of the light pulse parameters which enables the generation of light bullets in nonlinear optical materials. including highly nonlinear optical glasses and semiconductor materials such as semiconductor crystals and/or multiple quantum well semiconductor materials.

Strong-field two-photon transition by phase shaping

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

Lee, Sangkyung; Lim, Jongseok; Ahn, Jaewook

2010-08-15

We demonstrate the ultrafast coherent control of a nonlinear two-photon absorption in a dynamically shifted energy level structure. We use a spectrotemporal laser-pulse shaping that is programed to preserve the resonant absorption condition during the intense laser-field interaction. Experiments carried out in the strong-field regime of two-photon absorption in the ground state of atomic cesium reveal that the analytically obtained offset and curvature of a laser spectrum compensate the effect of both static and dynamic energy shifts of the given light-atom interaction.

Complete energy conversion by autoresonant three-wave mixing in nonuniform media.

PubMed

Yaakobi, O; Caspani, L; Clerici, M; Vidal, F; Morandotti, R

2013-01-28

Resonant three-wave interactions appear in many fields of physics e.g. nonlinear optics, plasma physics, acoustics and hydrodynamics. A general theory of autoresonant three-wave mixing in a nonuniform media is derived analytically and demonstrated numerically. It is shown that due to the medium nonuniformity, a stable phase-locked evolution is automatically established. For a weak nonuniformity, the efficiency of the energy conversion between the interacting waves can reach almost 100%. One of the potential applications of our theory is the design of highly-efficient optical parametric amplifiers.

Determination of nonlinear genetic architecture using compressed sensing.

PubMed

Ho, Chiu Man; Hsu, Stephen D H

2015-01-01

One of the fundamental problems of modern genomics is to extract the genetic architecture of a complex trait from a data set of individual genotypes and trait values. Establishing this important connection between genotype and phenotype is complicated by the large number of candidate genes, the potentially large number of causal loci, and the likely presence of some nonlinear interactions between different genes. Compressed Sensing methods obtain solutions to under-constrained systems of linear equations. These methods can be applied to the problem of determining the best model relating genotype to phenotype, and generally deliver better performance than simply regressing the phenotype against each genetic variant, one at a time. We introduce a Compressed Sensing method that can reconstruct nonlinear genetic models (i.e., including epistasis, or gene-gene interactions) from phenotype-genotype (GWAS) data. Our method uses L1-penalized regression applied to nonlinear functions of the sensing matrix. The computational and data resource requirements for our method are similar to those necessary for reconstruction of linear genetic models (or identification of gene-trait associations), assuming a condition of generalized sparsity, which limits the total number of gene-gene interactions. An example of a sparse nonlinear model is one in which a typical locus interacts with several or even many others, but only a small subset of all possible interactions exist. It seems plausible that most genetic architectures fall in this category. We give theoretical arguments suggesting that the method is nearly optimal in performance, and demonstrate its effectiveness on broad classes of nonlinear genetic models using simulated human genomes and the small amount of currently available real data. A phase transition (i.e., dramatic and qualitative change) in the behavior of the algorithm indicates when sufficient data is available for its successful application. Our results indicate that predictive models for many complex traits, including a variety of human disease susceptibilities (e.g., with additive heritability h (2)∼0.5), can be extracted from data sets comprised of n ⋆∼100s individuals, where s is the number of distinct causal variants influencing the trait. For example, given a trait controlled by ∼10 k loci, roughly a million individuals would be sufficient for application of the method.

Analysis of dynamic channel power equalization by using nonlinear amplifying Sagnac interferometer for ASK-WDM optical transmission

NASA Astrophysics Data System (ADS)

Qu, Feng; Liu, Xiaoming; Zhao, Jianhui

2004-05-01

A power equalization using an asymmetric nonlinear amplifying Sagnac interferometer (NASI) for ASK modulation is studied numerically. A nonreciprocal phase bias was proposed to be introduced into the structure. The nonreciprocal phase bias reduces not only the demanding for amplifier power or fiber non-linearity, but also increase the dynamic input power range. The power equalization is demonstrated for RZ modulation by nonlinear phase analysis and eye diagram simulation.

Characteristic study of head-on collision of dust-ion acoustic solitons of opposite polarity with kappa distributed electrons

NASA Astrophysics Data System (ADS)

Parveen, Shahida; Mahmood, Shahzad; Adnan, Muhammad; Qamar, Anisa

2016-09-01

The head on collision between two dust ion acoustic (DIA) solitary waves, propagating in opposite directions, is studied in an unmagnetized plasma constituting adiabatic ions, static dust charged (positively/negatively) grains, and non-inertial kappa distributed electrons. In the linear limit, the dispersion relation of the dust ion acoustic (DIA) solitary wave is obtained using the Fourier analysis. For studying characteristic head-on collision of DIA solitons, the extended Poincaré-Lighthill-Kuo method is employed to obtain Korteweg-de Vries (KdV) equations with quadratic nonlinearities and investigated the phase shifts in their trajectories after the interaction. It is revealed that only compressive solitary waves can exist for the positive dust charged concentrations while for negative dust charge concentrations both the compressive and rarefactive solitons can propagate in such dusty plasma. It is found that for specific sets of plasma parameters, the coefficient of nonlinearity disappears in the KdV equation for the negative dust charged grains. Therefore, the modified Korteweg-de Vries (mKdV) equations with cubic nonlinearity coefficient, and their corresponding phase shift and trajectories, are also derived for negative dust charged grains plasma at critical composition. The effects of different plasma parameters such as superthermality, concentration of positively/negatively static dust charged grains, and ion to electron temperature ratio on the colliding soliton profiles and their corresponding phase shifts are parametrically examined.

Interactions and scattering of quantum vortices in a polariton fluid.

PubMed

Dominici, Lorenzo; Carretero-González, Ricardo; Gianfrate, Antonio; Cuevas-Maraver, Jesús; Rodrigues, Augusto S; Frantzeskakis, Dimitri J; Lerario, Giovanni; Ballarini, Dario; De Giorgi, Milena; Gigli, Giuseppe; Kevrekidis, Panayotis G; Sanvitto, Daniele

2018-04-13

Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions in a resonant polariton fluid created in a solid-state microcavity. By tracking the vortices on picosecond time scales, we reveal the role of nonlinearity, as well as of density and phase gradients, in driving their rotational dynamics. Such effects are also responsible for the split of composite spin-vortex molecules into elementary half-vortices, when seeding opposite vorticity between the two spinorial components. Remarkably, we also observe that vortices placed in close proximity experience a pull-push scenario leading to unusual scattering-like events that can be described by a tunable effective potential. Understanding vortex interactions can be useful in quantum hydrodynamics and in the development of vortex-based lattices, gyroscopes, and logic devices.

A theoretical investigation of soliton induced supercontinuum generation in liquid core photonic crystal fiber and dual core optical fiber

NASA Astrophysics Data System (ADS)

Porsezian, K.; Nithyanandan, K.; Vasantha Jayakantha Raja, R.; Ganapathy, R.

2013-07-01

The supercontinuum generation (SCG) in liquid core photonic crystal fiber (LCPCF) with versatile nonlinear response and the spectral broadening in dual core optical fiber is presented. The analysis is presented in two phase, phase I deals with the SCG in LCPCF with the effect of saturable nonlinearity and re-orientational nonlinearity. We identify and discuss the generic nature of the saturable nonlinearity and reorientational nonlinearity in the SCG, using suitable model. For the physical explanation, modulational instability and soliton fission techniques is implemented to investigate the impact of saturable nonlinear response and slow nonlinear response, respectively. It is observed that the saturable nonlinearity inevitably suppresses the MI and the subsequent SCG. On the other hand, the re-orientational nonlinearity contributes to the slow nonlinear response in addition to the conventional fast response due to the electronic contribution. The phase II features the exclusive investigation of the spectral broadening in the dual core optical fiber.

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.

Probing polariton dynamics in trapped ions with phase-coherent two-dimensional spectroscopy

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

Gessner, Manuel; Schlawin, Frank; Buchleitner, Andreas

2015-06-07

We devise a phase-coherent three-pulse protocol to probe the polariton dynamics in a trapped-ion quantum simulation. In contrast to conventional nonlinear signals, the presented scheme does not change the number of excitations in the system, allowing for the investigation of the dynamics within an N-excitation manifold. In the particular case of a filling factor one (N excitations in an N-ion chain), the proposed interaction induces coherent transitions between a delocalized phonon superfluid and a localized atomic insulator phase. Numerical simulations of a two-ion chain demonstrate that the resulting two-dimensional spectra allow for the unambiguous identification of the distinct phases, andmore » the two-dimensional line shapes efficiently characterize the relevant decoherence mechanism.« less

Estimating phase synchronization in dynamical systems using cellular nonlinear networks

NASA Astrophysics Data System (ADS)

Sowa, Robert; Chernihovskyi, Anton; Mormann, Florian; Lehnertz, Klaus

2005-06-01

We propose a method for estimating phase synchronization between time series using the parallel computing architecture of cellular nonlinear networks (CNN’s). Applying this method to time series of coupled nonlinear model systems and to electroencephalographic time series from epilepsy patients, we show that an accurate approximation of the mean phase coherence R —a bivariate measure for phase synchronization—can be achieved with CNN’s using polynomial-type templates.

Nonlinear wavenumber shift of large amplitude Langmuir waves

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

Li, Dehui, E-mail: dhli@ipp.ac.cn; Wang, Shaojie

2016-07-15

Nonlinear particle-in-cell simulation is carried out to investigate the nonlinear behavior of the Langmuir wave launched with a fixed frequency in a uniform plasma. It is found that in the strong driving case, the launched wave propagates in a phase velocity larger than that predicted by the linear theory; there appears a nonlinear down-shift of wavenumber. The phase velocity of the nonlinear wave and the down-shift of the wavenumber are demonstrated to be determined by the velocity of nonlinearly accelerated resonant electrons.

Z-scan theory for nonlocal nonlinear media with simultaneous nonlinear refraction and nonlinear absorption.

PubMed

Rashidian Vaziri, Mohammad Reza

2013-07-10

In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.

Phase collapse and revival of a 1-mode Bose-Einstein condensate induced by an off-resonant optical probe field and superselection rules

NASA Astrophysics Data System (ADS)

Arruda, L. G. E.; Prataviera, G. A.; de Oliveira, M. C.

2018-02-01

Phase collapse and revival for Bose-Einstein condensates are nonlinear phenomena appearing due to atomic collisions. While it has been observed in a general setting involving many modes, for one-mode condensates its occurrence is forbidden by the particle number superselection rule (SSR), which arises because there is no phase reference available. We consider a single mode atomic Bose-Einstein condensate interacting with an off-resonant optical probe field. We show that the condensate phase revival time is dependent on the atom-light interaction, allowing optical control on the atomic collapse and revival dynamics. Incoherent effects over the condensate phase are included by considering a continuous photo-detection over the probe field. We consider conditioned and unconditioned photo-counting events and verify that no extra control upon the condensate is achieved by the probe photo-detection, while further inference of the atomic system statistics is allowed leading to a useful test of the SSR on particle number and its imposition on the kind of physical condensate state.

Interactions of nonlocal dark solitons under competing cubic-quintic nonlinearities.

PubMed

Chen, Wei; Shen, Ming; Kong, Qian; Shi, Jielong; Wang, Qi; Krolikowski, Wieslaw

2014-04-01

We investigate analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities. It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton separation. We demonstrate these results by approximate variational approach and direct numerical simulation.

Parametric phase conjugation for the second harmonic of a nonlinear ultrasonic beam

NASA Astrophysics Data System (ADS)

Brysev, A. P.; Bunkin, F. V.; Hamilton, M. F.; Klopotov, R. V.; Krutyanskii, L. M.; Yan, K.

2003-01-01

The effect of phase conjugation for the second harmonic of a focused ultrasonic beam was investigated experimentally and by numerical simulation. An ultrasonic pulse with the carrier frequency f=3 MHz was emitted into water and focused at a point between the source and the phase conjugating system. The phase conjugation for the second harmonic of the incident wave (2 f=6 MHz) was performed in a magnetostrictive ceramic as a result of the parametric interaction of the incident wave with the pumping magnetic field (the pumping frequency was f p=4 f=12 MHz). The axial and focal distributions of sound pressure in the incident and conjugated beams were measured using a broadband PVDF membrane hydrophone. The corresponding calculations were performed by solving numerically the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation allowing for the nonlinearity, diffraction, and thermoviscous absorption. The results of measurements agreed well with the calculations and showed that the field of a conjugate wave adequately reproduces the field of the second harmonic of the incident wave. A certain advantage of focusing with the phase conjugation for the second harmonic was demonstrated in comparison with the operation at the doubled frequency of the incident wave. The results of this study can serve as a basis for the utilization of the phase conjugation of harmonics in ultrasonic tomography and nondestructive testing.

Near-planar TS waves and longitudinal vortices in channel flow: Nonlinear interaction and focusing

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1989-01-01

The nonlinear interaction between planar or near-planar Tollmien-Schlichting waves and longitudinal vortices, induced or input, is considered theoretically for channel flows at high Reynolds numbers. Several kinds of nonlinear interaction, dependent on the input amplitudes and wavenumbers or on previously occurring interactions, are found and inter-related. The first, Type 1, is studied the most here and it usually produces spanwise focusing of both the wave and the vortex motion, within a finite scaled time, along with enhancement of both their amplitudes. This then points to the nonlinear interaction Type 2 where new interactive effects come into force to drive the wave and the vortex nonlinearly. Types 3, 4 correspond to still higher amplitudes, with 3 being related to 2, while 4 is connected with a larger-scale interaction 5 studied in an allied paper. Both 3, 4 are subsets of the full three-dimensional triple-deck-lie interaction, 6. The strongest nonlinear interactions are those of 4, 5, 6 since they alter the mean-flow profile substantially, i.e., by an 0(1) relative amount. All the types of nonlinear interaction however can result in the formation of focussed responses in the sense of spanwise concentrations and/or amplifications of vorticity and wave amplitude.

Nonlinear optical properties of thick composite media with vanadium dioxide nanoparticles. I. Self-defocusing of radiation in the visible and near-IR regions

NASA Astrophysics Data System (ADS)

Ostrosablina, A. A.; Sidorov, A. I.

2005-07-01

This paper presents the experimental and theoretical results of a study of the interaction of pulsed laser radiation with thick composite media containing nanoparticles of vanadium dioxide (VO2). It establishes that the reversible semiconductor-metal phase transition that occurs in VO2 nanoparticles under the action of radiation can produce self-defocusing of radiation in the visible and near-IR regions because of the formation of a photoinduced dynamic lens. An analysis is carried out of how the radiation intensity affects the dynamics of these processes. It is shown that photoinduced absorption and scattering play a role in forming the nonlinear optical response.

Comparison of qubit and qutrit like entangled squeezed and coherent states of light

NASA Astrophysics Data System (ADS)

Najarbashi, G.; Mirzaei, S.

2016-10-01

Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trends are compared with those obtained for qubit and qutrit like entangled coherent states (ECS).

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.

Controls-structures interaction guest investigator program: Overview and phase 1 experimental results and future plans

NASA Technical Reports Server (NTRS)

Smith-Taylor, Rudeen; Tanner, Sharon E.

1993-01-01

The NASA Controls-Structures Interaction (CSI) Guest Investigator program is described in terms of its support of the development of CSI technologies. The program is based on the introduction of CSI researchers from industry and academia to available test facilities for experimental validation of technologies and methods. Phase 1 experimental results are reviewed with attention given to their use of the Mini-MAST test facility and the facility for the Advance Control Evaluation of Structures. Experiments were conducted regarding the following topics: collocated/noncollocated controllers, nonlinear math modeling, controller design, passive/active suspension systems design, and system identification and fault isolation. The results demonstrate that significantly enhanced performance from the control techniques can be achieved by integrating knowledge of the structural dynamics under consideration into the approaches.

Interaction of pulsating and spinning waves in condensed phase combustion

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

Booty, M.R.; Margolis, S.B.; Matkowsky, B.J.

1986-10-01

The authors employ a nonlinear stability analysis in the neighborhood of a multiple bifurcation point to describe the interaction of pulsating and spinning modes of condensed phase combustion. Such phenomena occur in the synthesis of refractory materials. In particular, they consider the propagation of combustion waves in a long thermally insulated cylindrical sample and show that steady, planar combustion is stable for a modified activation energy/melting parameter less than a critical value. Above this critical value primary bifurcation states, corresponding to time-periodic pulsating and spinning modes of combustion, emanate from the steadily propagating solution. By varying the sample radius, themore » authors split a multiple bifurcation point to obtain bifurcation diagrams which exhibit secondary, tertiary, and quarternary branching to various types of quasi-periodic combustion waves.« less

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.

Effect of dynamical phase on the resonant interaction among tsunami edge wave modes

USGS Publications Warehouse

Geist, Eric L.

2018-01-01

Different modes of tsunami edge waves can interact through nonlinear resonance. During this process, edge waves that have very small initial amplitude can grow to be as large or larger than the initially dominant edge wave modes. In this study, the effects of dynamical phase are established for a single triad of edge waves that participate in resonant interactions. In previous studies, Jacobi elliptic functions were used to describe the slow variation in amplitude associated with the interaction. This analytical approach assumes that one of the edge waves in the triad has zero initial amplitude and that the combined phase of the three waves φ = θ1 + θ2 − θ3 is constant at the value for maximum energy exchange (φ = 0). To obtain a more general solution, dynamical phase effects and non-zero initial amplitudes for all three waves are incorporated using numerical methods for the governing differential equations. Results were obtained using initial conditions calculated from a subduction zone, inter-plate thrust fault geometry and a stochastic earthquake slip model. The effect of dynamical phase is most apparent when the initial amplitudes and frequencies of the three waves are within an order of magnitude. In this case, non-zero initial phase results in a marked decrease in energy exchange and a slight decrease in the period of the interaction. When there are large differences in frequency and/or initial amplitude, dynamical phase has less of an effect and typically one wave of the triad has very little energy exchange with the other two waves. Results from this study help elucidate under what conditions edge waves might be implicated in late, large-amplitude arrivals.

Effect of Dynamical Phase on the Resonant Interaction Among Tsunami Edge Wave Modes

NASA Astrophysics Data System (ADS)

Geist, Eric L.

2018-02-01

Different modes of tsunami edge waves can interact through nonlinear resonance. During this process, edge waves that have very small initial amplitude can grow to be as large or larger than the initially dominant edge wave modes. In this study, the effects of dynamical phase are established for a single triad of edge waves that participate in resonant interactions. In previous studies, Jacobi elliptic functions were used to describe the slow variation in amplitude associated with the interaction. This analytical approach assumes that one of the edge waves in the triad has zero initial amplitude and that the combined phase of the three waves φ = θ 1 + θ 2 - θ 3 is constant at the value for maximum energy exchange (φ = 0). To obtain a more general solution, dynamical phase effects and non-zero initial amplitudes for all three waves are incorporated using numerical methods for the governing differential equations. Results were obtained using initial conditions calculated from a subduction zone, inter-plate thrust fault geometry and a stochastic earthquake slip model. The effect of dynamical phase is most apparent when the initial amplitudes and frequencies of the three waves are within an order of magnitude. In this case, non-zero initial phase results in a marked decrease in energy exchange and a slight decrease in the period of the interaction. When there are large differences in frequency and/or initial amplitude, dynamical phase has less of an effect and typically one wave of the triad has very little energy exchange with the other two waves. Results from this study help elucidate under what conditions edge waves might be implicated in late, large-amplitude arrivals.

Effect of Dynamical Phase on the Resonant Interaction Among Tsunami Edge Wave Modes

NASA Astrophysics Data System (ADS)

Geist, Eric L.

2018-04-01

Different modes of tsunami edge waves can interact through nonlinear resonance. During this process, edge waves that have very small initial amplitude can grow to be as large or larger than the initially dominant edge wave modes. In this study, the effects of dynamical phase are established for a single triad of edge waves that participate in resonant interactions. In previous studies, Jacobi elliptic functions were used to describe the slow variation in amplitude associated with the interaction. This analytical approach assumes that one of the edge waves in the triad has zero initial amplitude and that the combined phase of the three waves φ = θ 1 + θ 2 - θ 3 is constant at the value for maximum energy exchange ( φ = 0). To obtain a more general solution, dynamical phase effects and non-zero initial amplitudes for all three waves are incorporated using numerical methods for the governing differential equations. Results were obtained using initial conditions calculated from a subduction zone, inter-plate thrust fault geometry and a stochastic earthquake slip model. The effect of dynamical phase is most apparent when the initial amplitudes and frequencies of the three waves are within an order of magnitude. In this case, non-zero initial phase results in a marked decrease in energy exchange and a slight decrease in the period of the interaction. When there are large differences in frequency and/or initial amplitude, dynamical phase has less of an effect and typically one wave of the triad has very little energy exchange with the other two waves. Results from this study help elucidate under what conditions edge waves might be implicated in late, large-amplitude arrivals.

Nonlinear dynamics of trions under strong optical excitation in monolayer MoSe2.

PubMed

Ye, Jialiang; Yan, Tengfei; Niu, Binghui; Li, Ying; Zhang, Xinhui

2018-02-05

By employing ultrafast transient reflection measurements based on two-color pump-probe spectroscopy, the population and valley polarization dynamics of trions in monolayer MoSe 2 were investigated at relatively high excitation densities under near-resonant excitation. Both the nonlinear dynamic photobleaching of the trion resonance and the redshift of the exciton resonance were found to be responsible for the excitation-energy- and density-dependent transient reflection change as a result of many-body interactions. Furthermore, from the polarization-resolved measurements, it was revealed that the initial fast population and polarization decay process upon strong photoexcitation observed for trions was determined by trion formation, transient phase-space filling and the short valley lifetime of excitons. The results provide a basic understanding of the nonlinear dynamics of population and valley depolarization of trions, as well as exciton-trion correlation in atomically thin MoSe 2 and other transition metal dichalcogenide materials.

Effect of control-beam polarization and power on optical time-domain demultiplexing in a new nonlinear optical loop mirror design

NASA Astrophysics Data System (ADS)

Grendár, Drahomír; Pottiez, Olivier; Dado, Milan; Müllerová, Jarmila; Dubovan, Jozef

2009-05-01

A new scheme of a control-beam-driven nonlinear optical loop mirror (NOLM) with a birefringent twisted fiber and a symmetrical coupler designed for optical time division demultiplexing (OTDM) is analyzed. The theoretical model of the proposed NOLM scheme considers the evolution of polarization states of data and control beams and the mutual interactions of the data and control beams due to the cross-phase modulation (XPM). Attention is given to the optical switching commanded by the control-beam power and by the manipulation of nonlinear polarization rotation of the data and control beam. The simulations of NOLM transmissions demonstrate that the cross talk between demultiplexed and nondemultiplexed beams as an important parameter for optical switching by the presented NOLM can be significantly reduced. The results show that the device can be of interest for all-optical signal manipulations in optical communication networks.

Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure

NASA Technical Reports Server (NTRS)

Ooijevaar, T. H.; Rogge, M. D.; Loendersloot, R.; Warnet, L.; Akkerman, R.; deBoer, A.

2013-01-01

One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.

Analytical description of the ternary melt and solution crystallization with a non-linear phase diagram

NASA Astrophysics Data System (ADS)

Toropova, L. V.; Alexandrov, D. V.

2018-05-01

The directional solidification of a ternary system with an extended phase transition region is theoretically studied. A mathematical model is developed to describe quasi-stationary solidification, and its analytical solution is constructed with allowance for a nonlinear liquids line equation. We demonstrate that the phase diagram nonlinearity leads to substantial changes of analytical solutions.

A Study of Electron and Phonon Dynamics by Broadband Two-Dimensional THz Time-Domain Spectroscopy

NASA Astrophysics Data System (ADS)

Fu, Zhengping

Terahertz (THz) wave interacts with semiconductors in many ways, such as resonant excitation of lattice vibration, intraband transition and polaron formation. Different from the optical waves, THz wave has lower photon energy (1 THz = 4.14 meV) and is suitable for studying dynamics of low-energy excitations. Recently the studies of the interaction of THz wave and semiconductors have been extending from the linear regime to the nonlinear regime, owing to the advance of the high-intensity THz generation and detection methods. Two-dimensional (2D) spectroscopy, as a useful tool to unravel the nonlinearity of materials, has been well developed in nuclear magnetic resonance and infrared region. However, the counterpart in THz region has not been well developed and was only demonstrated at frequency around 20 THz due to the lack of intense broadband THz sources. Using laser-induced plasma as the THz source, we developed collinear broadband 2D THz time-domain spectroscopy covering from 0.5 THz to 20 THz. Broadband intense THz pulses emitted from laser-induced plasma provide access to a variety of nonlinear properties of materials. Ultrafast optical and THz pulses make it possible to resolve the transient change of the material properties with temporal resolution of tens of femtoseconds. This thesis focuses on the linear and nonlinear interaction of the THz wave with semiconductors. Since a great many physical processes, including vibrational motion of lattice and plasma oscillation, has resonant frequency in the THz range, rich physics can be studies in our experiment. The thesis starts from the linear interaction of the THz wave with semiconductors. In the narrow band gap semiconductor InSb, the plasma absorption edge, Restrahlen band and dispersion of polaritons are observed. The nonlinear response of InSb in high THz field is verified in the frequency-resolved THz Z-scan experiment. The third harmonic generations due to the anharmonicity of plasma oscillation and the second order signal due to the plasma-phonon interaction are observed in 2D THz transmission spectra. In this thesis, the coherent phonons excited by THz pulses are experimentally demonstrated for the first time in both GaAs and InSb. The resonant excitation using THz pulses enables the coherent control of the lattice motion via direct interaction of atoms and electromagnetic wave, without inducing electronic transition as reported in the optical excitation of coherent phonons. The classic model is used to explain both excitation and detection mechanisms. An increase of the damping rate of the coherent lattice motion due to higher carrier density is observed in our experiment. Transient reflectivity change of GaAs induced by THz pulses is studied in 2D THz-pump/optical-probe configuration. Using the perturbative analysis of nonlinear electrooptic effect, we conclude that the nonlinear response of GaAs to two phase-locked THz pulses is mainly caused by the nonlinearity of the electronic response.

Correction of Phase Distortion by Nonlinear Optical Techniques

DTIC Science & Technology

1981-05-01

I I I I ifi 00 o o \\] CORRECTION OF PHASE DISTORTION BY NONLINEAR OPTICAL TECHNIQUES op Hughes Research Laboratories 3011 Malibu Canyon...CORRECTION OF PHASE DISTORTION BY NONLINEAR OPTICAL TECHNIQUES • , — •■ FBiMowmln»"Own. we^owr^wwcw n R.C./Lind| W.B./Browne C.R. Giuliano, R.K... phase conjugation. Adaptive optics , Laser compensation, SBS, Four-wave mixing. 20. ABSTRACT (ConllmM on i tmrr and Identity bv block number

Merging and energy exchange between optical filaments

NASA Astrophysics Data System (ADS)

Georgieva, D. A.; Kovachev, L. M.

2015-10-01

We investigate nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing Pcr trough the processes of cross-phase modulation (CPM) and degenerate four-photon parametric mixing (FPPM). When there is no initial phase difference between the pulses we observe attraction between pulses due to CPM. The final result is merging between the pulses in a single filament with higher power. By method of moments it is found that the attraction depends on the distance between the pulses and has potential character. In the second case we study energy exchange between filaments. This process is described through FPPM scheme and requests initial phase difference between the waves.

Merging and energy exchange between optical filaments

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

Georgieva, D. A., E-mail: dgeorgieva@tu-sofia.bg; Kovachev, L. M.

2015-10-28

We investigate nonlinear interaction between collinear femtosecond laser pulses with power slightly above the critical for self-focusing P{sub cr} trough the processes of cross-phase modulation (CPM) and degenerate four-photon parametric mixing (FPPM). When there is no initial phase difference between the pulses we observe attraction between pulses due to CPM. The final result is merging between the pulses in a single filament with higher power. By method of moments it is found that the attraction depends on the distance between the pulses and has potential character. In the second case we study energy exchange between filaments. This process is describedmore » through FPPM scheme and requests initial phase difference between the waves.« less

Nonlinear evolution dynamics of holographic superconductor model with scalar self-interaction

NASA Astrophysics Data System (ADS)

Li, Ran; Zi, Tieguang; Zhang, Hongbao

2018-04-01

We investigate the holographic superconductor model that is described by the Einstein-Maxwell theory with the self-interaction term λ |Ψ |4 of complex scalar field in asymptotic anti-de Sitter (AdS) spacetime. Below critical temperature Tc, the planar Reissner-Nordström-AdS black hole is unstable due to the near-horizon scalar condensation instability. We study the full nonlinear development of this instability by numerically solving the gravitational dynamics in the asymptotic AdS spacetime, and observe a dynamical process from the perturbed Reissner-Nordström-AdS black hole to a hairy black hole when the initial black hole temperature T

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

NASA Astrophysics Data System (ADS)

Peter, Simon; Leine, Remco I.

2017-11-01

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

Long Coherence Length 193 nm Laser for High-Resolution Nano-Fabrication

DTIC Science & Technology

2008-06-27

in the non-linear optical up-converter, as well as specifying their interaction lengths, phase -matching angles, coatings, temperatures of operation...when optical path differences between interfering beams become comparable to the temporal coherence length of the source, the fringe contrast diminishes...switched, intracavity frequency doubled Nd:YAG laser drives an optical parametric oscillator (OPO) running at 710 nm. A portion of the 532 nm light

Dynamical formation of a Reissner-Nordström black hole with scalar hair in a cavity

NASA Astrophysics Data System (ADS)

Sanchis-Gual, Nicolas; Degollado, Juan Carlos; Herdeiro, Carlos; Font, José A.; Montero, Pedro J.

2016-08-01

In a recent Letter [Sanchis-Gual et al., Phys. Rev. Lett. 116, 141101 (2016)], we presented numerical relativity simulations, solving the full Einstein-Maxwell-Klein-Gordon equations, of superradiantly unstable Reissner-Nordström black holes (BHs), enclosed in a cavity. Low frequency, spherical perturbations of a charged scalar field trigger this instability. The system's evolution was followed into the nonlinear regime, until it relaxed into an equilibrium configuration, found to be a hairy BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. Here, we investigate the impact of adding self-interactions to the scalar field. In particular, we find sufficiently large self-interactions suppress the exponential growth phase, known from linear theory, and promote a nonmonotonic behavior of the scalar field energy. Furthermore, we discuss in detail the influence of the various parameters in this model: the initial BH charge, the initial scalar perturbation, the scalar field charge, the mass, and the position of the cavity's boundary (mirror). We also investigate the "explosive" nonlinear regime previously reported to be akin to a bosenova. A mode analysis shows that the "explosions" can be interpreted as the decay into the BH of modes that exit the superradiant regime.

An assessment of the retention behaviour of polycyclic aromatic hydrocarbons on reversed phase stationary phases: selectivity and retention on C18 and phenyl-type surfaces.

PubMed

Kayillo, Sindy; Dennis, Gary R; Shalliker, R Andrew

2006-09-08

In this manuscript the retention and selectivity of a set of linear and non-linear PAHs were evaluated on five different reversed-phase columns. These phases included C18 and C18 Aqua stationary phases, as well as three phenyl phases: Propyl-phenyl, Synergi polar-RP and Cosmosil 5PBB phase. Overall, the results revealed that the phenyl-type columns offered better separation performance for the linear PAHs, while the separation of the structural isomer PAHs was enhanced on the C18 columns. The Propyl-phenyl column was found to have the highest molecular-stationary phase interactions, as evidenced by the greatest rate of change in 'S' (0.71) as a function of the molecular weight in the PAH homologous series, despite having the lowest surface coverage (3% carbon load) (where S is the slope of a plot of logk versus the solvent composition). In contrast, the C18 Aqua column, having the highest surface coverage (15% carbon load) was found to have the second lowest molecular-stationary phase interactions (rate of change in S=0.61). Interestingly, the Synergi polar-RP column, which also is a phenyl stationary phase behaved more 'C18-like' than 'phenyl-like' in many of the tests undertaken. This is probably not unexpected since all five phases were reversed phase.

From non-linear magnetoacoustics and spin reorientation transition to magnetoelectric micro/nano-systems

NASA Astrophysics Data System (ADS)

Tiercelin, Nicolas; Preobrazhensky, Vladimir; BouMatar, Olivier; Talbi, Abdelkrim; Giordano, Stefano; Dusch, Yannick; Klimov, Alexey; Mathurin, Théo.; Elmazria, Omar; Hehn, Michel; Pernod, Philippe

2017-09-01

The interaction of a strongly nonlinear spin system with a crystalline lattice through magnetoelastic coupling results in significant modifications of the acoustic properties of magnetic materials, especially in the vicinity of magnetic instabilities associated with the spin-reorientation transition (SRT). The magnetoelastic coupling transfers the critical properties of the magnetic subsystem to the elastic one, which leads to a strong decrease of the sound velocity in the vicinity of the SRT, and allows a large control over acoustic nonlinearities. The general principles of the non-linear magneto-acoustics (NMA) will be introduced and illustrated in `bulk' applications such as acoustic wave phase conjugation, multi-phonon coupling, explosive instability of magneto-elastic vibrations, etc. The concept of the SRT coupled to magnetoelastic interaction has been transferred into nanostructured magnetoelastic multilayers with uni-axial anisotropy. The high sensitivity and the non-linear properties have been demonstrated in cantilever type actuators, and phenomena such as magneto-mechanical RF demodulation have been observed. The combination of the magnetic layers with piezoelectric materials also led to stress-mediated magnetoelectric (ME) composites with high ME coefficients, thanks to the SRT. The magnetoacoustic effects of the SRT have also been studied for surface acoustic waves propagating in the magnetoelastic layers and found to be promising for highly sensitive magnetic field sensors working at room temperature. On the other hand, mechanical stress is a very efficient way to control the magnetic subsystem. The principle of a very energy efficient stress-mediated magnetoelectric writing and reading in a magnetic memory is described.

Uniform strongly interacting soliton gas in the frame of the Nonlinear Schrodinger Equation

NASA Astrophysics Data System (ADS)

Gelash, Andrey; Agafontsev, Dmitry

2017-04-01

The statistical properties of many soliton systems play the key role in the fundamental studies of integrable turbulence and extreme sea wave formation. It is well known that separated solitons are stable nonlinear coherent structures moving with constant velocity. After collisions with each other they restore the original shape and only acquire an additional phase shift. However, at the moment of strong nonlinear soliton interaction (i.e. when solitons are located close) the wave field are highly complicated and should be described by the theory of inverse scattering transform (IST), which allows to integrate the KdV equation, the NLSE and many other important nonlinear models. The usual approach of studying the dynamics and statistics of soliton wave field is based on relatively rarefied gas of solitons [1,2] or restricted by only two-soliton interactions [3]. From the other hand, the exceptional role of interacting solitons and similar coherent structures - breathers in the formation of rogue waves statistics was reported in several recent papers [4,5]. In this work we study the NLSE and use the most straightforward and general way to create many soliton initial condition - the exact N-soliton formulas obtained in the theory of the IST [6]. We propose the recursive numerical scheme for Zakharov-Mikhailov variant of the dressing method [7,8] and discuss its stability with respect to increasing the number of solitons. We show that the pivoting, i.e. the finding of an appropriate order for recursive operations, has a significant impact on the numerical accuracy. We use the developed scheme to generate statistical ensembles of 32 strongly interacting solitons, i.e. solve the inverse scattering problem for the high number of discrete eigenvalues. Then we use this ensembles as initial conditions for numerical simulations in the box with periodic boundary conditions and study statics of obtained uniform strongly interacting gas of NLSE solitons. Author thanks the support of the Russian Science Foundation (Grand No. 14-22-00174) [1] D. Dutykh, E. Pelinovsky, Numerical simulation of a solitonic gas in kdv and kdv-bbm equations, Physics Letters A 378 (42) (2014) 3102-3110. [2] E. Shurgalina, E. Pelinovsky, Nonlinear dynamics of a soliton gas: Modified korteweg-de vries equation framework, Physics Letters A 380 (24) (2016) 2049-2053. [3] E. N. Pelinovsky, E. Shurgalina, A. Sergeeva, T. G. Talipova, G. El, R. H. Grimshaw, Two-soliton interaction as an elementary act of soliton turbulence in integrable systems, Physics Letters A 377 (3) (2013) 272-275 [4] J. Soto-Crespo, N. Devine, N. Akhmediev, Integrable turbulence and rogue waves: Breathers or solitons?, Physical review letters 116 (10) (2016) 103901. [5] D. S. Agafontsev, V. E. Zakharov, Integrable turbulence and formation of rogue waves, Nonlinearity 28 (8) (2015) 2791. [6] V. E. Zakharov, A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP 34 (1) (1972) 62. [7] V. Zakharov, A. Mikhailov, Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Sov. Phys.-JETP (Engl. Transl.) 47 (6) (1978). [8] A. A. Gelash, V. E. Zakharov, Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability, Nonlinearity 27 (4) (2014) R1.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Space time neural networks for tether operations in space

NASA Technical Reports Server (NTRS)

Lea, Robert N.; Villarreal, James A.; Jani, Yashvant; Copeland, Charles

1993-01-01

A space shuttle flight scheduled for 1992 will attempt to prove the feasibility of operating tethered payloads in earth orbit. due to the interaction between the Earth's magnetic field and current pulsing through the tether, the tethered system may exhibit a circular transverse oscillation referred to as the 'skiprope' phenomenon. Effective damping of skiprope motion depends on rapid and accurate detection of skiprope magnitude and phase. Because of non-linear dynamic coupling, the satellite attitude behavior has characteristic oscillations during the skiprope motion. Since the satellite attitude motion has many other perturbations, the relationship between the skiprope parameters and attitude time history is very involved and non-linear. We propose a Space-Time Neural Network implementation for filtering satellite rate gyro data to rapidly detect and predict skiprope magnitude and phase. Training and testing of the skiprope detection system will be performed using a validated Orbital Operations Simulator and Space-Time Neural Network software developed in the Software Technology Branch at NASA's Lyndon B. Johnson Space Center.

Large conditional single-photon cross-phase modulation

NASA Astrophysics Data System (ADS)

Beck, Kristin; Hosseini, Mahdi; Duan, Yiheng; Vuletic, Vladan

2016-05-01

Deterministic optical quantum logic requires a nonlinear quantum process that alters the phase of a quantum optical state by π through interaction with only one photon. Here, we demonstrate a large conditional cross-phase modulation between a signal field, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. This approach avoids fundamental limitations associated with multimode effects for traveling optical photons. We measure a conditional cross-phase shift of up to π / 3 between the retrieved signal and control photons, and confirm deterministic entanglement between the signal and control modes by extracting a positive concurrence. With a moderate improvement in cavity finesse, our system can reach a coherent phase shift of p at low loss, enabling deterministic and universal photonic quantum logic. Preprint: arXiv:1512.02166 [quant-ph

Phase walk analysis of leptokurtic time series.

PubMed

Schreiber, Korbinian; Modest, Heike I; Räth, Christoph

2018-06-01

The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

ac Stark-mediated quantum control with femtosecond two-color laser pulses

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

Serrat, Carles

2005-11-15

A critical dependence of the quantum interference on the optical Stark spectral shift produced when two-color laser pulses interact with a two-level medium is observed. The four-wave mixing of two ultrashort phase-locked {omega}-3{omega} laser pulses propagating coherently in a two-level system depends on the pulses' relative phase. The phase dominating the efficiency of the coupling to the anti-Stokes Raman component is found to be determined by the sign of the total ac Stark shift induced in the system, in such a way that the phase sensitivity disappears precisely where the ac Stark effect due to both pulses is compensated. Amore » coherent control scheme based on this phenomenon can be contemplated as the basis for nonlinear optical spectroscopy techniques.« less

Is there evidence for the existence of nonlinear behavior within the interplanetary solar sector structure?

NASA Astrophysics Data System (ADS)

Brown, A. G.; Francis, N. M.; Broomhead, D. S.; Cannon, P. S.; Akram, A.

1999-06-01

Using data from the Sweden and Britain Radar Experiment (SABRE) VHF coherent radar, Yeoman et al. [1990] found evidence for two and four sector structures during the declining phase of solar cycle (SC) 21. No such obvious harmonic features were present during the ascending phase of SC 22. It was suggested that the structure of the heliospheric current sheet might exhibit nonlinear behavior during the latter period. A direct test of this suggestion, using established nonlinear methods, would require the computation of the fractal dimension of the data, for example. However, the quality of the SABRE data is insufficient for this purpose. Therefore we have tried to answer a simpler question: Is there any evidence that the SABRE data was generated by a (low-dimensional) nonlinear process? If this were the case, it would be a powerful indicator of nonlinear behavior in the solar current sheet. Our approach has been to use a system of orthogonal linear filters to separate the data into linearly uncorrelated time series. We then look for nonlinear dynamical relationships between these time series, using radial basis function models (which can be thought of as a class of neural networks). The presence of such a relationship, indicated by the ability to model one filter output given another, would equate to the presence of nonlinear properties within the data. Using this technique, evidence is found for the presence of low-level nonlinear behavior during both phases of the solar cycle investigated in this study. The evidence for nonlinear behavior is stronger during the descending phase of SC 21. However, it is not possible to distinguish between nonlinear dynamics and a nonlinearly transformed colored Gaussian noise process in either instance, using the available data. Therefore, in conclusion, we find insufficient evidence within the SABRE data set to support the suggestion of increased nonlinear dynamical behavior during the ascending phase of SC 22. In fact, nonlinear dynamics would seem to exert very little influence within the measurement time series at all, given the observed data. Therefore it is likely that stochastic or unresolved high-dimensional nonlinear mechanisms are responsible for the observed spectrum complexity during the ascending phase of SC 22.

Phased-array sources based on nonlinear metamaterial nanocavities

PubMed Central

Wolf, Omri; Campione, Salvatore; Benz, Alexander; Ravikumar, Arvind P.; Liu, Sheng; Luk, Ting S.; Kadlec, Emil A.; Shaner, Eric A.; Klem, John F.; Sinclair, Michael B.; Brener, Igal

2015-01-01

Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization. As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (∼5 μm): a beam splitter and a polarizing beam splitter. Proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum. PMID:26126879

Time series with tailored nonlinearities

NASA Astrophysics Data System (ADS)

Räth, C.; Laut, I.

2015-10-01

It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide

PubMed Central

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P. K. A.

2014-01-01

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W−1/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems. PMID:25417847

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide.

PubMed

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P K A

2014-11-24

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W(-1)/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems.

Designing an ultrafast laser virtual laboratory using MATLAB GUIDE

NASA Astrophysics Data System (ADS)

Cambronero-López, F.; Gómez-Varela, A. I.; Bao-Varela, C.

2017-05-01

In this work we present a virtual simulator developed using the MATLAB GUIDE environment based on the numerical resolution of the nonlinear Schrödinger equation (NLS) and using the split step method for the study of the spatial-temporal propagation of nonlinear ultrashort laser pulses. This allows us to study the spatial-temporal propagation of ultrafast pulses as well as the influence of high-order spectral phases such as group delay dispersion and third-order dispersion on pulse compression in time. The NLS can describe several nonlinear effects, in particular in this paper we consider the Kerr effect, cross-polarized wave generation and cubic-quintic propagation in order to highlight the potential of this equation combined with the GUIDE environment. Graphical user interfaces are commonly used in science and engineering teaching due to their educational value, and have proven to be an effective way to engage and motivate students. Specifically, the interactive graphical interfaces presented provide the visualization of some of the most important nonlinear optics phenomena and allows users to vary the values of the main parameters involved.

Stepwise pH-gradient elution for the preparative separation of natural anthraquinones by multiple liquid-liquid partition.

PubMed

Hynninen, P H; Räisänen, R

2001-01-01

Preparative-scale separation of substituted anthraquinones by multiple liquid-liquid partition was studied using isopropylmethyl ketone (IMK)/aqueous phosphate buffer (aq.) as the solvent system and the Hietala apparatus with 100 partition units as the partition equipment. The lower (aq.) phase was chosen as mobile, while the upper (IMK) phase remained stationary. Hence, the principle of stepwise pH-gradient elution could be utilized to separate the components in two complex mixtures of hydroxyanthraquinones and hydroxyanthraquinone carboxylic acids, isolated from the fungus Dermocybe sanguinea. In spite of the nonlinearity of the partition isotherms for these anthraquinones, implying deviations from the Nernst partition law, remarkable separations were achieved for the components in each mixture. Every anthraquinone carboxylic acid showed markedly irregular partition behavior, appearing in the effluent as two more or less resolved concentration zones. Such splitting was attributed to the formation of relatively stable sandwich-dimers, which were in a slow equilibrium with the monomers in the more nonpolar organic phase. At lower pH-values, only the polar monomers were distributed into the mobile aqueous phase and moved forward, whereas the nonpolar sandwich-dimers remained almost entirely in the stationary organic phase and lagged behind. When the pH of the mobile aqueous phase was raised high enough, the firmly linked dimers were monomerized and emerged from the apparatus as a second concentration profile. Intermolecular hydrogen bonding and pi-pi interaction between the pi-systems of two anthraquinone molecules in a parallel orientation were considered responsible for the nonlinear and markedly irregular partition behavior of the natural anthraquinones studied. The nonlinearity of the partition behavior of the hydroxyanthraquinones lacking the carboxyl group, appeared merely as excessive broadening of the experimental concentration profile, which impaired the resolution between the components only insignificantly. Thus, e.g. the main components, dermocybin and emodin, could both be obtained from Separation 1 in a purity of at least 99%.

Analysis of complex neural circuits with nonlinear multidimensional hidden state models

PubMed Central

Friedman, Alexander; Slocum, Joshua F.; Tyulmankov, Danil; Gibb, Leif G.; Altshuler, Alex; Ruangwises, Suthee; Shi, Qinru; Toro Arana, Sebastian E.; Beck, Dirk W.; Sholes, Jacquelyn E. C.; Graybiel, Ann M.

2016-01-01

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain. PMID:27222584

Experimental phase synchronization detection in non-phase coherent chaotic systems by using the discrete complex wavelet approach

NASA Astrophysics Data System (ADS)

Ferreira, Maria Teodora; Follmann, Rosangela; Domingues, Margarete O.; Macau, Elbert E. N.; Kiss, István Z.

2017-08-01

Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with non-phase-coherent chaotic systems without state space reconstruction or pre-processing. The method correctly predicts the phase synchronization for a chemical experiment with three locally coupled, non-phase-coherent chaotic processes. The impact of different time-scales is demonstrated on the synchronization process that outlines the advantages of DCWA for analysis of experimental data.

A note on the generation of phase plane plots on a digital computer. [for solution of nonlinear differential equations

NASA Technical Reports Server (NTRS)

Simon, M. K.

1980-01-01

A technique is presented for generating phase plane plots on a digital computer which circumvents the difficulties associated with more traditional methods of numerical solving nonlinear differential equations. In particular, the nonlinear differential equation of operation is formulated.

Quantum limits to gravity estimation with optomechanics

NASA Astrophysics Data System (ADS)

Armata, F.; Latmiral, L.; Plato, A. D. K.; Kim, M. S.

2017-10-01

We present a table-top quantum estimation protocol to measure the gravitational acceleration g by using an optomechanical cavity. In particular, we exploit the nonlinear quantum light-matter interaction between an optical field and a massive mirror acting as mechanical oscillator. The gravitational field influences the system dynamics affecting the phase of the cavity field during the interaction. Reading out such a phase carried by the radiation leaking from the cavity, we provide an estimate of the gravitational acceleration through interference measurements. Contrary to previous studies, having adopted a fully quantum description, we are able to propose a quantum analysis proving the ultimate bound to the estimability of the gravitational acceleration and verifying optimality of homodyne detection. Noticeably, thanks to the light-matter decoupling at the measurement time, no initial cooling of the mechanical oscillator is demanded in principle.

Non-Fermi-liquid and topological states with strong spin-orbit coupling.

PubMed

Moon, Eun-Gook; Xu, Cenke; Kim, Yong Baek; Balents, Leon

2013-11-15

We argue that a class of strongly spin-orbit-coupled materials, including some pyrochlore iridates and the inverted band gap semiconductor HgTe, may be described by a minimal model consisting of the Luttinger Hamiltonian supplemented by Coulomb interactions, a problem studied by Abrikosov and collaborators. It contains twofold degenerate conduction and valence bands touching quadratically at the zone center. Using modern renormalization group methods, we update and extend Abrikosov's classic work and show that interactions induce a quantum critical non-Fermi-liquid phase, stable provided time-reversal and cubic symmetries are maintained. We determine the universal power-law exponents describing various observables in this Luttinger-Abrikosov-Beneslavskii state, which include conductivity, specific heat, nonlinear susceptibility, and the magnetic Gruneisen number. Furthermore, we determine the phase diagram in the presence of cubic and/or time-reversal symmetry breaking perturbations, which includes a topological insulator and Weyl semimetal phases. Many of these phases possess an extraordinarily large anomalous Hall effect, with the Hall conductivity scaling sublinearly with magnetization σ(xy)∼M0.51.

Nonlinear Plasma Experiments in Geospace with Gigawatts of RF Power at HAARP

NASA Astrophysics Data System (ADS)

Sheerin, J. P.; Rayyan, N.; Watkins, B. J.; Bristow, W. A.; Bernhardt, P. A.

2014-10-01

The HAARP phased-array HF transmitter at Gakona, AK delivers up to 3.6 GW (ERP) of HF power in the range of 2.8 - 10 MHz to the ionosphere with millisecond pointing, power modulation, and frequency agility. HAARP's unique features have enabled the conduct of a number of nonlinear plasma experiments in the interaction region of overdense ionospheric plasma including stimulated electromagnetic emissions (SEE), artificial aurora, artificial ionization layers, VLF wave-particle interactions in the magnetosphere, strong Langmuir turbulence (SLT) and suprathermal electron acceleration. Diagnostics include the Modular UHF Ionospheric Radar (MUIR) sited at HAARP, the SuperDARN-Kodiak HF radar, spacecraft radio beacons, HF receivers to record stimulated electromagnetic emissions (SEE) and telescopes and cameras for optical emissions. We report on short timescale ponderomotive overshoot effects, artificial field-aligned irregularities (AFAI), the aspect angle dependence of the intensity of the plasma line, and suprathermal electrons. Applications are made to the study and control of irregularities affecting spacecraft communication and navigation systems.

Vortex Chain in a Resonantly Pumped Polariton Superfluid

PubMed Central

Boulier, T.; Terças, H.; Solnyshkov, D. D.; Glorieux, Q.; Giacobino, E.; Malpuech, G.; Bramati, A.

2015-01-01

Exciton-polaritons are light-matter mixed states interacting via their exciton fraction. They can be excited, manipulated, and detected using all the versatile techniques of modern optics. An exciton-polariton gas is therefore a unique platform to study out-of-equilibrium interacting quantum fluids. In this work, we report the formation of a ring-shaped array of same sign vortices after injection of angular momentum in a polariton superfluid. The angular momentum is injected by a ℓ = 8 Laguerre-Gauss beam. In the linear regime, a spiral interference pattern containing phase defects is visible. In the nonlinear (superfluid) regime, the interference disappears and eight vortices appear, minimizing the energy while conserving the quantized angular momentum. The radial position of the vortices evolves in the region between the two pumps as a function of the density. Hydrodynamic instabilities resulting in the spontaneous nucleation of vortex-antivortex pairs when the system size is sufficiently large confirm that the vortices are not constrained by interference when nonlinearities dominate the system. PMID:25784592

Classical density-functional theory of inhomogeneous water including explicit molecular structure and nonlinear dielectric response.

PubMed

Lischner, Johannes; Arias, T A

2010-02-11

We present an accurate free-energy functional for liquid water written in terms of a set of effective potential fields in which fictitious noninteracting water molecules move. The functional contains an exact expression of the entropy of noninteracting molecules and thus provides an ideal starting point for the inclusion of complex intermolecular interactions which depend on the orientation of the interacting molecules. We show how an excess free-energy functional can be constructed to reproduce the following properties of water: the dielectric response; the experimental site-site correlation functions; the surface tension; the bulk modulus of the liquid and the variation of this modulus with pressure; the density of the liquid and the vapor phase; and liquid-vapor coexistence. As a demonstration, we present results for the application of this theory to the behavior of liquid water in a parallel plate capacitor. In particular, we make predictions for the dielectric response of water in the nonlinear regime, finding excellent agreement with known data.

Nonlinear dynamic behaviors of permanent magnet synchronous motors in electric vehicles caused by unbalanced magnetic pull

NASA Astrophysics Data System (ADS)

Xiang, Changle; Liu, Feng; Liu, Hui; Han, Lijin; Zhang, Xun

2016-06-01

Unbalanced magnetic pull (UMP) plays a key role in nonlinear dynamic behaviors of permanent magnet synchronous motors (PMSM) in electric vehicles. Based on Jeffcott rotor model, the stiffness characteristics of the rotor system of the PMSM are analyzed and the nonlinear dynamic behaviors influenced by UMP are investigated. In free vibration study, eigenvalue-based stability analysis for multiple equilibrium points is performed which offers an insight in system stiffness. Amplitude modulation effects are discovered of which the mechanism is explained and the period of modulating signal is carried out by phase analysis and averaging method. The analysis indicates that the effects are caused by the interaction of the initial phases of forward and backward whirling motions. In forced vibration study, considering dynamic eccentricity, frequency characteristics revealing softening type are obtained by harmonic balance method, and the stability of periodic solution is investigated by Routh-Hurwitz criterion. The frequency characteristics analysis indicates that the response amplitude is limited in the range between the amplitudes of the two kinds of equilibrium points. In the vicinity of the continuum of equilibrium points, the system hardly provides resistance to bending, and hence external disturbances easily cause loss of stability. It is useful for the design of the PMSM with high stability and low vibration and acoustic noise.

Pulse Shepherding in Nonlinear Fiber Optics

NASA Technical Reports Server (NTRS)

Yeh, C.; Bergman, L.

1996-01-01

In a wavelength division multiplexed fiber system, where pulses on different wavelength beams may co-propagate in a single mode fiber, the cross-phase-modulation (CPM) effects caused by the nonlinearity of the optical fiber are unavoidable. In other words, pulses on different wavelength beams can interact with and affect each other through the intensity dependence of the refractive index of the fiber. Although CPM will not cause energy to be exchanged among the beams, the pulse shapes and locations on these beams can be altered significantly. This phenomenon makes possible the manipulation and control of pulses co-propagating on different wavelength beams through the introduction of a shepherd pulse at a separate wavelength. How this can be accomplished is demonstrated in this paper.

Characterization of spiraling patterns in spatial rock-paper-scissors games.

PubMed

Szczesny, Bartosz; Mobilia, Mauro; Rucklidge, Alastair M

2014-09-01

The spatiotemporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatiotemporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair exchange, and hopping of individuals. By combining analytical and numerical methods, we obtain the model's phase diagram near its Hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase. The phases characterizing the cyclic competition away from the Hopf bifurcation (at low mutation rate) are also investigated. Our analytical approach relies on the careful analysis of the properties of the complex Ginzburg-Landau equation derived through a controlled (perturbative) multiscale expansion around the model's Hopf bifurcation. Our results allow us to clarify when spatial "rock-paper-scissors" competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility.

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Entrainment in nerve by a ferroelectric model (II): Quasi-periodic oscillation and the phase locking

NASA Astrophysics Data System (ADS)

Shirane, Kotaro; Tokimoto, Takayuki; Kushibe, Hiroyuki

1997-09-01

A nonlinear state equation for membrane excitation can be simplified by Leuchtag's ferroelectric model which is applied to a chemical network theory. A dissipative structure of such a membrane is described by an equilibrium space, η 3 + aη + b = 0, giving a cusp catastrophe, and the membrane is self-organized in the resting state under the condition, a < 0( T < Tc), where η corresponds to the membrane potential, and a and b imply dipole-dipole and dipole-ion interactions of channel proteins embedded in the membrane, respectively. As well known, a specific characteristic of nonlinear electrical phenomena in the membrane is a limit cycle arising through the entrainment by periodical stimuli or chaos. A phase transition between the equilibrium and the non-equilibrium states (a dissipative structure without the resting state) is described by a parameter giving the difference from thermal equilibrium. In this dynamic system, quasi-periodic oscillations which arise in periodic external fields and the phase locking, that is, entrainment, caused by changing I0 at ω ≠ ω n (ω n - the natural frequency of the membrane) are studied with parameters introduced into Zeeman's formulas of ȧ and ḃ.

Diagnostic-Photographic Determination of Drag/Lift/Torque Coefficients of High Speed Rigid Body in Water Column

DTIC Science & Technology

2008-01-01

various physical processes such as supercavitation and bubbles. A diagnostic- photographic method is developed in this study to determine the drag...nonlinear dynamics, body and multi-phase fluid interaction, supercavitation , and instability theory. The technical application of the hydrodynamics of...uV U ω= = − ×V e e e ei i , (29) where Eq.(9) is used. For a supercavitation area, a correction factor may be

Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry.

PubMed

Langoju, Rajesh; Patil, Abhijit; Rastogi, Pramod

2007-11-20

Signal processing methods based on maximum-likelihood theory, discrete chirp Fourier transform, and spectral estimation methods have enabled accurate measurement of phase in phase-shifting interferometry in the presence of nonlinear response of the piezoelectric transducer to the applied voltage. We present the statistical study of these generalized nonlinear phase step estimation methods to identify the best method by deriving the Cramér-Rao bound. We also address important aspects of these methods for implementation in practical applications and compare the performance of the best-identified method with other bench marking algorithms in the presence of harmonics and noise.

Gap Solitons of Superfluid Fermi Gas in FS Optical Lattices

NASA Astrophysics Data System (ADS)

Chen, Yan; Zhang, Ke-Zhi; He, Yong-Lin; Liu, Zhen-Lai; Zhu, Liao

2018-01-01

By employing the mean-field theory and hydrodynamic scheme, we study the gap solitons of superfluid Fermi gas in Fourier-Synthesized(FS) optical lattices. By means of numerical methods and variational approximation, the atomic interaction, the chemical potential, the potential depth of the lattice and relative phase of the Fermi system are derived along the Bose-Enstein condensation(BEC)side to the Bardeen-Cooper-Schrieffer (BCS)side. It means that the condition exciting gap solitons is obtained. Moreover, we analyze the fundamental gap soltions of the superfluid Fermi gas. It is found that the relative phase α impacts greatly on the properties of fundamental gap solitons for superfluid Fermi gas. Especially, the nonlinearity interaction term g decreases with α. Add, due to Fermi pressure, curvature changes of g in the BEC limit( γ = 1, here, γ is a function of an interaction parameter) is larger than that at unitary ( γ = 2/3). Spatial distribution of gap solitons exhibit very obvious different when the system transit from the BEC side to BCS side.

Model-free inference of direct network interactions from nonlinear collective dynamics.

PubMed

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

O Wave Interactions: Explosive Resonant Triads and Critical Layers.

NASA Astrophysics Data System (ADS)

Mahoney, Daniel J.

This thesis considers the phenomenon of explosive resonant triads in weakly nonlinear, dispersive wave systems. These are nearly linear waves with slowly varying amplitudes which become unbounded in finite time. It is shown that such interactions are much stronger than previously thought. These waves can be thought of as a nonlinear instability, in the sense that a weakly nonlinear perturbation to some system grows to such magnitudes that the behavior of the system is governed by strongly nonlinear effects. This may occur for systems which are linearly or neutrally stable. This is contrasted with previous resolutions of this problem, which treated such perturbations as being large amplitude, nearly linear waves. Analytical and numerical evidence is presented to support these claims. These waves represent a potentially important effect in a variety of physical systems, most notably plasma physics. Attention here is turned to their occurrence in fluid mechanics. Here previous work is extended to include flow systems with continuously varying basic velocities and densities. Many of the problems encountered here will be found to be of a singular nature themselves, and the techniques for analyzing these difficulties will be developed. This will involve the concept of a critical layer in a fluid, a level at which a wave phase speed equals the unperturbed fluid velocity in the direction of propagation. Examples of such waves in this context will be presented. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253 -1690.).

Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Dayyani, Z.; Sheykhi, A.; Dehghani, M. H.; Hajkhalili, S.

2018-02-01

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. First of all, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with the Van der Waals liquid-gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show that they depend on the dilaton coupling constant as well as on the nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in the case of T>T_c, we have no phase transition. When T=T_c, the system admits a second-order phase transition, while for T=T_f

Spin and wavelength multiplexed nonlinear metasurface holography

NASA Astrophysics Data System (ADS)

Ye, Weimin; Zeuner, Franziska; Li, Xin; Reineke, Bernhard; He, Shan; Qiu, Cheng-Wei; Liu, Juan; Wang, Yongtian; Zhang, Shuang; Zentgraf, Thomas

2016-06-01

Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam-Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption.

Spin and wavelength multiplexed nonlinear metasurface holography

PubMed Central

Ye, Weimin; Zeuner, Franziska; Li, Xin; Reineke, Bernhard; He, Shan; Qiu, Cheng-Wei; Liu, Juan; Wang, Yongtian; Zhang, Shuang; Zentgraf, Thomas

2016-01-01

Metasurfaces, as the ultrathin version of metamaterials, have caught growing attention due to their superior capability in controlling the phase, amplitude and polarization states of light. Among various types of metasurfaces, geometric metasurface that encodes a geometric or Pancharatnam–Berry phase into the orientation angle of the constituent meta-atoms has shown great potential in controlling light in both linear and nonlinear optical regimes. The robust and dispersionless nature of the geometric phase simplifies the wave manipulation tremendously. Benefitting from the continuous phase control, metasurface holography has exhibited advantages over conventional depth controlled holography with discretized phase levels. Here we report on spin and wavelength multiplexed nonlinear metasurface holography, which allows construction of multiple target holographic images carried independently by the fundamental and harmonic generation waves of different spins. The nonlinear holograms provide independent, nondispersive and crosstalk-free post-selective channels for holographic multiplexing and multidimensional optical data storages, anti-counterfeiting, and optical encryption. PMID:27306147

Down-conversion IM-DD RF photonic link utilizing MQW MZ modulator.

PubMed

Xu, Longtao; Jin, Shilei; Li, Yifei

2016-04-18

We present the first down-conversion intensity modulated-direct detection (IM-DD) RF photonic link that achieves frequency down-conversion using the nonlinear optical phase modulation inside a Mach-Zehnder (MZ) modulator. The nonlinear phase modulation is very sensitive and it can enable high RF-to-IF conversion efficiency. Furthermore, the link linearity is enhanced by canceling the nonlinear distortions from the nonlinear phase modulation and the MZ interferometer. Proof-of-concept measurement was performed. The down-conversion IM-DD link demonstrated 28dB improvement in distortion levels over that of a conventional IM-DD link using a LiNbO₃ MZ modulator.

Optical Rogue Waves in Vortex Turbulence.

PubMed

Gibson, Christopher J; Yao, Alison M; Oppo, Gian-Luca

2016-01-29

We present a spatiotemporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction, and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg-Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatiotemporal vortex-mediated turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability density functions (PDFs) with long tails typical of extreme optical events.

Thermodynamic output of single-atom quantum optical amplifiers and their phase-space fingerprint

NASA Astrophysics Data System (ADS)

Perl, Y.; Band, Y. B.; Boukobza, E.

2017-05-01

We analyze a resonant single-atom two-photon quantum optical amplifier both dynamically and thermodynamically. A detailed thermodynamic analysis shows that the nonlinear amplifier is thermodynamically equivalent to the linear amplifier. However, by calculating the Wigner quasiprobability distribution for various initial field states, we show that unique quantum features in optical phase space, absent in the linear amplifier, are retained for extended times, despite the fact that dissipation tends to wash out dynamical features observed at early evolution times. These features are related to the discrete nature of the two-photon matter-field interaction and fingerprint the initial field state at thermodynamic times.

Amplification of a seed pumped by a chirped laser in the strong coupling Brillouin regime

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

Schluck, F.; Lehmann, G.; Spatschek, K. H.

Seed amplification via Brillouin backscattering of a long pump laser-pulse is considered. The interaction takes place in the so called strong coupling regime. Pump chirping is applied to mitigate spontaneous Raman backscattering of the pump before interacting with the seed. The strong coupling regime facilitates stronger exponential growth and narrower seeds compared to the so called weak coupling regime, although in the latter the scaling with pump amplitude is stronger. Strong coupling is achieved when the pump laser amplitude exceeds a certain threshold. It is shown how the chirp influences both the linear as well as the nonlinear amplification process.more » First, linear amplification as well as the seed profiles are determined in dependence of the chirping rate. In contrast to the weak coupling situation, the evolution is not symmetric with respect to the sign of the chirping rate. In the nonlinear stage of the amplification, we find an intrinsic chirp of the seed pulse even for an un-chirped pump. We show that chirping the pump may have a strong influence on the shape of the seed in the nonlinear amplification phase. Also, the influence of pump chirp on the efficiency of Brillouin seed amplification is discussed.« less

EDITORIAL: Measurement techniques for multiphase flows Measurement techniques for multiphase flows

NASA Astrophysics Data System (ADS)

Okamoto, Koji; Murai, Yuichi

2009-11-01

Research on multiphase flows is very important for industrial applications, including power stations, vehicles, engines, food processing and so on. Multiphase flows originally have nonlinear features because of multiphase systems. The interaction between the phases plays a very interesting role in the flows. The nonlinear interaction causes the multiphase flows to be very complicated. Therefore techniques for measuring multiphase flows are very useful in helping to understand the nonlinear phenomena. The state-of-the-art measurement techniques were presented and discussed at the sixth International Symposium on Measurement Techniques for Multiphase Flows (ISMTMF2008) held in Okinawa, Japan, on 15-17 December 2008. This special feature of Measurement Science and Technology includes selected papers from ISMTMF2008. Okinawa has a long history as the Ryukyus Kingdom. China, Japan and many western Pacific countries have had cultural and economic exchanges through Okinawa for over 1000 years. Much technical and scientific information was exchanged at the symposium in Okinawa. The proceedings of ISMTMF2008 apart from these special featured papers were published in Journal of Physics: Conference Series vol. 147 (2009). We would like to express special thanks to all the contributors to the symposium and this special feature. This special feature will be a milestone in measurement techniques for multiphase flows.

Photonic Switching Devices Using Light Bullets

NASA Technical Reports Server (NTRS)

Goorjian, Peter M. (Inventor)

1997-01-01

The present invention is directed toward a unique ultra-fast, all-optical switching device or switch made with readily available, relatively inexpensive, highly nonlinear photonic glasses. These photonic glasses have a sufficiently negative group velocity dispersion and high nonlinear index of refraction to support stable light bullets. The light bullets counterpropagate through, and interact within the waveguide to selectively change each others' directions of propagation into predetermined channels. In one embodiment, the switch utilizes a rectangularly planar slab waveguide, and further includes two central channels and a plurality of lateral channels for guiding the light bullets into and out of the waveguide. One advantage presented by the present all-optical switching device lies in its practical use of light bullets, thus preventing the degeneration of the pulses due to dispersion and diffraction at the front and back of the pulses. Another feature of the switching device is the relative insensitivity of the collision process to the time difference in which the counter-propagating pulses enter the waveguide. since. contrary to conventional co-propagating spatial solitons, the relative phase of the colliding pulses does not affect the interaction of these pulses. Yet another feature of the present all-optical switching device is the selection of the light pulse parameters which enables the generation of light bullets in highly nonlinear glasses.

Large conditional single-photon cross-phase modulation

PubMed Central

Hosseini, Mahdi; Duan, Yiheng; Vuletić, Vladan

2016-01-01

Deterministic optical quantum logic requires a nonlinear quantum process that alters the phase of a quantum optical state by π through interaction with only one photon. Here, we demonstrate a large conditional cross-phase modulation between a signal field, stored inside an atomic quantum memory, and a control photon that traverses a high-finesse optical cavity containing the atomic memory. This approach avoids fundamental limitations associated with multimode effects for traveling optical photons. We measure a conditional cross-phase shift of π/6 (and up to π/3 by postselection on photons that remain in the system longer than average) between the retrieved signal and control photons, and confirm deterministic entanglement between the signal and control modes by extracting a positive concurrence. By upgrading to a state-of-the-art cavity, our system can reach a coherent phase shift of π at low loss, enabling deterministic and universal photonic quantum logic. PMID:27519798

Evolution of diffraction and self-diffraction phenomena in thin films of Gelite Bloom/Hibiscus Sabdariffa

NASA Astrophysics Data System (ADS)

Cano-Lara, Miroslava; Severiano-Carrillo, Israel; Trejo-Durán, Mónica; Alvarado-Méndez, Edgar

2017-09-01

In this work, we present a study of non-linear optical response in thin films elaborated with Gelite Bloom and extract of Hibiscus Sabdariffa. Non-linear refraction and absorption effects were studied experimentally (Z-scan technique) and numerically, by considering the transmittance as non-linear absorption and refraction contribution. We observe large phase shifts to far field, and diffraction due to self-phase modulation of the sample. Diffraction and self-diffraction effects were observed as time function. The aim of studying non-linear optical properties in thin films is to eliminate thermal vortex effects that occur in liquids. This is desirable in applications such as non-linear phase contrast, optical limiting, optics switches, etc. Finally, we find good agreement between experimental and theoretical results.

Time-dependent photon heat transport through a mesoscopic Josephson device

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

Lu, Wen-Ting; Zhao, Hong-Kang, E-mail: zhaohonk@bit.edu.cn

The time-oscillating photon heat current through a dc voltage biased mesoscopic Josephson Junction (MJJ) has been investigated by employing the nonequilibrium Green’s function approach. The Landauer-like formula of photon heat current has been derived in both of the Fourier space and its time-oscillating versions, where Coulomb interaction, self inductance, and magnetic flux take effective roles. Nonlinear behaviors are exhibited in the photon heat current due to the quantum nature of MJJ and applied external dc voltage. The magnitude of heat current decreases with increasing the external bias voltage, and subtle oscillation structures appear as the superposition of different photon heatmore » branches. The overall period of heat current with respect to time is not affected by Coulomb interaction, however, the magnitude and phase of it vary considerably by changing the Coulomb interaction. - Highlights: • The time-oscillating photon heat current through a mesoscopic Josephson Junction has been investigated. • The Landauer-like formula of photon heat current has been derived by the nonequilibrium Green’s function approach. • Nonlinear behaviors are exhibited in the photon heat current resulting from the self inductance and Coulomb interaction. • The oscillation structure of heat current is composed of the superposition of oscillations with different periods.« less

Phased-array sources based on nonlinear metamaterial nanocavities

DOE PAGES

Wolf, Omri; Campione, Salvatore; Benz, Alexander; ...

2015-07-01

Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization.more » As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (~5 μm): a beam splitter and a polarizing beam splitter. As a result, proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum.« less

On the estimation of phase synchronization, spurious synchronization and filtering

NASA Astrophysics Data System (ADS)

Rios Herrera, Wady A.; Escalona, Joaquín; Rivera López, Daniel; Müller, Markus F.

2016-12-01

Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M. Chavez et al., J. Neurosci. Methods 154, 149 (2006)]. If this condition is not fulfilled, band-pass filtering seems to be the adequate technique in order to pre-process data for a posterior synchronization analysis. However, it was reported that band-pass filtering might induce spurious synchronization [L. Xu et al., Phys. Rev. E 73, 065201(R), (2006); J. Sun et al., Phys. Rev. E 77, 046213 (2008); and J. Wang and Z. Liu, EPL 102, 10003 (2013)], a statement that without further specification causes uncertainty over all measures that aim to quantify phase synchronization of broadband field data. We show by using signals derived from different test frameworks that appropriate filtering does not induce spurious synchronization. Instead, filtering in the time domain tends to wash out existent phase interrelations between signals. Furthermore, we show that measures derived for the estimation of phase synchronization like the mean phase coherence are also useful for the detection of interrelations between time series, which are not necessarily derived from coupled self-sustained nonlinear oscillators.

Interaction of Airy-Gaussian beams in saturable media

NASA Astrophysics Data System (ADS)

Zhou, Meiling; Peng, Yulian; Chen, Chidao; Chen, Bo; Peng, Xi; Deng, Dongmei

2016-08-01

Based on the nonlinear Schrödinger equation, the interactions of the two Airy-Gaussian components in the incidence are analyzed in saturable media, under the circumstances of the same amplitude and different amplitudes, respectively. It is found that the interaction can be both attractive and repulsive depending on the relative phase. The smaller the interval between two Airy-Gaussian components in the incidence is, the stronger the intensity of the interaction. However, with the equal amplitude, the symmetry is shown and the change of quasi-breathers is opposite in the in-phase case and out-of-phase case. As the distribution factor is increased, the phenomena of the quasi-breather and the self-accelerating of the two Airy-Gaussian components are weakened. When the amplitude is not equal, the image does not have symmetry. The obvious phenomenon of the interaction always arises on the side of larger input power in the incidence. The maximum intensity image is also simulated. Many of the characteristics which are contained within other images can also be concluded in this figure. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374108 and 10904041), the Foundation for the Author of Guangdong Province Excellent Doctoral Dissertation (Grant No. SYBZZXM201227), and the Foundation of Cultivating Outstanding Young Scholars (“Thousand, Hundred, Ten” Program) of Guangdong Province, China. CAS Key Laboratory of Geospace Environment, University of Science and Technology of China.

Nonlinear and quantum optics near nanoparticles

NASA Astrophysics Data System (ADS)

Dhayal, Suman

We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 4-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 7-level atoms near nanoparticles. This could be used as a prototype to study any n-level atomic system experimentally in the presence of ensembles of quantum emitters. In the last chapter, we suggested a variant of a pulse-shaping technique applicable in stimulated Raman spectroscopy (SRS) for detection of atoms and molecules in multiscattering media. We used discrete-dipole approximation to obtain the fields created by the nanoparticles.

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong

2018-03-01

We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).

Extreme wave formation in unidirectional sea due to stochastic wave phase dynamics

NASA Astrophysics Data System (ADS)

Wang, Rui; Balachandran, Balakumar

2018-07-01

The authors consider a stochastic model based on the interaction and phase coupling amongst wave components that are modified envelope soliton solutions to the nonlinear Schrödinger equation. A probabilistic study is carried out and the resulting findings are compared with ocean wave field observations and laboratory experimental results. The wave height probability distribution obtained from the model is found to match well with prior data in the large wave height region. From the eigenvalue spectrum obtained through the Inverse Scattering Transform, it is revealed that the deep-water wave groups move at a speed different from the linear group speed, which justifies the inclusion of phase correction to the envelope solitary wave components. It is determined that phase synchronization amongst elementary solitary wave components can be critical for the formation of extreme waves in unidirectional sea states.

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

Nonlinear oscillations and waves in multi-species cold plasmas

NASA Astrophysics Data System (ADS)

Verma, Prabal Singh

2016-12-01

The spatio-temporal evolution of nonlinear oscillations in multi-species plasma is revisited to provide more insight into the physics of phase mixing by constructing two sets of nonlinear solutions up to the second order. The first solution exhibits perfect oscillations in the linear regime and phase mixing appears only nonlinearly in the second order as a response to the ponderomotive forces. This response can be both direct and indirect. The indirect contribution of the ponderomotive forces appears through self-consistently generated low frequency fields. Furthermore, the direct and indirect contributions of the ponderomotive forces on the phase mixing process is explored and it is found that the indirect contribution is negligible in an electron-ion plasma and it disappears in the case of electron-positron plasma, yet represents an equal contribution in the electron-positron-ion plasma. However, the second solution does not exhibit any phase mixing due to the absence of ponderomotive forces but results in an undistorted nonlinear traveling wave. These investigations have relevance for laboratory/astrophysical multi-species plasma.

Analysis of nonlinear modulation between sound and vibrations in metallic structure and its use for damage detection

NASA Astrophysics Data System (ADS)

Liu, Bin; Gang, Tie; Wan, Chuhao; Wang, Changxi; Luo, Zhiwei

2015-07-01

Vibro-acoustic modulation technique is a nonlinear ultrasonic method in nondestructive testing. This technique detects the defects by monitoring the modulation components generated by the interaction between the vibration and the ultrasound wave due to the nonlinear material behaviour caused by the damage. In this work, a swept frequency signal was used as high frequency excitation, then the Hilbert transform based amplitude and phase demodulation and synchronous demodulation (SD) were used to extract the modulation information from the received signal, the results were graphed in the time-frequency domain after the short time Fourier transform. The demodulation results were quite different from each other. The reason for the difference was investigated by analysing the demodulation process of the two methods. According to the analysis and the subsequent verification test, it was indicated that the SD method was more proper for the test and a new index called MISD was defined to evaluate the structure quality in the Vibro-acoustic modulation test with swept probing excitation.

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.

Nonlinear Magnus-induced dynamics and Shapiro spikes for ac and dc driven skyrmions on periodic quasi-one-dimensional substrates

NASA Astrophysics Data System (ADS)

Reichhardt, Charles; Reichhardt, Cynthia J. Olson

We numerically examine skyrmions interacting with a periodic quasi-one-dimensional substrate. When we drive the skyrmions perpendicular to the substrate periodicity direction, a rich variety of nonlinear Magnus-induced effects arise, in contrast to an overdamped system that shows only a linear velocity-force curve for this geometry. The skyrmion velocity-force curve is strongly nonlinear and we observe a Magnus-induced speed-up effect when the pinning causes the Magnus velocity response to align with the dissipative response. At higher applied drives these components decouple, resulting in strong negative differential conductivity. For skyrmions under combined ac and dc driving, we find a new class of phase locking phenomena in which the velocity-force curves contain a series of what we call Shapiro spikes, distinct from the Shapiro steps observed in overdamped systems. There are also regimes in which the skyrmion moves in the direction opposite to the applied dc drive to give negative mobility.

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Broer-Kaup-Kupershmidt system in the shallow water of uniform depth

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Mao, Bing-Qing

2017-03-01

Under investigation in this paper is a (2+1)-dimensional Broer-Kaup-Kupershmidt system for the nonlinear and dispersive long gravity waves on two horizontal directions in the shallow water of uniform depth. Bilinear forms, Bäcklund transformation and Lax pair are derived based on the Bell polynomials and symbolic computation. One- and two-soliton solutions with a real function ϕ(y) are constructed via the Hirota method, where y is the scaled space coordinate. Propagation and interaction of the solitons are illustrated graphically: (i) ϕ(y) affects the shape of the solitons. (ii) Interaction of the solitons including the elastic and inelastic interactions are discussed. When the solitons' interaction is elastic, the amplitude, velocity and shape of the soliton remain invariant after the interaction except for a phase shift, and the smaller-amplitude soliton has a larger phase shift. (iii) Height of the water surface above a horizontal bottom can be a bell-shaped soliton or an upside-down bell-shaped soliton under certain conditions, while horizontal velocity of the water wave always keeps bell-shaped.

Single-Cycle Terahertz Pulse Generation from OH1 Crystal via Cherenkov Phase Matching

NASA Astrophysics Data System (ADS)

Uchida, Hirohisa; Oota, Kengo; Okimura, Koutarou; Kawase, Kodo; Takeya, Kei

2018-06-01

OH1 crystal is an organic nonlinear optical crystal with a large nonlinear optical constant. However, it has dispersion of refractive indices in the terahertz (THz) frequency. This limits the frequencies that satisfy the phase matching conditions for THz wave generation. In this study, we addressed the phase matching conditions for THz wave generation by combining an OH1 crystal with prism-coupled Cherenkov phase matching. We observed the generation of single-cycle THz pulses with a spectrum covering a frequency range of 3 THz. These results prove that combining prism-coupled Cherenkov phase matching with nonlinear optical crystals yields a THz wave generation method that is insusceptible to crystal dispersion.

Single-Cycle Terahertz Pulse Generation from OH1 Crystal via Cherenkov Phase Matching

NASA Astrophysics Data System (ADS)

Uchida, Hirohisa; Oota, Kengo; Okimura, Koutarou; Kawase, Kodo; Takeya, Kei

2018-03-01

OH1 crystal is an organic nonlinear optical crystal with a large nonlinear optical constant. However, it has dispersion of refractive indices in the terahertz (THz) frequency. This limits the frequencies that satisfy the phase matching conditions for THz wave generation. In this study, we addressed the phase matching conditions for THz wave generation by combining an OH1 crystal with prism-coupled Cherenkov phase matching. We observed the generation of single-cycle THz pulses with a spectrum covering a frequency range of 3 THz. These results prove that combining prism-coupled Cherenkov phase matching with nonlinear optical crystals yields a THz wave generation method that is insusceptible to crystal dispersion.

Nonlinear phase noise tolerance for coherent optical systems using soft-decision-aided ML carrier phase estimation enhanced with constellation partitioning

NASA Astrophysics Data System (ADS)

Li, Yan; Wu, Mingwei; Du, Xinwei; Xu, Zhuoran; Gurusamy, Mohan; Yu, Changyuan; Kam, Pooi-Yuen

2018-02-01

A novel soft-decision-aided maximum likelihood (SDA-ML) carrier phase estimation method and its simplified version, the decision-aided and soft-decision-aided maximum likelihood (DA-SDA-ML) methods are tested in a nonlinear phase noise-dominant channel. The numerical performance results show that both the SDA-ML and DA-SDA-ML methods outperform the conventional DA-ML in systems with constant-amplitude modulation formats. In addition, modified algorithms based on constellation partitioning are proposed. With partitioning, the modified SDA-ML and DA-SDA-ML are shown to be useful for compensating the nonlinear phase noise in multi-level modulation systems.

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

NASA Astrophysics Data System (ADS)

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

2010-06-01

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

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

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

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

Multidimensional discrete compactons in nonlinear Schrödinger lattices with strong nonlinearity management

DOE PAGES

D'Ambroise, J.; Salerno, M.; Kevrekidis, P. G.; ...

2015-11-19

The existence of multidimensional lattice compactons in the discrete nonlinear Schrödinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast modulations, an effective averaged dynamical equation arises with coupling constants involving Bessel functions of the first and zeroth kinds. We show that these terms allow one to solve, at this averaged level, for exact discrete compacton solution configurations in the corresponding stationary equation. We focus on seven types of compacton solutions. Single-site and vortex solutions are found to be always stable in the parametric regimes we examined.more » We also found that other solutions such as double-site in- and out-of-phase, four-site symmetric and antisymmetric, and a five-site compacton solution are found to have regions of stability and instability in two-dimensional parametric planes, involving variations of the strength of the coupling and of the nonlinearity. We also explore the time evolution of the solutions and compare the dynamics according to the averaged equations with those of the original dynamical system. Finally, the possible observation of compactons in Bose-Einstein condensates loaded in a deep two-dimensional optical lattice with interactions modulated periodically in time is also discussed.« less

Determination of nonlinear nanomechanical resonator-qubit coupling coefficient in a hybrid quantum system.

PubMed

Geng, Qi; Zhu, Ka-Di

2016-07-10

We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.

Nonlinear saturation of wave packets excited by low-energy electron horseshoe distributions.

PubMed

Krafft, C; Volokitin, A

2013-05-01

Horseshoe distributions are shell-like particle distributions that can arise in space and laboratory plasmas when particle beams propagate into increasing magnetic fields. The present paper studies the stability and the dynamics of wave packets interacting resonantly with electrons presenting low-energy horseshoe or shell-type velocity distributions in a magnetized plasma. The linear instability growth rates are determined as a function of the ratio of the plasma to the cyclotron frequencies, of the velocity and the opening angle of the horseshoe, and of the relative thickness of the shell. The nonlinear stage of the instability is investigated numerically using a symplectic code based on a three-dimensional Hamiltonian model. Simulation results show that the dynamics of the system is mainly governed by wave-particle interactions at Landau and normal cyclotron resonances and that the high-order normal cyclotron resonances play an essential role. Specific features of the dynamics of particles interacting simultaneously with two or more waves at resonances of different natures and orders are discussed, showing that such complex processes determine the main characteristics of the wave spectrum's evolution. Simulations with wave packets presenting quasicontinuous spectra provide a full picture of the relaxation of the horseshoe distribution, revealing two main phases of the evolution: an initial stage of wave energy growth, characterized by a fast filling of the shell, and a second phase of slow damping of the wave energy, accompanied by final adjustments of the electron distribution. The influence of the density inhomogeneity along the horseshoe on the wave-particle dynamics is also discussed.

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

NASA Astrophysics Data System (ADS)

Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

2017-10-01

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

Nonlinear mixing of electromagnetic waves in plasmas.

PubMed

Stefan, V; Cohen, B I; Joshi, C

1989-01-27

Recently, a strong research effort has been focused on applications of beat waves in plasma interactions. This research has important implications for various aspects of plasma physics and plasma technology. This article reviews the present status of the field and comments on plasma probing, heating of magnetically confined and laser plasmas, ionospheric plasma modification, beat-wave particle acceleration, beat-wave current drive in toroidal devices, beat wave-driven free-electron lasers, and phase conjugation with beat waves.

Wave Propagation Around Coronal Structures: Stratification, Buoyancy, Small Scale Formation

NASA Astrophysics Data System (ADS)

Tomlinson, S. M.; Rappazzo, F.; Velli, M.

2017-12-01

We study the propagation of waves in a coronal medium characterized by stratification and structure in density. temperature and magnetic field. It is well known that average gradients affect the propagation of Alfvén and other MHD waves via reflection, phase mixing, resonant absorption and other coupling phenomena. Here we discuss how the interplay of propagation on inhomogeneous, stratified structures with nonlinear interactions may lead to interesting effects including preferential heating, buoyancy, and plasma acceleration.

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1988-01-01

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

A Model for the Propagation of Nonlinear Surface Waves over Viscous Muds

DTIC Science & Technology

2007-07-05

grained, cohesive sedimentary 1993; Foda et al., 1993). With the exception of fluidization environments is well known. Extreme dissipation rates have...processes ( Foda et al., 1993; DeWit, 1995), these models focus on a single, well-defined mud phase. Although the models Corresponding author. Tel.: +1...However, surface-interface wave interactions ( Foda , 1989; Hill and Foda , our focus at the present is on a wave model which can be 1998; Jamali et al

Naturally stable Sagnac–Michelson nonlinear interferometer

DOE PAGES

Lukens, Joseph M.; Peters, Nicholas A.; Pooser, Raphael C.

2016-11-16

Interferometers measure a wide variety of dynamic processes by converting a phase change into an intensity change. Nonlinear interferometers, making use of nonlinear media in lieu of beamsplitters, promise substantial improvement in the quest to reach the ultimate sensitivity limits. Here we demonstrate a new nonlinear interferometer utilizing a single parametric amplifier for mode mixing conceptually, a nonlinear version of the conventional Michelson interferometer with its arms collapsed together. We observe up to 99.9% interference visibility and find evidence for noise reduction based on phase-sensitive gain. As a result, our configuration utilizes fewer components than previous demonstrations and requires nomore » active stabilization, offering new capabilities for practical nonlinear interferometric-based sensors.« less

Nonlinear unitary transformations of space-variant polarized light fields from self-induced geometric-phase optical elements

NASA Astrophysics Data System (ADS)

Kravets, Nina; Brasselet, Etienne

2018-01-01

We propose to couple the optical orientational nonlinearities of liquid crystals with their ability to self-organize to tailor them to control space-variant-polarized optical fields in a nonlinear manner. Experimental demonstration is made using a liquid crystal light valve that behaves like a light-driven geometric phase optical element. We also unveil two original nonlinear optical processes, namely self-induced separability and nonseparability. These results contribute to the advancement of nonlinear singular optics that is still in its infancy despite 25 years of effort, which may foster the development of nonlinear protocols to manipulate high-dimensional optical information both in the classical and quantum regimes.

Nonlocal nonlinear refraction in Hibiscus sabdariffa with large phase shifts.

PubMed

Ramírez-Martínez, D; Alvarado-Méndez, E; Trejo-Durán, M; Vázquez-Guevara, M A

2014-10-20

In this work we present a study of nonlinear optical properties in organic materials (hibiscus sabdariffa). Our results demonstrate that the medium exhibits a highly nonlocal nonlinear response. We show preliminary numerical results of the transmittance as nonlocal response by considering, simultaneously, the nonlinear absorption and refraction in media. Numerical results are accord to measurement obtained by Z- scan technique where we observe large phase shifts. We also analyze the far field diffraction ring patterns of the sample.

Phase Equilibrium and Crystal Growth Studies on AgGaSe2 and Related Nonlinear Optical Materials

DTIC Science & Technology

1989-09-01

identify by block number) IELD GROUP SUB-GROUP - "°Silver selenogallate, AgGaSe2, nonlinear optical materials, infrared materials, optical defects 19...materials has unique nonlinear infrared optical properties( 1-4 ) including high nonlinear coefficients, and the ability to be phase matched through a...have a milky appearance in thin section or when viewed with a commercial infrared image converter. Microscopic examination of AgGaSe2 in both reflected

Origin of nonlinear transport across the magnetically induced superconductor-metal-insulator transition in two dimensions.

PubMed

Seo, Y; Qin, Y; Vicente, C L; Choi, K S; Yoon, Jongsoo

2006-08-04

We have studied the effect of perpendicular magnetic fields and temperatures on nonlinear electronic transport in amorphous Ta superconducting thin films. The films exhibit a magnetic field-induced metallic behavior intervening the superconductor-insulator transition in the zero temperature limit. We show that the phase-identifying nonlinear transport in the superconducting and metallic phases arises from an intrinsic origin, not from an electron heating effect. The nonlinear transport is found to accompany an extraordinarily long voltage response time.

Solitary waves of surface plasmon polariton via phase shifts under Doppler broadening and Kerr nonlinearity

NASA Astrophysics Data System (ADS)

Ahmad, S.; Ahmad, A.; Bacha, B. A.; Khan, A. A.; Abdul Jabar, M. S.

2017-12-01

Surface Plasmon Polaritons (SPPs) are theoretically investigated at the interface of a dielectric metal and gold. The output pulse from the dielectric is used as the input pulse for the generation of SPPs. The SPPs show soliton-like behavior at the interface. The solitary form of a SPP is maintained under the effects of Kerr nonlinearity, Doppler broadening and Fresnel dragging whereas its phase shift is significantly modified. A 0.3radian phase shift is calculated in the presence of both Kerr nonlinearity and Fresnel dragging in the absence of plasma motion. The phase shift is enhanced to 60radian due to the combined effect of Doppler broadening, Kerr nonlinearity and Fresnel dragging. The results may have significant applications in nano-photonics, optical tweezers, photovoltaic devices, plasmonster and sensing technology.

Double Scaling in the Relaxation Time in the β -Fermi-Pasta-Ulam-Tsingou Model

NASA Astrophysics Data System (ADS)

Lvov, Yuri V.; Onorato, Miguel

2018-04-01

We consider the original β -Fermi-Pasta-Ulam-Tsingou system; numerical simulations and theoretical arguments suggest that, for a finite number of masses, a statistical equilibrium state is reached independently of the initial energy of the system. Using ensemble averages over initial conditions characterized by different Fourier random phases, we numerically estimate the time scale of equipartition and we find that for very small nonlinearity it matches the prediction based on exact wave-wave resonant interaction theory. We derive a simple formula for the nonlinear frequency broadening and show that when the phenomenon of overlap of frequencies takes place, a different scaling for the thermalization time scale is observed. Our result supports the idea that the Chirikov overlap criterion identifies a transition region between two different relaxation time scalings.

Thermal conductivity in one-dimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Politi, Antonio; Giardinà, Cristian; Livi, Roberto; Vassalli, Massimo

2000-03-01

Thermal conducitivity of one-dimensional nonlinear systems typically diverges in the thermodynamic limit, whenever the momentum is conserved (i.e. in the absence of interactions with an external substrate). Evidence comes from detailed studies of Fermi-Pasta-Ulam and diatomic Toda chains. Here, we discuss the first example of a one-dimensional system obeying Fourier law : a chain of coupled rotators. Numerical estimates of the thermal conductivity obtained by simulating a chain in contact with two thermal baths at different temperatures are found to be consistent with those ones based on linear response theory. The dynamics of the Fourier modes provides direct evidence of energy diffusion. The finiteness of the conductivity is traced back to the occurrence of phase-jumps. Our conclusions are confirmed by the analysis of two variants of the rotator model.

Equalization enhanced phase noise in Nyquist-spaced superchannel transmission systems using multi-channel digital back-propagation

PubMed Central

Xu, Tianhua; Liga, Gabriele; Lavery, Domaniç; Thomsen, Benn C.; Savory, Seb J.; Killey, Robert I.; Bayvel, Polina

2015-01-01

Superchannel transmission spaced at the symbol rate, known as Nyquist spacing, has been demonstrated for effectively maximizing the optical communication channel capacity and spectral efficiency. However, the achievable capacity and reach of transmission systems using advanced modulation formats are affected by fibre nonlinearities and equalization enhanced phase noise (EEPN). Fibre nonlinearities can be effectively compensated using digital back-propagation (DBP). However EEPN which arises from the interaction between laser phase noise and dispersion cannot be efficiently mitigated, and can significantly degrade the performance of transmission systems. Here we report the first investigation of the origin and the impact of EEPN in Nyquist-spaced superchannel system, employing electronic dispersion compensation (EDC) and multi-channel DBP (MC-DBP). Analysis was carried out in a Nyquist-spaced 9-channel 32-Gbaud DP-64QAM transmission system. Results confirm that EEPN significantly degrades the performance of all sub-channels of the superchannel system and that the distortions are more severe for the outer sub-channels, both using EDC and MC-DBP. It is also found that the origin of EEPN depends on the relative position between the carrier phase recovery module and the EDC (or MC-DBP) module. Considering EEPN, diverse coding techniques and modulation formats have to be applied for optimizing different sub-channels in superchannel systems. PMID:26365422

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.

Mesosphere Dynamics with Gravity Wave Forcing. 1; Diurnal and Semi-Diurnal Tides

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Mengel, J. G.; Chan, K. L.; Porter, H. S.; Einaudi, Franco (Technical Monitor)

2000-01-01

We present results from a nonlinear, 3D, time dependent numerical spectral model (NSM), which extends from the ground up into the thermosphere and incorporates Hines' Doppler Spread Parameterization for small-scale gravity waves (GW). Our focal point is the mesosphere that is dominated by wave interactions. We discuss diurnal and semi-diurnal tides ill the present paper (Part 1) and planetary waves in the companion paper (Part 2). To provide an understanding of the seasonal variations of tides, in particular with regard to gravity wave processes, numerical experiments are performed that lead to the following conclusions: 1. The large semiannual variations in tile diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. 2. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength. 3.Variations in eddy viscosity associated with GW interactions tend to peak in late spring and early fall and call also influence the DT. 4. The semidiurnal semidiurnal tide (SDT), and its phase in particular, is strongly influenced by the mean zonal circulation. 5. The SDT, individually, is amplified by GW's. But the DT filters out GW's such that the wave interaction effectively reduces the amplitude of the SDT, effectively producing a strong nonlinear interaction between the DT and SDT. 6.) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT.

Synchronization and Causality Across Time-scales: Complex Dynamics and Extremes in El Niño/Southern Oscillation

NASA Astrophysics Data System (ADS)

Jajcay, N.; Kravtsov, S.; Tsonis, A.; Palus, M.

2017-12-01

A better understanding of dynamics in complex systems, such as the Earth's climate is one of the key challenges for contemporary science and society. A large amount of experimental data requires new mathematical and computational approaches. Natural complex systems vary on many temporal and spatial scales, often exhibiting recurring patterns and quasi-oscillatory phenomena. The statistical inference of causal interactions and synchronization between dynamical phenomena evolving on different temporal scales is of vital importance for better understanding of underlying mechanisms and a key for modeling and prediction of such systems. This study introduces and applies information theory diagnostics to phase and amplitude time series of different wavelet components of the observed data that characterizes El Niño. A suite of significant interactions between processes operating on different time scales was detected, and intermittent synchronization among different time scales has been associated with the extreme El Niño events. The mechanisms of these nonlinear interactions were further studied in conceptual low-order and state-of-the-art dynamical, as well as statistical climate models. Observed and simulated interactions exhibit substantial discrepancies, whose understanding may be the key to an improved prediction. Moreover, the statistical framework which we apply here is suitable for direct usage of inferring cross-scale interactions in nonlinear time series from complex systems such as the terrestrial magnetosphere, solar-terrestrial interactions, seismic activity or even human brain dynamics.

Interactions of large amplitude solitary waves in viscous fluid conduits

NASA Astrophysics Data System (ADS)

Lowman, Nicholas K.; Hoefer, M. A.; El, G. A.

2014-07-01

The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behavior are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as "physical solitons." Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Resonant-Triad Interaction

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.

All-optical phase modulation in a cavity-polariton Mach–Zehnder interferometer

PubMed Central

Sturm, C.; Tanese, D.; Nguyen, H.S.; Flayac, H.; Galopin, E.; Lemaître, A.; Sagnes, I.; Solnyshkov, D.; Amo, A.; Malpuech, G.; Bloch, J.

2014-01-01

Quantum fluids based on light is a highly developing research field, since they provide a nonlinear platform for developing optical functionalities and quantum simulators. An important issue in this context is the ability to coherently control the properties of the fluid. Here we propose an all-optical approach for controlling the phase of a flow of cavity-polaritons, making use of their strong interactions with localized excitons. Here we illustrate the potential of this method by implementing a compact exciton–polariton interferometer, which output intensity and polarization can be optically controlled. This interferometer is cascadable with already reported polariton devices and is promising for future polaritonic quantum optic experiments. Complex phase patterns could be also engineered using this optical method, providing a key tool to build photonic artificial gauge fields. PMID:24513781

Dissipative structure in the photo-induced phase under steady light irradiation in the spin crossover complex.

PubMed

Nishihara, Taishi; Bousseksou, Azzdine; Tanaka, Koichiro

2013-12-16

We report the spatial and temporal dynamics of the photo-induced phase in the iron (II) spin crossover complex Fe(ptz)(6)(BF(4))(2) studied by image measurement under steady light irradiation and transient absorption measurement. The dynamic factors are derived from the spatial and temporal fluctuation of the image in the steady state under light irradiation between 65 and 100 K. The dynamic factors clearly indicate that the fluctuation has a resonant frequency that strongly depends on the temperature, and is proportional to the relaxation rate of the photo-induced phase. This oscillation of the speckle pattern under steady light irradiation is ascribed to the nonlinear interaction between the spin state and the lattice volume at the surface.

Reduction of the Nonlinear Phase Shift Induced by Stimulated Brillouin Scattering for Bi-Directional Pumping Configuration System Using Particle Swarm Optimization Algorithm

NASA Astrophysics Data System (ADS)

Al-Asadi, H. A.

2013-02-01

We present a theoretical analysis of an additional nonlinear phase shift of backward Stokes wave based on stimulated Brillouin scattering in the system with a bi-directional pumping scheme. We optimize three parameters of the system: the numerical aperture, the optical loss and the pumping wavelength to minimize an additional nonlinear phase shift of backward Stokes waves due to stimulated Brillouin scattering. The optimization is performed with various Brillouin pump powers and the optical reflectivity values are based on the modern, global evolutionary computation algorithm, particle swarm optimization. It is shown that the additional nonlinear phase shift of backward Stokes wave varies with different optical fiber lengths, and can be minimized to less than 0.07 rad according to the particle swarm optimization algorithm for 5 km. The bi-directional pumping configuration system is shown to be efficient when it is possible to transmit the power output to advanced when frequency detuning is negative and delayed when it is positive, with the optimum values of the three parameters to achieve the reduction of an additional nonlinear phase shift.

Nonlinear photomechanics of nematic networks: upscaling microscopic behaviour to macroscopic deformation

NASA Astrophysics Data System (ADS)

Chung, Hayoung; Choi, Joonmyung; Yun, Jung-Hoon; Cho, Maenghyo

2016-02-01

A liquid crystal network whose chromophores are functionalized by photochromic dye exhibits light-induced mechanical behaviour. As a result, the micro-scaled thermotropic traits of the network and the macroscopic phase behaviour are both influenced as light alternates the shape of the dyes. In this paper, we present an analysis of this photomechanical behaviour based on the proposed multiscale framework, which incorporates the molecular details of microstate evolution into a continuum-based understanding. The effects of trans-to-cis photoisomerization driven by actinic light irradiation are first examined using molecular dynamics simulations, and are compared against the predictions of the classical dilution model; this reveals certain characteristics of mesogenic interaction upon isomerization, followed by changes in the polymeric structure. We then upscale the thermotropic phase-related information with the aid of a nonlinear finite element analysis; macroscopic deflection with respect to the wide ranges of temperature and actinic light intensity are thereby examined, which reveals that the classical model underestimates the true deformation. This work therefore provides measures for analysing photomechanics in general by bridging the gap between the micro- and macro-scales.

FIBER AND INTEGRATED OPTICS: Efficiency of nonstationary transformation of the spatial coherence of pulsed laser radiation in a multimode optical fibre upon self-phase modulation

NASA Astrophysics Data System (ADS)

Kitsak, M. A.; Kitsak, A. I.

2007-08-01

The model scheme of the nonlinear mechanism of transformation (decreasing) of the spatial coherence of a pulsed laser field in an extended multimode optical fibre upon nonstationary interaction with the fibre core is theoretically analysed. The case is considered when the spatial statistics of input radiation is caused by phase fluctuations. The analytic expression is obtained which relates the number of spatially coherent radiation modes with the spatially energy parameters on the initial radiation and fibre parameters. The efficiency of decorrelation of radiation upon excitation of the thermal and electrostriction nonlinearities in the fibre is estimated. Experimental studies are performed which revealed the basic properties of the transformation of the spatial coherence of a laser beam in a multimode fibre. The experimental results are compared with the predictions of the model of radiation transfer proposed in the paper. It is found that the spatial decorrelation of a light beam in a silica multimode fibre is mainly restricted by stimulated Raman scattering.

A combined averaging and frequency mixing approach for force identification in weakly nonlinear high-Q oscillators: Atomic force microscope

NASA Astrophysics Data System (ADS)

Sah, Si Mohamed; Forchheimer, Daniel; Borgani, Riccardo; Haviland, David

2018-02-01

We present a polynomial force reconstruction of the tip-sample interaction force in Atomic Force Microscopy. The method uses analytical expressions for the slow-time amplitude and phase evolution, obtained from time-averaging over the rapidly oscillating part of the cantilever dynamics. The slow-time behavior can be easily obtained in either the numerical simulations or the experiment in which a high-Q resonator is perturbed by a weak nonlinearity and a periodic driving force. A direct fit of the theoretical expressions to the simulated and experimental data gives the best-fit parameters for the force model. The method combines and complements previous works (Platz et al., 2013; Forchheimer et al., 2012 [2]) and it allows for computationally more efficient parameter mapping with AFM. Results for the simulated asymmetric piecewise linear force and VdW-DMT force models are compared with the reconstructed polynomial force and show a good agreement. It is also shown that the analytical amplitude and phase modulation equations fit well with the experimental data.

Dynamics of shaping ultrashort optical dissipative solitary pulses in the actively mode-locked semiconductor laser with an external long-haul single-mode fiber cavity

NASA Astrophysics Data System (ADS)

Shcherbakov, Alexandre S.; Moreno Zarate, Pedro

2010-02-01

We describe the conditions of shaping regular trains of optical dissipative solitary pulses, excited by multi-pulse sequences of periodic modulating signals, in the actively mode-locked semiconductor laser heterostructure with an external long-haul single-mode silicon fiber exhibiting square-law dispersion, cubic Kerr nonlinearity, and linear optical losses. The presented model for the analysis includes three principal contributions associated with the modulated gain, optical losses, as well as linear and nonlinear phase shifts. In fact, the trains of optical dissipative solitary pulses appear within simultaneous presenting and a balance of mutually compensating interactions between the second-order dispersion and cubic-law Kerr nonlinearity as well as between active medium gain and linear optical losses in the combined cavity. Within such a model, a contribution of the nonlinear Ginzburg-Landau operator to shaping the parameters of optical dissipative solitary pulses is described via exploiting an approximate variational procedure involving the technique of trial functions. Finally, the results of the illustrating proof-of-principle experiments are briefly presented and discussed in terms of optical dissipative solitary pulses.

Out-of-unison resonance in weakly nonlinear coupled oscillators

PubMed Central

Hill, T. L.; Cammarano, A.; Neild, S. A.; Wagg, D. J.

2015-01-01

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems. PMID:25568619

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.

Solitons in a nonlinear model of spin transport in helical molecules

NASA Astrophysics Data System (ADS)

Albares, P.; Díaz, E.; Cerveró, Jose M.; Domínguez-Adame, F.; Diez, E.; Estévez, P. G.

2018-02-01

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the electron-lattice interaction, enabling the formation of a variety of stable solitons such as bright solitons, breathers, and rogue waves. A thorough study of the soliton solutions for both focusing and defocusing nonlinear interaction is presented and discussed.

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

Guo, Peijun; Weimer, Matthew S.; Emery, Jonathan D.

Actively tunable optical transmission through artificial metamaterials holds great promise for next-generation nanophotonic devices and metasurfaces. Plasmonic nanostructures and phase change materials have been extensively studied to this end due to their respective strong interactions with light and tunable dielectric constants under external stimuli. Seamlessly integrating plasmonic components with phase change materials, as demonstrated in the present work, can facilitate phase change by plasmonically enabled light confinement and meanwhile make use of the high sensitivity of plasmon resonances to the variation of dielectric constant associated with the phase change. The hybrid platform here is composed of plasmonic indium tin-oxide nanorodmore » arrays (ITO-NRAs) conformally coated with an ultrathin layer of a prototypical phase change material, vanadium dioxide (VO2), which enables all-optical modulation of the infrared as well as the visible spectral ranges. The interplay between the intrinsic plasmonic nonlinearity of ITO-NRAs and the phase transition induced permittivity change of VO2 gives rise to spectral and temporal responses that cannot be achieved with individual material components alone.« less

The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave

DOE PAGES

TenCate, J. A.; Malcolm, A. E.; Feng, X.; ...

2016-06-06

Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less

Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

NASA Astrophysics Data System (ADS)

Jahanbakhsh, F.; Honarasa, G.

2018-04-01

The potential of nonharmonic systems has several applications in the field of quantum physics. The photon-added coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function, Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.

Engineered second-harmonic diffraction from highly transmissive metasurfaces composed of complementary split-ring resonators.

PubMed

Yang, Xin; Zhang, Chi; Wan, Mingjie; Chen, Zhuo; Wang, Zhenlin

2016-07-01

We theoretically and experimentally investigated the optical second-harmonic (SH) diffraction from metasurfaces based on gold complementary split-ring resonators (CSRRs). We have demonstrated that the generated SH currents are mostly parallel to the incident polarization and are asymmetric with respect to the base of a CSRR, thus allowing us to impose the phase change of π on the SH radiation by reversing the CSRR's orientation. We verified this concept of geometry-induced nonlinear phase by designing and fabricating a nonlinear metasurface consisting of supercells of CSRRs with opposite orientations that can function as a SH beam splitter. The ability to control the phase of the local nonlinearity coupled with the high transmittance at both fundamental and SHG wavelengths makes the CSRRs good candidates for the construction of highly efficient three-dimensional nonlinear metamaterials and suitable for applications in nonlinear beam shaping.

Twisting Anderson pseudospins with light: Quench dynamics in THz-pumped BCS superconductors

NASA Astrophysics Data System (ADS)

Chou, Yang-Zhi; Liao, Yunxiang; Foster, Matthew

We study the preparation and the detection of coherent far-from-equilibrium BCS superconductor dynamics in THz pump-probe experiments. In a recent experiment, an intense monocycle THz pulse with center frequency ω = Δ was injected into a superconductor with BCS gap Δ the post-pump evolution was detected via the optical conductivity. It was argued that nonlinear coupling of the pump to the Anderson pseudospins of the superconductor induces coherent dynamics of the Higgs mode Δ (t) . We validate this picture in a 2D BCS model with a combination of exact numerics and the Lax reduction, and we compute the dynamical phase diagram. The main effect of the pump is to scramble the orientations of Anderson pseudospins along the Fermi surface by twisting them in the xy-plane. We show that more intense pulses can induce a far-from-equilibrium gapless phase (phase I), originally predicted in the context of interaction quenches. We show that the THz pump can reach phase I at much lower energy densities than an interaction quench, and we demonstrate that Lax reduction provides a quantitative tool for computing coherent BCS dynamics. We also compute the optical conductivity for the states discussed here.

Extended phase-matching properties of periodically poled potassium niobate crystals for mid-infrared polarization-entangled photon-pair generation.

PubMed

Lee, Kwang Jo; Lee, Sunmi; Shin, Heedeuk

2016-12-01

We report the extended phase-matching (EPM) properties of two kinds of periodically poled potassium niobate (KNbO₃ or KN) crystals (i.e., periodic 180°- and 90°-domain structures) that are highly useful for the generation of polarization-entangled photon pairs in the mid-infrared (IR) spectral region. Under the degenerate Type II spontaneous parametric downconversion process satisfying the EPM condition, an input single photon with a frequency of 2ω generates a pair of synchronized photons with identical frequencies of ω that are orthogonally polarized with respect to each other (i.e., the frequency-coincident, polarization-entangled biphoton states). Our simulation results illustrate that the EPM is achievable in the mid-IR spectral region: at the wavelengths of 3.80 μm and 4.03 μm for periodic 90°- and 180°-domain structures, respectively. We will describe in detail the EPM properties of both cases in terms of interaction types and the corresponding nonlinear optic coefficients, phase-matching bandwidths, and domain poling periods. The calculated EPM bandwidths are much broader than 200 nm in the mid-IR for both cases, exhibiting a great potential for nonlinear-optic signal processing in quantum communication systems operating in the mid-IR bands.

A Dynamic Laplacian for Identifying Lagrangian Coherent Structures on Weighted Riemannian Manifolds

NASA Astrophysics Data System (ADS)

Froyland, Gary; Kwok, Eric

2017-06-01

Transport and mixing in dynamical systems are important properties for many physical, chemical, biological, and engineering processes. The detection of transport barriers for dynamics with general time dependence is a difficult, but important problem, because such barriers control how rapidly different parts of phase space (which might correspond to different chemical or biological agents) interact. The key factor is the growth of interfaces that partition phase space into separate regions. The paper Froyland (Nonlinearity 28(10):3587-3622, 2015) introduced the notion of dynamic isoperimetry: the study of sets with persistently small boundary size (the interface) relative to enclosed volume, when evolved by the dynamics. Sets with this minimal boundary size to volume ratio were identified as level sets of dominant eigenfunctions of a dynamic Laplace operator. In this present work we extend the results of Froyland (Nonlinearity 28(10):3587-3622, 2015) to the situation where the dynamics (1) is not necessarily volume preserving, (2) acts on initial agent concentrations different from uniform concentrations, and (3) occurs on a possibly curved phase space. Our main results include generalised versions of the dynamic isoperimetric problem, the dynamic Laplacian, Cheeger's inequality, and the Federer-Fleming theorem. We illustrate the computational approach with some simple numerical examples.

Frequency comb generation by a continuous-wave-pumped optical parametric oscillator based on cascading quadratic nonlinearities.

PubMed

Ulvila, Ville; Phillips, C R; Halonen, Lauri; Vainio, Markku

2013-11-01

We report optical frequency comb generation by a continuous-wave pumped optical parametric oscillator (OPO) without any active modulation. The OPO is configured as singly resonant with an additional nonlinear crystal (periodically poled MgO:LiNbO3) placed inside the OPO for phase mismatched second harmonic generation (SHG) of the resonating signal beam. The phase mismatched SHG causes cascading χ(2) nonlinearities, which can substantially increase the effective χ(3) nonlinearity in MgO:LiNbO3, leading to spectral broadening of the OPO signal beam via self-phase modulation. The OPO generates a stable 4 THz wide (-30 dB) frequency comb centered at 1.56 μm.

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

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

Teng, L.-W.; Chang, M.-C.; Tseng, Y.-P.

2009-12-11

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation tomore » the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.« less

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

NASA Astrophysics Data System (ADS)

Teng, Lee-Wen; Chang, Mei-Chu; Tseng, Yu-Ping; I, Lin

2009-12-01

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation to the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.

Predictions of spray combustion interactions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Solomon, A. S. P.; Faeth, G. M.

1984-01-01

Mean and fluctuating phase velocities; mean particle mass flux; particle size; and mean gas-phase Reynolds stress, composition and temperature were measured in stationary, turbulent, axisymmetric, and flows which conform to the boundary layer approximations while having well-defined initial and boundary conditions in dilute particle-laden jets, nonevaporating sprays, and evaporating sprays injected into a still air environment. Three models of the processes, typical of current practice, were evaluated. The local homogeneous flow and deterministic separated flow models did not provide very satisfactory predictions over the present data base. In contrast, the stochastic separated flow model generally provided good predictions and appears to be an attractive approach for treating nonlinear interphase transport processes in turbulent flows containing particles (drops).

Frequency-Domain Channel Estimation and Equalization for Single Carrier Underwater Acoustic Communications

DTIC Science & Technology

2007-01-01

synchronization ; vm(k) white Gaussian noise with average power σ2. If the Doppler shift f m,k is significant, then it causes the received signal ym(k) to be time ...intersymbol interference (ISI) to extend over 20-300 symbols at a data rate of 2-10 kilosymbols per second. Another obstacle is the time -varying Doppler... synchronization that employs a phase-locked loop (PLL) or delay-locked loop (DLL). However, the DFE and PLL/DLL have to interact in a nonlinear fashion

Integral Equation for the Equilibrium State of Colliding Electron Beams

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

Warnock, Robert L.

2002-11-11

We study a nonlinear integral equation for the equilibrium phase distribution of stored colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. We prove existence of a unique solution, thus the existence of a unique equilibrium state, for sufficiently small current. This is done for the Chao-Ruth model of the beam-beam interaction in one degree of freedom. We expect no difficulty in generalizing the argument to more realistic models.

Suppression of superconductivity in disordered interacting wires.

PubMed

Pesin, D A; Andreev, A V

2006-09-15

We study superconductivity suppression due to thermal fluctuations in disordered wires using the replica nonlinear sigma-model (NLsigmaM). We show that in addition to the thermal phase slips there is another type of fluctuations that result in a finite resistivity. These fluctuations are described by saddle points in NLsigmaM and cannot be treated within the Ginzburg-Landau approach. The contribution of such fluctuations to the wire resistivity is evaluated with exponential accuracy. The magnetoresistance associated with this contribution is negative.

Stages of chaotic synchronization.

PubMed

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

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

Xi, P. W.; Lawrence Livermore National Laboratory, Livermore, California 94550; Xu, X. Q.

We demonstrate that the occurrence of Edge-Localized-Modes (ELM) crashes does not depend only on the linear peeling-ballooning threshold, but also relies on nonlinear processes. Wave-wave interaction constrains the growth time of a mode, thus inducing a shift in the criterion for triggering an ELM crash. An ELM crash requires the P-B growth rate to exceed a critical value γ>γ{sub c}, where γ{sub c} is set by 1/τ{sup ¯}{sub c}, and τ{sup ¯}{sub c} is the averaged mode phase coherence time. For 0

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

Nonlinear Dirac cones

NASA Astrophysics Data System (ADS)

Bomantara, Raditya Weda; Zhao, Wenlei; Zhou, Longwen; Gong, Jiangbin

2017-09-01

Physics arising from two-dimensional (2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such 2D Dirac cones are often characterized by a π Berry phase and are destroyed by a perturbative mass term. By considering mean-field nonlinearity in a minimal two-band Chern insulator model, we obtain a different type of Dirac cone that is robust to local perturbations without symmetry restrictions. Due to a different pseudospin texture, the Berry phase of the Dirac cone is no longer quantized in π , and can be continuously tuned as an order parameter. Furthermore, in an Aharonov-Bohm (AB) interference setup to detect such Dirac cones, the adiabatic AB phase is found to be π both theoretically and computationally, offering an observable topological invariant and a fascinating example where the Berry phase and AB phase are fundamentally different. We hence discover a nonlinearity-induced quantum phase transition from a known topological insulating phase to an unusual gapless topological phase.

Nonlinear interaction and wave breaking with a submerged porous structure

NASA Astrophysics Data System (ADS)

Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.

2016-12-01

Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.

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

Quasi-superradiant soliton state of matter in quantum metamaterials

NASA Astrophysics Data System (ADS)

Asai, Hidehiro; Kawabata, Shiro; Savel'ev, Sergey E.; Zagoskin, Alexandre M.

2018-02-01

Strong interaction of a system of quantum emitters (e.g., two-level atoms) with electromagnetic field induces specific correlations in the system accompanied by a drastic increase of emitted radiation (superradiation or superfluorescence). Despite the fact that since its prediction this phenomenon was subject to a vigorous experimental and theoretical research, there remain open question, in particular, concerning the possibility of a first order phase transition to the superradiant state from the vacuum state. In systems of natural and charge-based artificial atom this transition is prohibited by "no-go" theorems. Here we demonstrate numerically and confirm analytically a similar transition in a one-dimensional quantum metamaterial - a chain of artificial atoms (qubits) strongly interacting with classical electromagnetic fields in a transmission line. The system switches from vacuum state to the quasi-superradiant (QS) phase with one or several magnetic solitons and finite average occupation of qubit excited states along the transmission line. A quantum metamaterial in the QS phase circumvents the "no-go" restrictions by considerably decreasing its total energy relative to the vacuum state by exciting nonlinear electromagnetic solitons.

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

Simultaneous concentration and purification through gradient deformation chromatography

NASA Technical Reports Server (NTRS)

Velayudhan, A.; Hendrickson, R. L.; Ladisch, M. R.; Mitchell, C. A. (Principal Investigator)

1995-01-01

Mobile-phase additives, commonly used to modulate absorbate retention in gradient elution chromatography, are usually assumed to be either linearly retained or unretained. Previous theoretical work from our laboratory has shown that these modulators, such as salts in ion-exchange and hydrophobic interaction chromatography and organic modifiers in reversed-phase chromatography, can absorb nonlinearly, giving rise to gradient deformation. Consequently, adsorbate peaks that elute in the vicinity of the head of the deformed gradient may exhibit unusual shapes, form shoulders, and/or be concentrated. These effects for a reversed-phase sorbent with aqueous acetonitrile (ACN) as the modulator are verified experimentally. Gradient deformation is demonstrated experimentally and agrees with simulations based on ACN isotherm parameters that are independently determined from batch equilibrium studies using the layer model. Unusual absorbate peak shapes were found experimentally for single-component injections of phenylalanine, similar to those calculated by the simulations. A binary mixture of tryptophan and phenylalanine is used to demonstrate simultaneous concentration and separation, again in agreement with simulations. The possibility of gradient deformation in ion-exchange and hydrophobic interaction chromatography is discussed.

Intermodulation Atomic Force Microscopy and Spectroscopy

NASA Astrophysics Data System (ADS)

Hutter, Carsten; Platz, Daniel; Tholen, Erik; Haviland, David; Hansson, Hans

2009-03-01

We present a powerful new method of dynamic AFM, which allows to gain far more information about the tip-surface interaction than standard amplitude or phase imaging, while scanning at comparable speed. Our method, called intermodulation atomic force microscopy (ImAFM), employs the manifestly nonlinear phenomenon of intermodulation to extract information about tip-surface forces. ImAFM uses one eigenmode of a mechanical resonator, the latter driven at two frequencies to produce many spectral peaks near its resonace, where sensitivity is highest [1]. We furthermore present a protocol for decoding the combined information encoded in the spectrum of intermodulation peaks. Our theoretical framework suggests methods to enhance the gained information by using a different parameter regime as compared to Ref. [1]. We also discuss strategies for solving the inverse problem, i.e., for extracting the nonlinear tip-surface interaction from the response, also naming limitations of our theoretical analysis. We will further report on latest progress to experimentally employ our new protocol.[3pt] [1] D. Platz, E. A. Tholen, D. Pesen, and D. B. Haviland, Appl. Phys. Lett. 92, 153106 (2008).

Non-linear scale interactions in a forced turbulent boundary layer

NASA Astrophysics Data System (ADS)

Duvvuri, Subrahmanyam; McKeon, Beverley

2015-11-01

A strong phase-organizing influence exerted by a single synthetic large-scale spatio-temporal mode on directly-coupled (through triadic interactions) small scales in a turbulent boundary layer forced by a spatially-impulsive dynamic wall-roughness patch was previously demonstrated by the authors (J. Fluid Mech. 2015, vol. 767, R4). The experimental set-up was later enhanced to allow for simultaneous forcing of multiple scales in the flow. Results and analysis are presented from a new set of novel experiments where two distinct large scales are forced in the flow by a dynamic wall-roughness patch. The internal non-linear forcing of two other scales with triadic consistency to the artificially forced large scales, corresponding to sum and difference in wavenumbers, is dominated by the latter. This allows for a forcing-response (input-output) type analysis of the two triadic scales, and naturally lends itself to a resolvent operator based model (e.g. McKeon & Sharma, J. Fluid Mech. 2010, vol. 658, pp. 336-382) of the governing Navier-Stokes equations. The support of AFOSR (grant #FA 9550-12-1-0469, program manager D. Smith) is gratefully acknowledged.

Detuned resonances of Tollmien-Schlichting waves in an airfoil boundary layer: Experiment, theory, and direct numerical simulation

NASA Astrophysics Data System (ADS)

Würz, W.; Sartorius, D.; Kloker, M.; Borodulin, V. I.; Kachanov, Y. S.; Smorodsky, B. V.

2012-09-01

Transition prediction in two-dimensional laminar boundary layers developing on airfoil sections at subsonic speeds and very low turbulence levels is still a challenge. The commonly used semi-empirical prediction tools are mainly based on linear stability theory and do not account for nonlinear effects present unavoidably starting with certain stages of transition. One reason is the lack of systematic investigations of the weakly nonlinear stages of transition, especially of the strongest interactions of the instability modes predominant in non-self-similar boundary layers. The present paper is devoted to the detailed experimental, numerical, and theoretical study of weakly nonlinear subharmonic resonances of Tollmien-Schlichting waves in an airfoil boundary layer, representing main candidates for the strongest mechanism of these initial nonlinear stages. The experimental approach is based on phase-locked hot-wire measurements under controlled disturbance conditions using a new disturbance source being capable to produce well-defined, complex wave compositions in a wide range of streamwise and spanwise wave numbers. The tests were performed in a low-turbulence wind tunnel at a chord Reynolds number of Re = 0.7 × 106. Direct numerical simulations (DNS) were utilized to provide a detailed comparison for the test cases. The results of weakly nonlinear theory (WNT) enabled a profound understanding of the underlying physical mechanisms observed in the experiments and DNS. The data obtained in experiment, DNS and WNT agree basically and provide a high degree of reliability of the results. Interactions occurring between components of various initial frequency-wavenumber spectra of instability waves are investigated by systematic variation of parameters. It is shown that frequency-detuned and spanwise-wavenumber-detuned subharmonic-type resonant interactions have an extremely large spectral width. Similar to results obtained for self-similar base flows it is found that the amplification factors in the frequency-detuned resonances can be even higher than in tuned cases, in spite of the strong base-flow non-self-similarity. An explanation of this unusual phenomenon is found based on the theoretical analysis and comparison of experimental, theoretical, and DNS data.

Nonlinear excited waves on the interventricular septum

NASA Astrophysics Data System (ADS)

Bekki, Naoaki; Harada, Yoshifumi; Kanai, Hiroshi

2012-11-01

Using a novel ultrasonic noninvasive imaging method, we observe some phase singularities in propagating excited waves on a human cardiac interventricular septum (IVS) for a healthy young male. We present a possible physical model explaining one-dimensional dynamics of phase singularities in nonlinearly excited waves on the IVS. We show that at least one of the observed phase singularities in the excited waves on the IVS can be explained by the Bekki-Nozaki hole solution of the complex Ginzburg-Landau equation without any adjustable parameters. We conclude that the complex Ginzburg-Landau equation is such a suitable model for one-dimensional dynamics of cardiac phase singularities in nonlinearly excited waves on the IVS.

GEOPHYSICS, ASTRONOMY AND ASTROPHYSICS: Numerical method of studying nonlinear interactions between long waves and multiple short waves

NASA Astrophysics Data System (ADS)

Xie, Tao; Kuang, Hai-Lan; William, Perrie; Zou, Guang-Hui; Nan, Cheng-Feng; He, Chao; Shen, Tao; Chen, Wei

2009-07-01

Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically, the solution is less tractable in more general cases involving multiple short waves. In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water. Specifically, this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves. Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train. From simulation results, we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train (expressed as wave train 2) leads to the energy focusing of the other short wave train (expressed as wave train 3). This mechanism occurs on wave components with a narrow frequency bandwidth, whose frequencies are near that of wave train 3.

Experimental and numerical investigations of temporally and spatially periodic modulated wave trains

NASA Astrophysics Data System (ADS)

Houtani, H.; Waseda, T.; Tanizawa, K.

2018-03-01

A number of studies on steep nonlinear waves were conducted experimentally with the temporally periodic and spatially evolving (TPSE) wave trains and numerically with the spatially periodic and temporally evolving (SPTE) ones. The present study revealed that, in the vicinity of their maximum crest height, the wave profiles of TPSE and SPTE modulated wave trains resemble each other. From the investigation of the Akhmediev-breather solution of the nonlinear Schrödinger equation (NLSE), it is revealed that the dispersion relation deviated from the quadratic dependence of frequency on wavenumber and became linearly dependent instead. Accordingly, the wave profiles of TPSE and SPTE breathers agree. The range of this agreement is within the order of one wave group of the maximum crest height and persists during the long-term evolution. The findings extend well beyond the NLSE regime and can be applied to modulated wave trains that are highly nonlinear and broad-banded. This was demonstrated from the numerical wave tank simulations with a fully nonlinear potential flow solver based on the boundary element method, in combination with the nonlinear wave generation method based on the prior simulation with the higher-order spectral model. The numerical wave tank results were confirmed experimentally in a physical wave tank. The findings of this study unravel the fundamental nature of the nonlinear wave evolution. The deviation of the dispersion relation of the modulated wave trains occurs because of the nonlinear phase variation due to quasi-resonant interaction, and consequently, the wave geometry of temporally and spatially periodic modulated wave trains coincides.

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 [

Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes

NASA Astrophysics Data System (ADS)

Peter, Simon; Scheel, Maren; Krack, Malte; Leine, Remco I.

2018-02-01

Determining frequency response curves is a common task in the vibration analysis of nonlinear systems. Measuring nonlinear frequency responses is often challenging and time consuming due to, e.g., coexisting stable or unstable vibration responses and structure-exciter-interaction. The aim of the current paper is to develop a method for the synthesis of nonlinear frequency responses near an isolated resonance, based on data that can be easily and automatically obtained experimentally. The proposed purely experimental approach relies on (a) a standard linear modal analysis carried out at low vibration levels and (b) a phase-controlled tracking of the backbone curve of the considered forced resonance. From (b), the natural frequency and vibrational deflection shape are directly obtained as a function of the vibration level. Moreover, a damping measure can be extracted by power considerations or from the linear modal analysis. In accordance with the single nonlinear mode assumption, the near-resonant frequency response can then be synthesized using this data. The method is applied to a benchmark structure consisting of a cantilevered beam attached to a leaf spring undergoing large deflections. The results are compared with direct measurements of the frequency response. The proposed approach is fast, robust and provides a good estimate for the frequency response. It is also found that direct frequency response measurement is less robust due to bifurcations and using a sine sweep excitation with a conventional force controller leads to underestimation of maximum vibration response.

Quantitative EEG analysis using error reduction ratio-causality test; validation on simulated and real EEG data.

PubMed

Sarrigiannis, Ptolemaios G; Zhao, Yifan; Wei, Hua-Liang; Billings, Stephen A; Fotheringham, Jayne; Hadjivassiliou, Marios

2014-01-01

To introduce a new method of quantitative EEG analysis in the time domain, the error reduction ratio (ERR)-causality test. To compare performance against cross-correlation and coherence with phase measures. A simulation example was used as a gold standard to assess the performance of ERR-causality, against cross-correlation and coherence. The methods were then applied to real EEG data. Analysis of both simulated and real EEG data demonstrates that ERR-causality successfully detects dynamically evolving changes between two signals, with very high time resolution, dependent on the sampling rate of the data. Our method can properly detect both linear and non-linear effects, encountered during analysis of focal and generalised seizures. We introduce a new quantitative EEG method of analysis. It detects real time levels of synchronisation in the linear and non-linear domains. It computes directionality of information flow with corresponding time lags. This novel dynamic real time EEG signal analysis unveils hidden neural network interactions with a very high time resolution. These interactions cannot be adequately resolved by the traditional methods of coherence and cross-correlation, which provide limited results in the presence of non-linear effects and lack fidelity for changes appearing over small periods of time. Copyright © 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Impact of Tidal-Stream Turbines on the Generation of the Higher Tidal Harmonics

NASA Astrophysics Data System (ADS)

Potter, Daniel; Ilic, Suzana; Folkard, Andrew

2016-04-01

The higher tidal harmonics result from the interaction of the astronomic tides with both themselves and each other through non-linear processes. In shallower waters such as those near the coast these non-linear processes become more significant and thus, so too do the higher tidal harmonics become more significant. The interaction of the tide with tidal-stream turbines (TSTs), through thrust and drag processes will be non-linear and as such will contribute to the generation of higher tidal harmonics, thus changing the nature of the tide downstream of the turbines. The change to the tide may potentially impact on the downstream energy resource (Robins et al. 2015) and sediment transport processes (Pingree & Griffiths 1979). This paper will present analytical results, which suggest that TSTs will impact on the generation of all higher harmonics but with odd overtides being impacted more than even overtides, the most important examples of which are the M6 and M4 tides respectively, which are the first odd and even overtides of the M2 tide. Change in phase and amplitude of the M6 tide by TSTs will distort the tide but will not cause an asymmetry between the flood and ebb of the tide. Change in the phase and amplitude of the M4 can not only distort the tide but also cause asymmetry. Hence any change to the M4 tide by the turbines is more significant, despite the magnitude of change to the M6 being greater. In order to gain a fuller understanding of the way in which TSTs change the tide downstream and the significance of any change for transport processes or energy resource, a numerical modelling study will be carried out, which will be presented in a future paper. Robins, P.E., Neill, S.P., Lewis, M. & Ward, S.L., 2015. Characterising the spatial and temporal variability of the tidal-stream energy resource over the northwest European shelf seas. Applied Energy, 147: 510-522. Pingree, R.D. & Griffiths, D.K., 1979. Sand transport paths around the British Isles resulting from M2 and M4 tidal interactions. J. Mar. Biol. Ass. U.K., 59: 497-513

Synthesis and Characterization of Novel Nonlinear Optical Materials

NASA Astrophysics Data System (ADS)

Liang, Cheryl Shuang

1992-01-01

Nonlinear optic materials are becoming increasingly important because of their many technological applications, such as second harmonic generation (SHG), optical switching, and waveguides for optical transmission. Currently, there is a demand for crystals transparent in the UV region, which would make the third and higher harmonic generations feasible. Compounds with the general stoichiometry ABCO _4 structural systems have shown to be promising candidates for frequency doubling into the UV region. The stuffed tridymite structure in which these ABCO_4 compounds crystallize is very tolerant to substitution, and over two hundred compounds have been synthesized up to date. While the presently available theories of optical nonlinearity have been applied to many inorganic solids, the threatened structure theory applied for ferroelectric properties can also be used to describe the structure/property relationship in the ABCO_4 structural family. Compounds synthesized for this study, ALiPO_4 (A = Sr, Ba, Pb) have shown that the SHG of these materials can be maximized by bringing each system close to its structural phase transition or by inducing stress in the pure phase structure. Studies have shown that the dielectric coefficients of KNbO_3 increase by more than tenfold with tantalum doping. This prompted the investigation of a mixed niobium/tantalum containing channelled tetrahedra/octahedra open framework, K_{2/3}Li _{1/3}Nb_ {rm 2-x}Ta_{ rm x}PO_8. These compounds are capable of ion exchange, where other cations are used to replace potassium. The cation-framework interaction mimics the guest-host relationship characteristic of many traditional zeolitic materials. This interaction also enables us to determine the role of the cation in framework polarizability, which can be measured by SHG intensities. Through ion exchange, many isostructural compounds can be made at low temperatures. A family of layered rubidium niobium/tantalum oxide compounds have been synthesized in an extension of the investigation of the above host-guest interaction. X -ray diffraction data have shown successful incorporation of n-butyl ammonium chloride followed by exchange of an organic salt which has very large SHG intensity, N-methylstilbazolium chloride, into the layers.

Active Nonlinear Feedback Control for Aerospace Systems. Processor

DTIC Science & Technology

1990-12-01

relating to the role of nonlinearities in feedback control. These area include Lyapunov function theory, chaotic controllers, statistical energy analysis , phase robustness, and optimal nonlinear control theory.

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;

Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing

NASA Astrophysics Data System (ADS)

Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng

2017-05-01

Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.

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

Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition

NASA Technical Reports Server (NTRS)

Smith, F. T.

1988-01-01

The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.

A rocket-borne experiment called 'MINIX' was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction eXperiment and was carried out on August 29, 1983. The objective of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere, such as the ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no ohmic heating effects were detected.

Transport equations for subdiffusion with nonlinear particle interaction.

PubMed

Straka, P; Fedotov, S

2015-02-07

We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent. Copyright © 2014 Elsevier Ltd. All rights reserved.

Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity.

PubMed

Dory, Constantin; Fischer, Kevin A; Müller, Kai; Lagoudakis, Konstantinos G; Sarmiento, Tomas; Rundquist, Armand; Zhang, Jingyuan L; Kelaita, Yousif; Vučković, Jelena

2016-04-26

Strongly coupled quantum dot-cavity systems provide a non-linear configuration of hybridized light-matter states with promising quantum-optical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dot-cavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dot-photonic crystal cavity based quantum-bit. By controlling the excitation power and phase in a two-pulse excitation scheme we achieve access to the full Bloch sphere. Quantum-optical simulations are in good agreement with our experiments and provide insight into the decoherence mechanisms.

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.

Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity

NASA Astrophysics Data System (ADS)

Dory, Constantin; Fischer, Kevin A.; Müller, Kai; Lagoudakis, Konstantinos G.; Sarmiento, Tomas; Rundquist, Armand; Zhang, Jingyuan L.; Kelaita, Yousif; Vučković, Jelena

2016-04-01

Strongly coupled quantum dot-cavity systems provide a non-linear configuration of hybridized light-matter states with promising quantum-optical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dot-cavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dot-photonic crystal cavity based quantum-bit. By controlling the excitation power and phase in a two-pulse excitation scheme we achieve access to the full Bloch sphere. Quantum-optical simulations are in good agreement with our experiments and provide insight into the decoherence mechanisms.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Spectroscopic and DFT-based computational studies on the molecular electronic structural characteristics and the third-order nonlinear property of an organic NLO crystal: (E)-N‧-(4-chlorobenzylidene)-4-methylbenzenesulfonohydrazide

NASA Astrophysics Data System (ADS)

Sasikala, V.; Sajan, D.; Joseph, Lynnette; Balaji, J.; Prabu, S.; Srinivasan, P.

2017-04-01

Single crystals of (E)-N‧-(4-chlorobenzylidene)-4-methylbenzenesulfonohydrazide (CBMBSH) have been grown by slow evaporation crystal growth method. The structure stabilizing intramolecular donor-acceptor interactions and the presence of the Nsbnd H⋯O, Csbnd H⋯O and Csbnd H⋯C(π) hydrogen bonds in the crystal were confirmed by vibrational spectroscopic and DFT methods. The linear optical absorption characteristics of the solvent phase of CBMBSH were investigated using UV-Vis-NIR spectroscopic and TD-DFT approaches. The 2PA assisted RSA nonlinear absorption and the optical limiting properties of CBMBSH were studied using the open-aperture Z-scan method. The topological characteristics of the electron density have been determined using the quantum theory of atoms in molecules method.

Research on ponderomotive driven Vlasov–Poisson system in electron acoustic wave parametric region

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

Xiao, C. Z.; Huang, T. W.; Liu, Z. J.

2014-03-15

Theoretical analysis and corresponding 1D Particle-in-Cell (PIC) simulations of ponderomotive driven Vlasov–Poisson system in electron acoustic wave (EAW) parametric region are demonstrated. Theoretical analysis identifies that under the resonant condition, a monochromatic EAW can be excited when the wave number of the drive ponderomotive force satisfies 0.26≲k{sub d}λ{sub D}≲0.53. If k{sub d}λ{sub D}≲0.26, nonlinear superposition of harmonic waves can be resonantly excited, called kinetic electrostatic electron nonlinear waves. Numerical simulations have demonstrated these wave excitation and evolution dynamics, in consistence with the theoretical predictions. The physical nature of these two waves is supposed to be interaction of harmonic waves, andmore » their similar phase space properties are also discussed.« less

Protein Crystallization: Specific Phenomena and General Insights on Crystallization Kinetics

NASA Technical Reports Server (NTRS)

Rosenberger, F.

1998-01-01

Experimental and simulation studies of the nucleation and growth kinetics of proteins have revealed phenomena that are specific for macromolecular crystallization, and others that provide a more detailed understanding of solution crystallization in general. The more specific phenomena, which include metastable liquid-liquid phase separations and gelation prior to solid nucleation, are due to the small ratio of the intermolecular interaction-range to the size of molecules involved. The apparently more generally applicable mechanisms include the cascade-like formation of macrosteps, as an intrinsic morphological instability that roots in the coupled bulk transport and nonlinear interface kinetics in systems with mixed growth rate control. Analyses of this nonlinear response provide (a) criteria for the choice of bulk transport conditions to minimize structural defect formation, and (b) indications that the "slow" protein crystallization kinetics stems from the mutual retardation of growth steps.

Interaction of finite-amplitude sound with air-filled porous materials

NASA Technical Reports Server (NTRS)

Nelson, D. A.

1985-01-01

The propagation of high intensity sound waves through an air-filled porus material was studied. The material is assumed: (1) to be rigid, incompressible, and homogeneous, and (2) to be adequately described by two properties: resistivity r and porosity. The resulting wave equation is still nonlinear, however, because of the u sgn(u) term in the resistivity. The equation is solved in the frequency domain as an infinite set of coupled inhomogeneous Helmholtz equations, one for each harmonic. An approximate but analytical solution leads to predictions of excess attenuation, saturation, and phase speed reduction for the fundamental component. A more general numerical solution is used to calculate the propagation curves for the higher harmonics. The u sgn(u) nonlinearity produces a cubic distortion pattern; when the input signal is a pure tone, only odd harmonic distortion products are generated.

The Equilibrium State of Colliding Electron Beams

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

Warnock, R

2003-12-12

We study a nonlinear integral equation that is a necessary condition on the equilibrium phase space distribution function of stored, colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in one degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, asmore » would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.« less

Optical image encryption system using nonlinear approach based on biometric authentication

NASA Astrophysics Data System (ADS)

Verma, Gaurav; Sinha, Aloka

2017-07-01

A nonlinear image encryption scheme using phase-truncated Fourier transform (PTFT) and natural logarithms is proposed in this paper. With the help of the PTFT, the input image is truncated into phase and amplitude parts at the Fourier plane. The phase-only information is kept as the secret key for the decryption, and the amplitude distribution is modulated by adding an undercover amplitude random mask in the encryption process. Furthermore, the encrypted data is kept hidden inside the face biometric-based phase mask key using the base changing rule of logarithms for secure transmission. This phase mask is generated through principal component analysis. Numerical experiments show the feasibility and the validity of the proposed nonlinear scheme. The performance of the proposed scheme has been studied against the brute force attacks and the amplitude-phase retrieval attack. Simulation results are presented to illustrate the enhanced system performance with desired advantages in comparison to the linear cryptosystem.

Response phase mapping of nonlinear joint dynamics using continuous scanning LDV measurement method

NASA Astrophysics Data System (ADS)

Di Maio, D.; Bozzo, A.; Peyret, Nicolas

2016-06-01

This study aims to present a novel work aimed at locating discrete nonlinearities in mechanical assemblies. The long term objective is to develop a new metric for detecting and locating nonlinearities using Scanning LDV systems (SLDV). This new metric will help to improve the modal updating, or validation, of mechanical assemblies presenting discrete and sparse nonlinearities. It is well established that SLDV systems can scan vibrating structures with high density of measurement points and produc e highly defined Operational Deflection Shapes (ODSs). This paper will present some insights on how to use response phase mapping for locating nonlinearities of a bolted flange. This type of structure presents two types of nonlinearities, which are geometr ical and frictional joints. The interest is focussed on the frictional joints and, therefore, the ability to locate which joint s are responsible for nonlinearity is seen highly valuable for the model validation activities.

Numerical investigation of differential phase noise and its power penalty for optical amplification using semiconductor optical amplifiers in DPSK applications

NASA Astrophysics Data System (ADS)

Hong, Wei; Huang, Dexiu; Zhang, Xinliang; Zhu, Guangxi

2007-11-01

A thorough simulation and evaluation of phase noise for optical amplification using semiconductor optical amplifier (SOA) is very important for predicting its performance in differential phase shift keyed (DPSK) applications. In this paper, standard deviation and probability distribution of differential phase noise are obtained from the statistics of simulated differential phase noise. By using a full-wave model of SOA, the noise performance in the entire operation range can be investigated. It is shown that nonlinear phase noise substantially contributes to the total phase noise in case of a noisy signal amplified by a saturated SOA and the nonlinear contribution is larger with shorter SOA carrier lifetime. Power penalty due to differential phase noise is evaluated using a semi-analytical probability density function (PDF) of receiver noise. Obvious increase of power penalty at high signal input powers can be found for low input OSNR, which is due to both the large nonlinear differential phase noise and the dependence of BER vs. receiving power curvature on differential phase noise standard deviation.

Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

PubMed

Ryzhov, Eugene A

2017-11-01

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

The Alfvénic nature of energy transfer mediation in localized, strongly nonlinear Alfvén wavepacket collisions

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.

2018-02-01

In space and astrophysical plasmas, violent events or instabilities inject energy into turbulent motions at large scales. Nonlinear interactions among the turbulent fluctuations drive a cascade of energy to small perpendicular scales at which the energy is ultimately converted into plasma heat. Previous work with the incompressible magnetohydrodynamic (MHD) equations has shown that this turbulent energy cascade is driven by the nonlinear interaction between counterpropagating Alfvén waves - also known as Alfvén wave collisions. Direct numerical simulations of weakly collisional plasma turbulence enables deeper insight into the nature of the nonlinear interactions underlying the turbulent cascade of energy. In this paper, we directly compare four cases: both periodic and localized Alfvén wave collisions in the weakly and strongly nonlinear limits. Our results reveal that in the more realistic case of localized Alfvén wave collisions (rather than the periodic case), all nonlinearly generated fluctuations are Alfvén waves, which mediates nonlinear energy transfer to smaller perpendicular scales.

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

Alexanian, Moorad

The fidelity for cloning coherent states is improved over that provided by optimal Gaussian and non-Gaussian cloners for the subset of coherent states that are prepared with known phases. Gaussian quantum cloning duplicates all coherent states with an optimal fidelity of 2/3. Non-Gaussian cloners give optimal single-clone fidelity for a symmetric 1-to-2 cloner of 0.6826. Coherent states that have known phases can be cloned with a fidelity of 4/5. The latter is realized by a combination of two beam splitters and a four-wave mixer operated in the nonlinear regime, all of which are realized by interaction Hamiltonians that are quadraticmore » in the photon operators. Therefore, the known Gaussian devices for cloning coherent states are extended when cloning coherent states with known phases by considering a nonbalanced beam splitter at the input side of the amplifier.« less

Non-destructive phase and intensity distributed measurements of the nonlinear stage of modulation instability in optical fibers

NASA Astrophysics Data System (ADS)

Mussot, Arnaud; Naveau, Corentin; Szriftgiser, Pascal; Copie, François; Kudlinski, Alexandre; Conforti, Matteo; Trillo, Stefano

2018-02-01

We report a novel experimental setup to perform distributed characterization in intensity and phase of the nonlinear stage of modulation instability by means of a non-invasive experimental setup : a heterodyne time domain reflectometer.

Modelling and control of a microgrid including photovoltaic and wind generation

NASA Astrophysics Data System (ADS)

Hussain, Mohammed Touseef

Extensive increase of distributed generation (DG) penetration and the existence of multiple DG units at distribution level have introduced the notion of micro-grid. This thesis develops a detailed non-linear and small-signal dynamic model of a microgrid that includes PV, wind and conventional small scale generation along with their power electronics interfaces and the filters. The models developed evaluate the amount of generation mix from various DGs for satisfactory steady state operation of the microgrid. In order to understand the interaction of the DGs on microgrid system initially two simpler configurations were considered. The first one consists of microalternator, PV and their electronics, and the second system consists of microalternator and wind system each connected to the power system grid. Nonlinear and linear state space model of each microgrid are developed. Small signal analysis showed that the large participation of PV/wind can drive the microgrid to the brink of unstable region without adequate control. Non-linear simulations are carried out to verify the results obtained through small-signal analysis. The role of the extent of generation mix of a composite microgrid consisting of wind, PV and conventional generation was investigated next. The findings of the smaller systems were verified through nonlinear and small signal modeling. A central supervisory capacitor energy storage controller interfaced through a STATCOM was proposed to monitor and enhance the microgrid operation. The potential of various control inputs to provide additional damping to the system has been evaluated through decomposition techniques. The signals identified to have damping contents were employed to design the supervisory control system. The controller gains were tuned through an optimal pole placement technique. Simulation studies demonstrate that the STATCOM voltage phase angle and PV inverter phase angle were the best inputs for enhanced stability boundaries.

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.

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

NASA Technical Reports Server (NTRS)

Prosser, William H.

1987-01-01

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial stength in graphite/epoxy composites.

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation.

PubMed

Rajeswaran, Jeevanantham; Blackstone, Eugene H

2017-02-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.

"Big Bang" as a result result of the curvature-driven first-order phase transition in the early cold Universe

NASA Astrophysics Data System (ADS)

Pashitskii, E. A.; Pentegov, V. I.

We suggest that the "Big Bang" may be a result of the first-order phase transition driven by changing scalar curvature of the 4D space-time in the expanding cold Universe, filled with nonlinear scalar field φ and neutral matter with equation of state p = vɛ (where p and ɛ are pressure and energy density of matter). We consider a Lagrangian for scalar field in curved space-time with nonlinearity φ, which along with the quadratic term -ΣR|φ|2 (where Σ is interaction constant and R is scalar curvature) contains a term ΣR(φ +φ+) linear in φ. Due to this term the condition for the extrema of the potential energy of the scalar field is given by a cubic equation. Provided v > 1/3 the scalar curvature R = [κ(3v-1)ɛ - 4Γ (where κ and Γ are Einstein's gravitational and cosmological constants) decreases along with decreasing " in the process of the Universe's expansion, and at some critical value Rc < 0 a first-order phase transition occurs, driven by an "external field" parameter proportional to R. Given certain conditions the critical radius of the early Universe at the point of the first-order phase transition may reach arbitrary large values, so this scenario of unrestricted "inflation" of the Universe may be called "hyperinflation". Beyond the point of phase transition the system is rolling down into the potential minimum releasing the potential energy of scalar field with subsequent powerful heating of the Universe playing the role of "Big Bang".

Conformal Coating of a Phase Change Material on Ordered Plasmonic Nanorod Arrays for Broadband All-Optical Switching.

PubMed

Guo, Peijun; Weimer, Matthew S; Emery, Jonathan D; Diroll, Benjamin T; Chen, Xinqi; Hock, Adam S; Chang, Robert P H; Martinson, Alex B F; Schaller, Richard D

2017-01-24

Actively tunable optical transmission through artificial metamaterials holds great promise for next-generation nanophotonic devices and metasurfaces. Plasmonic nanostructures and phase change materials have been extensively studied to this end due to their respective strong interactions with light and tunable dielectric constants under external stimuli. Seamlessly integrating plasmonic components with phase change materials, as demonstrated in the present work, can facilitate phase change by plasmonically enabled light confinement and meanwhile make use of the high sensitivity of plasmon resonances to the variation of dielectric constant associated with the phase change. The hybrid platform here is composed of plasmonic indium-tin-oxide nanorod arrays (ITO-NRAs) conformally coated with an ultrathin layer of a prototypical phase change material, vanadium dioxide (VO 2 ), which enables all-optical modulation of the infrared as well as the visible spectral ranges. The interplay between the intrinsic plasmonic nonlinearity of ITO-NRAs and the phase transition induced permittivity change of VO 2 gives rise to spectral and temporal responses that cannot be achieved with individual material components alone.

A two-dimensional computational study on the fluid-structure interaction cause of wing pitch changes in dipteran flapping flight.

PubMed

Ishihara, Daisuke; Horie, T; Denda, Mitsunori

2009-01-01

In this study, the passive pitching due to wing torsional flexibility and its lift generation in dipteran flight were investigated using (a) the non-linear finite element method for the fluid-structure interaction, which analyzes the precise motions of the passive pitching of the wing interacting with the surrounding fluid flow, (b) the fluid-structure interaction similarity law, which characterizes insect flight, (c) the lumped torsional flexibility model as a simplified dipteran wing, and (d) the analytical wing model, which explains the characteristics of the passive pitching motion in the simulation. Given sinusoidal flapping with a frequency below the natural frequency of the wing torsion, the resulting passive pitching in the steady state, under fluid damping, is approximately sinusoidal with the advanced phase shift. We demonstrate that the generated lift can support the weight of some Diptera.

Quantification of cardiorespiratory interactions based on joint symbolic dynamics.

PubMed

Kabir, Muammar M; Saint, David A; Nalivaiko, Eugene; Abbott, Derek; Voss, Andreas; Baumert, Mathias

2011-10-01

Cardiac and respiratory rhythms are highly nonlinear and nonstationary. As a result traditional time-domain techniques are often inadequate to characterize their complex dynamics. In this article, we introduce a novel technique to investigate the interactions between R-R intervals and respiratory phases based on their joint symbolic dynamics. To evaluate the technique, electrocardiograms (ECG) and respiratory signals were recorded in 13 healthy subjects in different body postures during spontaneous and controlled breathing. Herein, the R-R time series were extracted from ECG and respiratory phases were obtained from abdomen impedance belts using the Hilbert transform. Both time series were transformed into ternary symbol vectors based on the changes between two successive R-R intervals or respiratory phases. Subsequently, words of different symbol lengths were formed and the correspondence between the two series of words was determined to quantify the interaction between cardiac and respiratory cycles. To validate our results, respiratory sinus arrhythmia (RSA) was further studied using the phase-averaged characterization of the RSA pattern. The percentage of similarity of the sequence of symbols, between the respective words of the two series determined by joint symbolic dynamics, was significantly reduced in the upright position compared to the supine position (26.4 ± 4.7 vs. 20.5 ± 5.4%, p < 0.01). Similarly, RSA was also reduced during upright posture, but the difference was less significant (0.11 ± 0.02 vs. 0.08 ± 0.01 s, p < 0.05). In conclusion, joint symbolic dynamics provides a new efficient technique for the analysis of cardiorespiratory interaction that is highly sensitive to the effects of orthostatic challenge.

Blended particle filters for large-dimensional chaotic dynamical systems

PubMed Central

Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.

2014-01-01

A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase space are introduced here. These blended particle filters are constructed in this paper through a mathematical formalism involving conditional Gaussian mixtures combined with statistically nonlinear forecast models compatible with this structure developed recently with high skill for uncertainty quantification. Stringent test cases for filtering involving the 40-dimensional Lorenz 96 model with a 5-dimensional adaptive subspace for nonlinear blended filtering in various turbulent regimes with at least nine positive Lyapunov exponents are used here. These cases demonstrate the high skill of the blended particle filter algorithms in capturing both highly non-Gaussian dynamical features as well as crucial nonlinear statistics for accurate filtering in extreme filtering regimes with sparse infrequent high-quality observations. The formalism developed here is also useful for multiscale filtering of turbulent systems and a simple application is sketched below. PMID:24825886

Efficient extreme-UV-to-extreme-UV conversion by four-wave mixing with intense near-IR pulses in highly charged ion plasmas

NASA Astrophysics Data System (ADS)

Chu, Hsu-hsin; Wang, Jyhpyng

2018-05-01

Nonlinear optics in the extreme-ultraviolet (EUV) has been limited by lack of transparent media and small conversion efficiency. To overcome this problem we explore the advantage of using multiply charged ion plasmas as the interacting media between EUV and intense near-infrared (NIR) pulses. Such media are transparent to EUV and can withstand intense NIR driving pulses without damage. We calculate the third-order nonlinear polarizabilities of Ar2 + and Ar3 + ions for EUV and NIR four-wave mixing by using the well-proven Cowan code and find that the EUV-to-EUV conversion efficiency as high as 26% can be expected for practical experimental configurations using multi-terawatt NIR lasers. Such a high efficiency is possible because the driving pulse intensity can be scaled up to several orders of magnitude higher than in conventional nonlinear media, and the group-velocity and phase mismatch are insignificant at the experimental plasma densities. This effective scheme of wave mixing can be utilized for ultrafast EUV waveform measurement and control as well as wavelength conversion.

Spectra of Baroclinic Inertia-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1996-01-01

Baroclinic inertia-gravity (IG) waves form a persistent background of thermocline depth and sea surface height oscillations. They also contribute to the kinetic energy of horizontal motions in the subsurface layer. Measured by the ratio of water particle velocity to wave phase speed, the wave nonlinearity may be rather high. Given a continuous supply of energy from external sources, nonlinear wave-wave interactions among IG waves would result in inertial cascades of energy, momentum, and wave action. Based on a recently developed theory of wave turbulence in scale-dependent systems, these cascades are investigated and IG wave spectra are derived for an arbitrary degree of wave nonlinearity. Comparisons with satellite-altimetry-based spectra of surface height variations and with energy spectra of horizontal velocity fluctuations show good agreement. The well-known spectral peak at the inertial frequency is thus explained as a result of the inverse cascade. Finally, we discuss a possibility of inferring the internal Rossby radius of deformation and other dynamical properties of the upper thermocline from the spectra of SSH (sea surface height) variations based on altimeter measurements.

Nonlinear Response Of MSSS Bridges Under Earthquake Ground Motions: Case Studies

DOT National Transportation Integrated Search

1999-10-01

This report presents the results of the second phase of a comprehensive analytical study on the seismic response of highway bridges in New Jersey. The overall objective of this phase of the study was to evaluate the nonlinear seismic response of actu...

Bounded tracking for nonminimum phase nonlinear systems with fast zero dynamics

DOT National Transportation Integrated Search

1996-12-01

A PostScript file. In this paper, tracking control laws for nonminimum phase nonlinear systems with both fast and slow, possibly unstable, zero dynamics are derived. The fast zero dynamics arise from a perturbation of a nominal system. These fast zer...

Theory of Self-Phase Modulation and Spectral Broadening

NASA Astrophysics Data System (ADS)

Shen, Y. R.; Yang, Guo-Zhen

Self-phase modulation refers to the phenomenon in which a laser beam propagating in a medium interacts with the medium and imposes a phase modulation on itself. It is one of those very fascinating effects discovered in the early days of nonlinear optics (Bloembergen and Lallemand, 1966; Brewer, 1967; Cheung et al., 1968; Lallemand, 1966; Jones and Stoicheff, 1964; Shimizu, 1967; Stoicheff, 1963). The physical origin of the phenomenon lies in the fact that the strong field of a laser beam is capable of inducing an appreciable intensity-dependent refractive index change in the medium. The medium then reacts back and inflicts a phase change on the incoming wave, resulting in self-phase modulation (SPM). Since a laser beam has a finite cross section, and hence a transverse intensity profile, SPM on the beam should have a transverse spatial dependence, equivalent to a distortion of the wave front. Consequently, the beam will appear to have self-diffracted. Such a self-diffraction action, resulting from SPM in space, is responsible for the well-known nonlinear optical phenomena of self-focusing and self-defocusing (Marburger, 1975; Shen, 1975). It can give rise to a multiple ring structure in the diffracted beam if the SPM is sufficiently strong (Durbin et al., 1981; Santamato and Shen, 1984). In the case of a pulsed laser input, the temporal variation of the laser intensity leads to an SPM in time. Since the time derivative of the phase of a wave is simply the angular frequency of the wave, SPM also appears as a frequency modulation. Thus, the output beam appears with a self-induced spectral broadening (Cheung et al., 1968; Gustafson et al., 1969; Shimizu, 1967).

Manipulating femtosecond laser interactions in bulk glass and thin-film with spatial light modulation (Conference Presentation)

NASA Astrophysics Data System (ADS)

Alimohammadian, Ehsan; Ho, Stephen; Ertorer, Erden; Gherghe, Sebastian; Li, Jianzhao; Herman, Peter R.

2017-03-01

Spatial Light Modulators (SLM) are emerging as a power tool for laser beam shaping whereby digitally addressed phase shifts can impose computer-generated hologram patterns on incoming laser light. SLM provide several additional advantages with ultrashort-pulsed lasers in controlling the shape of both surface and internal interactions with materials. Inside transparent materials, nonlinear optical effects can confine strong absorption only to the focal volume, extend dissipation over long filament tracks, or reach below diffraction-limited spot sizes. Hence, SLM beam shaping has been widely adopted for laser material processing applications that include parallel structuring, filamentation, fiber Bragg grating formation and optical aberration correction. This paper reports on a range of SLM applications we have studied in femtosecond processing of transparent glasses and thin films. Laser phase-fronts were tailored by the SLM to compensate for spherical surface aberration, and to further address the nonlinear interactions that interplay between Kerr-lens self-focusing and plasma defocusing effects over shallow and deep focusing inside the glass. Limits of strong and weak focusing were examined around the respective formation of low-loss optical waveguides and long uniform filament tracks. Further, we have employed the SLM for beam patterning inside thin film, exploring the limits of phase noise, resolution and fringe contrast during interferometric intra-film structuring. Femtosecond laser pulses of 200 fs pulse duration and 515 nm wavelength were shaped by a phase-only LCOS-SLM (Hamamatsu X10468-04). By imposing radial phase profiles, axicon, grating and beam splitting gratings, volume shape control of filament diameter, length, and uniformity as well as simultaneous formation of multiple filaments has been demonstrated. Similarly, competing effects of spherical surface aberration, self-focusing, and plasma de-focusing were studied and delineated to enable formation of low-loss optical waveguides over shallow and deep focusing conditions. Lastly, SLM beam shaping has been successfully extended to interferometric processing inside thin transparent film, enabling the arbitrary formation of uniform or non-uniform, symmetric or asymmetric patterns of flexible shape on nano-scale dimensions without phase-noise degradation by the SLM patterning. We present quantized structuring of thin films by a single laser pulse, demonstrating λ/2nfilm layer ejection control, blister formation, nano-cavities, and film colouring. Closed intra-film nanochannels with high aspect ratio (20:1) have been formed inside 3.5 um thick silica, opening new prospects for sub-cellular studies and lab-in-film concepts that integrate on CMOS silicon technologies.

The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice

NASA Astrophysics Data System (ADS)

Xu, Quan; Tian, Qiang

2005-04-01

The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.

Analysis and gyrokinetic simulation of MHD Alfven wave interactions

NASA Astrophysics Data System (ADS)

Nielson, Kevin Derek

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ rhoi ≳ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfven wave turbulence.

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1988-01-01

The nonlinear reaction between two oblique 3-D Tollmein-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an imcompressible boundary layer. The same theory applies to the destabilization of an incident vortex motion by subharmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlionear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial differential system for the vortex flow coupled with an ordinary-differential one for the TS pressure. The solution properties found sometimes produce a breakup within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasi-parallel ones governed by the full nonlinear triple-deck response.

Simulation program of nonlinearities applied to telecommunication systems

NASA Technical Reports Server (NTRS)

Thomas, C.

1979-01-01

In any satellite communication system, the problems of distorsion created by nonlinear devices or systems must be considered. The subject of this paper is the use of the Fast Fourier Transform (F.F.T.) in the prediction of the intermodulation performance of amplifiers, mixers, filters. A nonlinear memory-less model is chosen to simulate amplitude and phase nonlinearities of the device in the simulation program written in FORTRAN 4. The experimentally observed nonlinearity parameters of a low noise 3.7-4.2 GHz amplifier are related to the gain and phase coefficients of Fourier Service Series. The measured results are compared with those calculated from the simulation in the cases where the input signal is composed of two, three carriers and noise power density.

Experimental Measurement of the Nonlinear Interaction between Counterpropagating Alfv'en Waves in the LaPD

NASA Astrophysics Data System (ADS)

Schroeder, J. W. R.; Drake, D. J.; Howes, G. G.; Skiff, F.; Kletzing, C. A.; Carter, T. A.; Dorfman, S.; Auerbach, D.

2012-10-01

Turbulence plays an important role in the transport of mass and energy in many space and astrophysical plasmas ranging from galaxy clusters to Earth's magnetosphere. One active topic of research is the application of idealized Alfv'enic turbulence models to plasma conditions relevant to space and astrophysical plasmas. Alfv'enic turbulence models based on incompressible magnetohydrodynamics (MHD) contain a nonlinear interaction that drives the cascade of energy to smaller scales. We describe experiments at the Large Plasma Device (LaPD) that focus on the interaction of an Alfv'en wave traveling parallel to the mean magnetic field with a counterpropagating Alfv'en wave. Theory predicts the nonlinear interaction of the two primary waves will produce a secondary daughter Alfv'en wave. In this study, we present the first experimental identification of the daughter wave generated by nonlinear interactions between the primary Alfv'en waves.

Harmonic Phase Response of Nonlinear Radar Targets

DTIC Science & Technology

2015-10-01

while allowing its harmonics to pass through. The weak harmonic responses are then amplified to allow for easier detection and measurement . 4...where the phase of the 2nd and 3rd harmonic of the received electromagnetic wave from nonlinear targets was measured and plotted against the frequency

On the Connection Between Microbursts and Nonlinear Electronic Structures in Planetary Radiation Belts

NASA Technical Reports Server (NTRS)

Osmane, Adnane; Wilson, Lynn B., III; Blum, Lauren; Pulkkinen, Tuija I.

2016-01-01

Using a dynamical-system approach, we have investigated the efficiency of large-amplitude whistler waves for causing microburst precipitation in planetary radiation belts by modeling the microburst energy and particle fluxes produced as a result of nonlinear wave-particle interactions. We show that wave parameters, consistent with large amplitude oblique whistlers, can commonly generate microbursts of electrons with hundreds of keV-energies as a result of Landau trapping. Relativistic microbursts (greater than 1 MeV) can also be generated by a similar mechanism, but require waves with large propagation angles Theta (sub k)B greater than 50 degrees and phase-speeds v(sub phi) greater than or equal to c/9. Using our result for precipitating density and energy fluxes, we argue that holes in the distribution function of electrons near the magnetic mirror point can result in the generation of double layers and electron solitary holes consistent in scales (of the order of Debye lengths) to nonlinear structures observed in the radiation belts by the Van Allen Probes. Our results indicate a relationship between nonlinear electrostatic and electromagnetic structures in the dynamics of planetary radiation belts and their role in the cyclical production of energetic electrons (E greater than or equal to 100 keV) on kinetic timescales, which is much faster than previously inferred.

Fermi-Pasta-Ulam recurrence and modulation instability

NASA Astrophysics Data System (ADS)

Kuznetsov, E. A.

2017-01-01

We give a qualitative conceptual explanation of the Fermi-Pasta-Ulam (FPU) like recurrence in the onedimensional focusing nonlinear Schrodinger equation (NLSE). The recurrence can be considered as a result of the nonlinear development of the modulation instability. All known exact localized solitary wave solutions describing propagation on the background of the modulationally unstable condensate show the recurrence to the condensate state after its interaction with solitons. The condensate state locally recovers its original form with the same amplitude but a different phase after soliton leave its initial region. Based on the integrability of the NLSE, we demonstrate that the FPU recurrence takes place not only for condensate, but also for a more general solution in the form of the cnoidal wave. This solution is periodic in space and can be represented as a solitonic lattice. That lattice reduces to isolated soliton solution in the limit of large distance between solitons. The lattice transforms into the condensate in the opposite limit of dense soliton packing. The cnoidal wave is also modulationally unstable due to soliton overlapping. The recurrence happens at the nonlinear stage of the modulation instability. Due to generic nature of the underlying mathematical model, the proposed concept can be applied across disciplines and nonlinear systems, ranging from optical communications to hydrodynamics.

Electron spin resonance modes in a strong-leg ladder in the Tomonaga-Luttinger liquid phase

NASA Astrophysics Data System (ADS)

Ozerov, M.; Maksymenko, M.; Wosnitza, J.; Honecker, A.; Landee, C. P.; Turnbull, M. M.; Furuya, S. C.; Giamarchi, T.; Zvyagin, S. A.

2015-12-01

Magnetic excitations in the strong-leg quantum spin ladder compound (C7H10N) 2CuBr4 (known as DIMPY) in the field-induced Tomonaga-Luttinger spin-liquid phase are studied by means of high-field electron spin resonance (ESR) spectroscopy. The presence of a gapped ESR mode with unusual nonlinear frequency-field dependence is revealed experimentally. Using a combination of analytic and exact-diagonalization methods, we compute the dynamical structure factor and identify this mode with longitudinal excitations in the antisymmetric channel. We argue that these excitations constitute a fingerprint of the spin dynamics in a strong-leg spin-1/2 Heisenberg antiferromagnetic ladder and owe their ESR observability to the uniform Dzyaloshinskii-Moriya interaction.

Dynamic interaction of two-phase debris flow with pyramidal defense structures: An optimal strategy to efficiently protecting the desired area

NASA Astrophysics Data System (ADS)

Kattel, Parameshwari; Kafle, Jeevan; Fischer, Jan-Thomas; Mergili, Martin; Tuladhar, Bhadra Man; Pudasaini, Shiva P.

2017-04-01

In this work we analyze the dynamic interaction of two phase debris flows with pyramidal obstacles. To simulate the dynamic interaction of two-phase debris flow (a mixture of solid particles and viscous fluid) with obstacles of different dimensions and orientations, we employ the general two-phase mass flow model (Pudasaini, 2012). The model consists of highly non-linear partial differential equations representing the mass and momentum conservations for both solid and fluid. Besides buoyancy, the model includes some dominant physical aspects of the debris flows such as generalized drag, virtual mass and non-Newtonian viscous stress as induced by the gradient of solid-volume-fraction. Simulations are performed with high-resolution numerical schemes to capture essential dynamics, including the strongly re-directed flow with multiple stream lines, mass arrest and debris-vacuum generation when the rapidly cascading debris mass suddenly encounters the obstacle. The solid and fluid phases show fundamentally different interactions with obstacles, flow spreading and dispersions, run-out dynamics, and deposition morphology. A forward-facing pyramid deflects the mass wider, and a rearward-facing pyramid arrests a portion of solid-mass at its front. Our basic study reveals that appropriately installed obstacles, their dimensions and orientations have a significant influence on the flow dynamics, material redistribution and redirection. The precise knowledge of the change in dynamics is of great importance for the optimal and effective protection of designated areas along the mountain slopes and the runout zones. Further important results are, that specific installations lead to redirect either solid, or fluid, or both, in the desired amounts and directions. The present method of the complex interactions of real two-phase mass flows with the obstacles may help us to construct defense structures and to design advanced and physics-based engineering solutions for the prevention and mitigation of natural hazards caused by geophysical mass flows. References: Pudasaini, S. P. (2012): A general two-phase debris flow model. J. Geophys. Res. 117, F03010, doi: 10.1029/ 2011JF002186.

Rewriting the rules governing high intensity interactions of light with matter

NASA Astrophysics Data System (ADS)

Borisov, Alex B.; McCorkindale, John C.; Poopalasingam, Sankar; Longworth, James W.; Simon, Peter; Szatmári, Sándor; Rhodes, Charles K.

2016-04-01

The trajectory of discovery associated with the study of high-intensity nonlinear radiative interactions with matter and corresponding nonlinear modes of electromagnetic propagation through material that have been conducted over the last 50 years can be presented as a landscape in the intensity/quantum energy [I-ħω] plane. Based on an extensive series of experimental and theoretical findings, a universal zone of anomalous enhanced electromagnetic coupling, designated as the fundamental nonlinear domain, can be defined. Since the lower boundaries of this region for all atomic matter correspond to ħω ~ 103 eV and I  ≈  1016 W cm-2, it heralds a future dominated by x-ray and γ-ray studies of all phases of matter including nuclear states. The augmented strength of the interaction with materials can be generally expressed as an increase in the basic electromagnetic coupling constant in which the fine structure constant α  →  Z 2 α, where Z denotes the number of electrons participating in an ordered response to the driving field. Since radiative conditions strongly favoring the development of this enhanced electromagnetic coupling are readily produced in self-trapped plasma channels, the processes associated with the generation of nonlinear interactions with materials stand in natural alliance with the nonlinear mechanisms that induce confined propagation. An experimental example involving the Xe (4d105s25p6) supershell for which Z  ≅  18 that falls in the specified anomalous nonlinear domain is described. This yields an effective coupling constant of Z 2 α  ≅  2.4  >  1, a magnitude comparable to the strong interaction and a value rendering as useless conventional perturbative analyses founded on an expansion in powers of α. This enhancement can be quantitatively understood as a direct consequence of the dominant role played by coherently driven multiply-excited states in the dynamics of the coupling. It is also conclusively demonstrated by an abundance of data that the utterly peerless champion of the experimental campaign leading to the definition of the fundamental nonlinear domain was excimer laser technology. The basis of this unique role was the ability to satisfy simultaneously a triplet (ω, I, P) of conditions stating the minimal values of the frequency ω, intensity I, and the power P necessary to enable the key physical processes to be experimentally observed and controllably combined. The historical confluence of these developments creates a solid foundation for the prediction of future advances in the fundamental understanding of ultra-high power density states of matter. The atomic findings graciously generalize to the composition of a nuclear stanza expressing the accessibility of the nuclear domain. With this basis serving as the launch platform, a cadenza of three grand challenge problems representing both new materials and new interactions is presented for future solution; they are (1) the performance of an experimental probe of the properties of the vacuum state associated with the dark energy at an intensity approaching the Schwinger/Heisenberg limit, (2) the attainment of amplification in the γ-ray region (~1 MeV) and the discovery of a nuclear excimer, and (3) the determination of a path to the projected super-heavy nuclear island of stability.

Rewriting the rules governing high intensity interactions of light with matter.

PubMed

Borisov, Alex B; McCorkindale, John C; Poopalasingam, Sankar; Longworth, James W; Simon, Peter; Szatmári, Sándor; Rhodes, Charles K

2016-04-01

The trajectory of discovery associated with the study of high-intensity nonlinear radiative interactions with matter and corresponding nonlinear modes of electromagnetic propagation through material that have been conducted over the last 50 years can be presented as a landscape in the intensity/quantum energy [I-ħω] plane. Based on an extensive series of experimental and theoretical findings, a universal zone of anomalous enhanced electromagnetic coupling, designated as the fundamental nonlinear domain, can be defined. Since the lower boundaries of this region for all atomic matter correspond to ħω ~ 10(3) eV and I  ≈  10(16) W cm(-2), it heralds a future dominated by x-ray and γ-ray studies of all phases of matter including nuclear states. The augmented strength of the interaction with materials can be generally expressed as an increase in the basic electromagnetic coupling constant in which the fine structure constant α  →  Z(2)α, where Z denotes the number of electrons participating in an ordered response to the driving field. Since radiative conditions strongly favoring the development of this enhanced electromagnetic coupling are readily produced in self-trapped plasma channels, the processes associated with the generation of nonlinear interactions with materials stand in natural alliance with the nonlinear mechanisms that induce confined propagation. An experimental example involving the Xe (4d(10)5s(2)5p(6)) supershell for which Z  ≅  18 that falls in the specified anomalous nonlinear domain is described. This yields an effective coupling constant of Z(2)α  ≅  2.4  >  1, a magnitude comparable to the strong interaction and a value rendering as useless conventional perturbative analyses founded on an expansion in powers of α. This enhancement can be quantitatively understood as a direct consequence of the dominant role played by coherently driven multiply-excited states in the dynamics of the coupling. It is also conclusively demonstrated by an abundance of data that the utterly peerless champion of the experimental campaign leading to the definition of the fundamental nonlinear domain was excimer laser technology. The basis of this unique role was the ability to satisfy simultaneously a triplet (ω, I, P) of conditions stating the minimal values of the frequency ω, intensity I, and the power P necessary to enable the key physical processes to be experimentally observed and controllably combined. The historical confluence of these developments creates a solid foundation for the prediction of future advances in the fundamental understanding of ultra-high power density states of matter. The atomic findings graciously generalize to the composition of a nuclear stanza expressing the accessibility of the nuclear domain. With this basis serving as the launch platform, a cadenza of three grand challenge problems representing both new materials and new interactions is presented for future solution; they are (1) the performance of an experimental probe of the properties of the vacuum state associated with the dark energy at an intensity approaching the Schwinger/Heisenberg limit, (2) the attainment of amplification in the γ-ray region (~1 MeV) and the discovery of a nuclear excimer, and (3) the determination of a path to the projected super-heavy nuclear island of stability.

Data based identification and prediction of nonlinear and complex dynamical systems

NASA Astrophysics Data System (ADS)

Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2016-07-01

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical systems theories with tools from statistical physics, optimization, engineering control, applied mathematics, and scientific computing enables the development of a number of paradigms to address the problem of nonlinear and complex systems reconstruction. In this Review, we describe the recent advances in this forefront and rapidly evolving field, with a focus on compressive sensing based methods. In particular, compressive sensing is a paradigm developed in recent years in applied mathematics, electrical engineering, and nonlinear physics to reconstruct sparse signals using only limited data. It has broad applications ranging from image compression/reconstruction to the analysis of large-scale sensor networks, and it has become a powerful technique to obtain high-fidelity signals for applications where sufficient observations are not available. We will describe in detail how compressive sensing can be exploited to address a diverse array of problems in data based reconstruction of nonlinear and complex networked systems. The problems include identification of chaotic systems and prediction of catastrophic bifurcations, forecasting future attractors of time-varying nonlinear systems, reconstruction of complex networks with oscillatory and evolutionary game dynamics, detection of hidden nodes, identification of chaotic elements in neuronal networks, reconstruction of complex geospatial networks and nodal positioning, and reconstruction of complex spreading networks with binary data.. A number of alternative methods, such as those based on system response to external driving, synchronization, and noise-induced dynamical correlation, will also be discussed. Due to the high relevance of network reconstruction to biological sciences, a special section is devoted to a brief survey of the current methods to infer biological networks. Finally, a number of open problems including control and controllability of complex nonlinear dynamical networks are discussed. The methods outlined in this Review are principled on various concepts in complexity science and engineering such as phase transitions, bifurcations, stabilities, and robustness. The methodologies have the potential to significantly improve our ability to understand a variety of complex dynamical systems ranging from gene regulatory systems to social networks toward the ultimate goal of controlling such systems.

Nonlinear wave-wave interactions in the subauroral ionosphere on the basis of ISIS-2 satellite observations of Siple station VLF signals

NASA Technical Reports Server (NTRS)

Ohnami, S.; Hayakawa, M.; Bell, T. F.; Ondoh, T.

1993-01-01

Nonlinear wave-wave interaction between signals from a ground-based VLF transmitter and narrow-band ELF emissions in the subauroral ionosphere is studied by means of the bispectrum and bicoherence analysis. A bicoherence analysis has indicated that the sideband structures around the Siple transmitter signal received onboard the ISIS satellite are due to the nonlinear interaction between the Siple VLF signal and the pre-existing ELF emission.

Vector breather-to-soliton transitions and nonlinear wave interactions induced by higher-order effects in an erbium-doped fiber

NASA Astrophysics Data System (ADS)

Sun, Wen-Rong; Wang, Lei; Xie, Xi-Yang

2018-06-01

Vector breather-to-soliton transitions for the higher-order nonlinear Schrödinger-Maxwell-Bloch (NLS-MB) system with sextic terms are investigated. The Lax pair and Darboux transformation (DT) of such system are constructed. With the DT, analytic vector breather solutions up to the second order are obtained. With appropriate choices of the spectra parameters, vector breather-to-soliton transitions happen. Interaction mechanisms of vector nonlinear waves (breather-soliton or soliton-soliton interactions) are displayed.

A multi-frequency inverse-phase error compensation method for projector nonlinear in 3D shape measurement

NASA Astrophysics Data System (ADS)

Mao, Cuili; Lu, Rongsheng; Liu, Zhijian

2018-07-01

In fringe projection profilometry, the phase errors caused by the nonlinear intensity response of digital projectors needs to be correctly compensated. In this paper, a multi-frequency inverse-phase method is proposed. The theoretical model of periodical phase errors is analyzed. The periodical phase errors can be adaptively compensated in the wrapped maps by using a set of fringe patterns. The compensated phase is then unwrapped with multi-frequency method. Compared with conventional methods, the proposed method can greatly reduce the periodical phase error without calibrating measurement system. Some simulation and experimental results are presented to demonstrate the validity of the proposed approach.

FIBER AND INTEGRATED OPTICS: Nonlinearity of a channel-waveguide phase modulator

NASA Astrophysics Data System (ADS)

Parygin, V. N.; Zhmakin, I. N.; Baglikov, V. B.

1993-09-01

The phase velocity of light in a channel waveguide using a LiNbO3 crystal is analyzed as a function of the voltage applied to the crystal. A refinement of the method of an effective refractive index is proposed. This refinement makes it possible to use the method near the cutoff for a waveguide mode. At voltages on the order of 10 V, the nonlinearity of the phase characteristic amounts to ~ 5 · 10- 4 of the linear phase shift.

Time-dependent photon heat transport through a mesoscopic Josephson device

NASA Astrophysics Data System (ADS)

Lu, Wen-Ting; Zhao, Hong-Kang

2017-02-01

The time-oscillating photon heat current through a dc voltage biased mesoscopic Josephson Junction (MJJ) has been investigated by employing the nonequilibrium Green's function approach. The Landauer-like formula of photon heat current has been derived in both of the Fourier space and its time-oscillating versions, where Coulomb interaction, self inductance, and magnetic flux take effective roles. Nonlinear behaviors are exhibited in the photon heat current due to the quantum nature of MJJ and applied external dc voltage. The magnitude of heat current decreases with increasing the external bias voltage, and subtle oscillation structures appear as the superposition of different photon heat branches. The overall period of heat current with respect to time is not affected by Coulomb interaction, however, the magnitude and phase of it vary considerably by changing the Coulomb interaction.

Nonlinear Directed Interactions Between HRV and EEG Activity in Children With TLE.

PubMed

Schiecke, Karin; Pester, Britta; Piper, Diana; Benninger, Franz; Feucht, Martha; Leistritz, Lutz; Witte, Herbert

2016-12-01

Epileptic seizure activity influences the autonomic nervous system (ANS) in different ways. Heart rate variability (HRV) is used as indicator for alterations of the ANS. It was shown that linear, nondirected interactions between HRV and EEG activity before, during, and after epileptic seizure occur. Accordingly, investigations of directed nonlinear interactions are logical steps to provide, e.g., deeper insight into the development of seizure onsets. Convergent cross mapping (CCM) investigates nonlinear, directed interactions between time series by using nonlinear state space reconstruction. CCM is applied to simulated and clinically relevant data, i.e., interactions between HRV and specific EEG components of children with temporal lobe epilepsy (TLE). In addition, time-variant multivariate Autoregressive model (AR)-based estimation of partial directed coherence (PDC) was performed for the same data. Influence of estimation parameters and time-varying behavior of CCM estimation could be demonstrated by means of simulated data. AR-based estimation of PDC failed for the investigation of our clinical data. Time-varying interval-based application of CCM on these data revealed directed interactions between HRV and delta-related EEG activity. Interactions between HRV and alpha-related EEG activity were visible but less pronounced. EEG components mainly drive HRV. The interaction pattern and directionality clearly changed with onset of seizure. Statistical relevant interactions were quantified by bootstrapping and surrogate data approach. In contrast to AR-based estimation of PDC CCM was able to reveal time-courses and frequency-selective views of nonlinear interactions for the further understanding of complex interactions between the epileptic network and the ANS in children with TLE.

Role of Interaction between Magnetic Rossby Waves and Tachocline Differential Rotation in Producing Solar Seasons

NASA Astrophysics Data System (ADS)

Dikpati, Mausumi; McIntosh, Scott W.; Bothun, Gregory; Cally, Paul S.; Ghosh, Siddhartha S.; Gilman, Peter A.; Umurhan, Orkan M.

2018-02-01

We present a nonlinear magnetohydrodynamic shallow-water model for the solar tachocline (MHD-SWT) that generates quasi-periodic tachocline nonlinear oscillations (TNOs) that can be identified with the recently discovered solar “seasons.” We discuss the properties of the hydrodynamic and magnetohydrodynamic Rossby waves that interact with the differential rotation and toroidal fields to sustain these oscillations, which occur due to back-and-forth energy exchanges among potential, kinetic, and magnetic energies. We perform model simulations for a few years, for selected example cases, in both hydrodynamic and magnetohydrodynamic regimes and show that the TNOs are robust features of the MHD-SWT model, occurring with periods of 2–20 months. We find that in certain cases multiple unstable shallow-water modes govern the dynamics, and TNO periods vary with time. In hydrodynamically governed TNOs, the energy exchange mechanism is simple, occurring between the Rossby waves and differential rotation. But in MHD cases, energy exchange becomes much more complex, involving energy flow among six energy reservoirs by means of eight different energy conversion processes. For toroidal magnetic bands of 5 and 35 kG peak amplitudes, both placed at 45° latitude and oppositely directed in north and south hemispheres, we show that the energy transfers responsible for TNO, as well as westward phase propagation, are evident in synoptic maps of the flow, magnetic field, and tachocline top-surface deformations. Nonlinear mode–mode interaction is particularly dramatic in the strong-field case. We also find that the TNO period increases with a decrease in rotation rate, implying that the younger Sun had more frequent seasons.

A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation

PubMed Central

Rajeswaran, Jeevanantham; Blackstone, Eugene H.

2014-01-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830

N-soliton interactions: Effects of linear and nonlinear gain and loss

NASA Astrophysics Data System (ADS)

Carretero-González, R.; Gerdjikov, V. S.; Todorov, M. D.

2017-10-01

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the nonlinear Schrödinger equation perturbed simultaneously by linear and nonlinear gain/loss terms. We derive the corresponding perturbed complex Toda chain in the case of a combination of linear, cubic, and/or quintic terms. We show that the soliton interactions dynamics for this reduced PCTC model compares favorably to full numerical results of the original perturbed nonlinear Schrödinger equation.

Algebraic motion of vertically displacing plasmas

NASA Astrophysics Data System (ADS)

Pfefferlé, D.; Bhattacharjee, A.

2018-02-01

The vertical motion of a tokamak plasma is analytically modelled during its non-linear phase by a free-moving current-carrying rod inductively coupled to a set of fixed conducting wires or a cylindrical conducting shell. The solutions capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the surrounding vacuum vessel. The plasma shape and profiles are assumed not to vary during the vertical drifting phase such that the plasma column behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented to come in contact with the wall due to steep effective potential barriers created by the induced Eddy currents. Resistivity in the wall allows the equilibrium point to drift towards the vessel on the slow timescale of flux penetration. The initial exponential motion of the plasma, understood as a resistive vertical instability, is succeeded by a non-linear "sinking" behaviour shown to be algebraic and decelerating. The acceleration of the plasma column often observed in experiments is thus concluded to originate from an early sharing of toroidal current between the core, the halo plasma, and the wall or from the thermal quench dynamics precipitating loss of plasma current.

Optical parametric oscillation in a random poly-crystalline medium: ZnSe ceramic

NASA Astrophysics Data System (ADS)

Ru, Qitian; Kawamori, Taiki; Lee, Nathaniel; Chen, Xuan; Zhong, Kai; Mirov, Mike; Vasilyev, Sergey; Mirov, Sergey B.; Vodopyanov, Konstantin L.

2018-02-01

We demonstrate an optical parametric oscillator (OPO) based on random phase matching in a polycrystalline χ(2) material, ZnSe. The subharmonic OPO utilized a 1.5-mm-long polished ZnSe ceramic sample placed at the Brewster's angle and was synchronously pumped by a Kerr-lens mode-locked Cr:ZnS laser with a central wavelength of 2.35 μm, a pulse duration of 62 fs, and a repetition frequency of 79 MHz. The OPO had a 90-mW pump threshold, and produced an ultrabroadband spectrum spanning 3-7.5 μm. The observed pump depletion was as high as 79%. The key to success in achieving the OPO action was choosing the average grain size of the ZnSe ceramic to be close to the coherence length ( 100 μm) for our 3-wave interaction. This is the first OPO that uses random polycrystalline material with quadratic nonlinearity and the first OPO based on ZnSe. Very likely, random phase matching in ZnSe and similar random polycrystalline materials (ZnS, CdS, CdSe, GaP) represents a viable route for generating few-cycle pulses and multi-octave frequency combs, thanks to a very broadband nonlinear response.

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

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.

Using surface lattice resonances to engineer nonlinear optical processes in metal nanoparticle arrays

NASA Astrophysics Data System (ADS)

Huttunen, Mikko J.; Rasekh, Payman; Boyd, Robert W.; Dolgaleva, Ksenia

2018-05-01

Collective responses of localized surface plasmon resonances, known as surface lattice resonances (SLRs) in metal nanoparticle arrays, can lead to high quality factors (˜100 ), large local-field enhancements, and strong light-matter interactions. SLRs have found many applications in linear optics, but little work of the influence of SLRs on nonlinear optics has been reported. Here we show how SLRs could be utilized to enhance nonlinear optical interactions. We devote special attention to the sum-frequency, difference-frequency, and third-harmonic generation processes because of their potential for the realization of novel sources of light. We also demonstrate how such arrays could be engineered to enhance higher-order nonlinear optical interactions through cascaded nonlinear processes. In particular, we demonstrate how the efficiency of third-harmonic generation could be engineered via cascaded second-order responses.

Nonlinear Spectroscopy.

DTIC Science & Technology

1985-03-20

Finally, the (linear) .response of a Fabry - Perot cavity to a phase modulated light wave is considered because of its relevance to phase locking a laser...prepared and therefore doesn’t contribute. This effect provides the remaining factor of two. IV. FABRY - PEROT We now calculate the response of a plane...mirror Fabry - Perot cavity to a phase-modulated laser beam. This linear problem, which contrasts with the nonlinear atomic case, is the basis of an

Influence of cross-phase modulation in SPM-based nonlinear optical loop mirror

NASA Astrophysics Data System (ADS)

Pitois, Stéphane

2005-09-01

We study the role of cross-phase modulation (CPM) occurring between the two counter-propagating parts of a signal wave in a standard SPM-based nonlinear optical fiber loop mirror (NOLM). For pulse train with high duty-cycle, we experimentally observe the influence of cross-phase modulation on NOLM transmittivity. Finally, we propose a solution based on properly designed dispersion imbalanced NOLM to overcome undesirable CPM effects.

BRIEF COMMUNICATIONS: Dynamics of lasing of two TEA CO2 lasers coupled by a nonlinear SF6 cell

NASA Astrophysics Data System (ADS)

Baranov, V. Yu; Dyad'kin, A. P.; Shpilyun, O. V.

1991-10-01

A study was made of the kinetics of stimulated emission from two TEA CO2 lasers in a system with frequency locking by phase conjugation as a result of a four-wave interaction of light [V. Yu. Baranov, A. P. Dyad'kin, V. V. Likhanskiĭ et al., Sov. J. Quantum Electron. 18, 1462 (1988)]. A simple method for ensuring two-pulse lasing with a variable time delay between the pulses in one gas-discharge chamber was proposed.

Nonlinear-optical properties of thick composite media with vanadium dioxide nanoparticles. II. Self-focusing of mid-IR radiation

NASA Astrophysics Data System (ADS)

Vinogradova, O. P.; Ostrosablina, A. A.; Sidorov, A. I.

2006-02-01

This paper presents the experimental and theoretical results of a study of the interaction of pulsed laser radiation with thick composite media containing nanoparticles of vanadium dioxide (VO2). It is established that the reversible semiconductor-metal phase transition that occurs in the VO2 nanoparticles under the action of radiation can produce self-focusing of the mid-IR radiation by the formation of a photoinduced dynamic lens. An analysis is carried out of how the radiation intensity affects the dynamics of the given process.

Supercontinuum generation in silicon waveguides relying on wave-breaking.

PubMed

Castelló-Lurbe, David; Silvestre, Enrique

2015-10-05

Four-wave-mixing processes enabled during optical wave-breaking (OWB) are exploited in this paper for supercontinuum generation. Unlike conventional approaches based on OWB, phase-matching is achieved here for these nonlinear interactions, and, consequently, new frequency production becomes more efficient. We take advantage of this kind of pulse propagation to obtain numerically a coherent octave-spanning mid-infrared supercontinuum generation in a silicon waveguide pumping at telecom wavelengths in the normal dispersion regime. This scheme shows a feasible path to overcome limits imposed by two-photon absorption on spectral broadening in silicon waveguides.

Continuous-Variable Triple-Photon States Quantum Entanglement

NASA Astrophysics Data System (ADS)

González, E. A. Rojas; Borne, A.; Boulanger, B.; Levenson, J. A.; Bencheikh, K.

2018-01-01

We investigate the quantum entanglement of the three modes associated with the three-photon states obtained by triple-photon generation in a phase-matched third-order nonlinear optical interaction. Although the second-order processes have been extensively dealt with, there is no direct analogy between the second and third-order mechanisms. We show, for example, the absence of quantum entanglement between the quadratures of the three modes in the case of spontaneous parametric triple-photon generation. However, we show robust, seeding-dependent, genuine triple-photon entanglement in the fully seeded case.

The Nernst effect in layered superconductors under a magnetic field

NASA Astrophysics Data System (ADS)

Tinh, Bui Duc; Thu, Le Minh; Hoc, Nguyen Quang

2016-08-01

We calculated the Nernst signal eN, describing the Nernst effect in type-II superconductor in the vortex-liquid regime, by using the time-dependent Ginzburg-Landau (TDGL) equation with thermal noise. The nonlinear interaction term in the TDGL equation is treated within self-consistent Gaussian approximation. The expression of the Nernst signal eN including all the Landau levels is presented in explicit form which is applicable essentially to the whole phase. Our results are compared with the recent experimental data on high-Tc superconductor.

Analysis of Synchronization Phenomena in Broadband Signals with Nonlinear Excitable Media

NASA Astrophysics Data System (ADS)

Chernihovskyi, Anton; Elger, Christian E.; Lehnertz, Klaus

2009-12-01

We apply the method of frequency-selective excitation waves in excitable media to characterize synchronization phenomena in interacting complex dynamical systems by measuring coincidence rates of induced excitations. We relax the frequency-selectivity of excitable media and demonstrate two applications of the method to signals with broadband spectra. Findings obtained from analyzing time series of coupled chaotic oscillators as well as electroencephalographic (EEG) recordings from an epilepsy patient indicate that this method can provide an alternative and complementary way to estimate the degree of phase synchronization in noisy signals.

Focusing of Finite-Amplitude Cylindrical and Spherical Sound Waves in a Viscous and Heat-Conducting Medium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chu, T.

1971-01-01

The focusing of acoustic pulses is studied analytically by considering the region of study in three parts: the converging, interaction and diverging regions. First, the linear problem of a pulse of infinitesimal amplitude is studied. For the spherical case, the expected phase change as a result of focusing is verified. The nonlinear case of finite-amplitude pulses leads to the development of M-waves, as determined by applying the method of matched-asymptotic expansions to Burges equation.

Continuous-Variable Triple-Photon States Quantum Entanglement.

PubMed

González, E A Rojas; Borne, A; Boulanger, B; Levenson, J A; Bencheikh, K

2018-01-26

We investigate the quantum entanglement of the three modes associated with the three-photon states obtained by triple-photon generation in a phase-matched third-order nonlinear optical interaction. Although the second-order processes have been extensively dealt with, there is no direct analogy between the second and third-order mechanisms. We show, for example, the absence of quantum entanglement between the quadratures of the three modes in the case of spontaneous parametric triple-photon generation. However, we show robust, seeding-dependent, genuine triple-photon entanglement in the fully seeded case.

Creation of long-term coherent optical memory via controlled nonlinear interactions in Bose-Einstein condensates.

PubMed

Zhang, Rui; Garner, Sean R; Hau, Lene Vestergaard

2009-12-04

A Bose-Einstein condensate confined in an optical dipole trap is used to generate long-term coherent memory for light, and storage times of more than 1 s are observed. Phase coherence of the condensate as well as controlled manipulations of elastic and inelastic atomic scattering processes are utilized to increase the storage fidelity by several orders of magnitude over previous schemes. The results have important applications for creation of long-distance quantum networks and for generation of entangled states of light and matter.

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

NASA Astrophysics Data System (ADS)

Biria, Saeid; Morim, Derek R.; An Tsao, Fu; Saravanamuttu, Kalaichelvi; Hosein, Ian D.

2017-10-01

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

Supercontinuum generation in quadratic nonlinear waveguides without quasi-phase matching.

PubMed

Guo, Hairun; Zhou, Binbin; Steinert, Michael; Setzpfandt, Frank; Pertsch, Thomas; Chung, Hung-ping; Chen, Yen-Hung; Bache, Morten

2015-02-15

Supercontinuum generation (SCG) is most efficient when the solitons can be excited directly at the pump laser wavelength. Quadratic nonlinear waveguides may induce an effective negative Kerr nonlinearity, so temporal solitons can be directly generated in the normal (positive) dispersion regime overlapping with common ultrafast laser wavelengths. There is no need for waveguide dispersion engineering. Here, we experimentally demonstrate SCG in standard lithium niobate (LN) waveguides without quasi-phase matching (QPM), pumped with femtosecond pulses in the normal dispersion regime. The observed large bandwidths (even octave spanning), together with other experimental data, indicate that negative nonlinearity solitons are indeed excited, which is backed up by numerical simulations. The QPM-free design reduces production complexity, extends the maximum waveguide length, and limits undesired spectral resonances. Finally, nonlinear crystals can be used where QPM is inefficient or impossible, which is important for mid-IR SCG. QPM-free waveguides in mid-IR nonlinear crystals can support negative nonlinearity solitons, as these waveguides have a normal dispersion at the emission wavelengths of mid-IR ultrafast lasers.

Membrane hydrophone phase characteristics through nonlinear acoustics measurements.

PubMed

Bloomfield, Philip E; Gandhi, Gaurav; Lewin, Peter A

2011-11-01

This work considers the need for both the amplitude and phase to fully characterize polyvinylidene fluoride (PVDF) membrane hydrophones and presents a comprehensive discussion of the nonlinear acoustic measurements utilized to extract the phase information and the experimental results taken with two widely used PVDF membrane hydrophones up to 100 MHz. A semi-empirical computer model utilized the hyperbolic propagation operator to predict the nonlinear pressure field and provide the complex frequency response of the corresponding source transducer. The PVDF hydrophone phase characteristics, which were obtained directly from the difference between the computer-modeled nonlinear field simulation and the corresponding measured harmonic frequency phase values, agree to within 10% with the phase predictions obtained from receive-transfer-function simulations based on software modeling of the membrane's physical properties. Cable loading effects and membrane hydrophone resonances were distinguished and identified through a series of impedance measurements and receive transfer function simulations on the hydrophones including their hard-wired coaxial cables. The results obtained indicate that the PVDF membrane hydrophone's phase versus frequency plot exhibits oscillations about a monotonically decreasing line. The maxima and minima inflection point slopes occur at the membrane thickness resonances and antiresonances, respectively. A cable resonance was seen at 100 MHz for the hydrophone with a 1-m cable attached, but not seen for the hydrophone with a shorter 0.65-m cable.

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.

Nonlinear dielectric properties of planar structures based on ferroelectric betaine phosphite films

NASA Astrophysics Data System (ADS)

Balashova, E. V.; Krichevtsov, B. B.; Svinarev, F. B.; Yurko, E. I.

2014-02-01

Ferroelectric films of partly deuterated betaine phosphite are grown on NdGaO3(001) substrates with an interdigitated system of electrodes on their surfaces by evaporation at room temperature. These films have a high capacitance in the ferroelectric phase transition range. The dielectric nonlinearity of the grown structures is studied in small-signal and strong-signal response modes and in the intermediate region between these two modes by measuring the capacitance in a dc bias field, dielectric hysteresis loops, and the Fourier spectra of an output signal in the Sawyer-Tower circuit. In the phase transition range, the capacitance control ratio at a bias voltage U bias = 40 V is K ≅ 7. The dielectric nonlinearity of the structures in the paraelectric phase is described by the Landau theory of second-order phase transitions. The additional contribution to the nonlinearity in the ferroelectric phase is related to the motion of domain walls and manifests itself when the input signal amplitude is higher than U st ˜ 0.7-1.0 V. The relaxation times of domain walls are determined from an analysis of the frequency dependences of the dielectric hysteresis.

Comparison between measured and predicted turbulence frequency spectra in ITG and TEM regimes

NASA Astrophysics Data System (ADS)

Citrin, J.; Arnichand, H.; Bernardo, J.; Bourdelle, C.; Garbet, X.; Jenko, F.; Hacquin, S.; Pueschel, M. J.; Sabot, R.

2017-06-01

The observation of distinct peaks in tokamak core reflectometry measurements—named quasi-coherent-modes (QCMs)—are identified as a signature of trapped-electron-mode (TEM) turbulence (Arnichand et al 2016 Plasma Phys. Control. Fusion 58 014037). This phenomenon is investigated with detailed linear and nonlinear gyrokinetic simulations using the Gene code. A Tore-Supra density scan is studied, which traverses through a linear (LOC) to saturated (SOC) ohmic confinement transition. The LOC and SOC phases are both simulated separately. In the LOC phase, where QCMs are observed, TEMs are robustly predicted unstable in linear studies. In the later SOC phase, where QCMs are no longer observed, ion-temperature-gradient (ITG) modes are identified. In nonlinear simulations, in the ITG (SOC) phase, a broadband spectrum is seen. In the TEM (LOC) phase, a clear emergence of a peak at the TEM frequencies is seen. This is due to reduced nonlinear frequency broadening of the underlying linear modes in the TEM regime compared with the ITG regime. A synthetic diagnostic of the nonlinearly simulated frequency spectra reproduces the features observed in the reflectometry measurements. These results support the identification of core QCMs as an experimental marker for TEM turbulence.

Active muscle response using feedback control of a finite element human arm model.

PubMed

Östh, Jonas; Brolin, Karin; Happee, Riender

2012-01-01

Mathematical human body models (HBMs) are important research tools that are used to study the human response in car crash situations. Development of automotive safety systems requires the implementation of active muscle response in HBM, as novel safety systems also interact with vehicle occupants in the pre-crash phase. In this study, active muscle response was implemented using feedback control of a nonlinear muscle model in the right upper extremity of a finite element (FE) HBM. Hill-type line muscle elements were added, and the active and passive properties were assessed. Volunteer tests with low impact loading resulting in elbow flexion motions were performed. Simulations of posture maintenance in a gravity field and the volunteer tests were successfully conducted. It was concluded that feedback control of a nonlinear musculoskeletal model can be used to obtain posture maintenance and human-like reflexive responses in an FE HBM.

Nonlinear stress waves in a perfectly flexible string. [for aerodynamic decelerating system

NASA Technical Reports Server (NTRS)

Fan, D.-N.; Mcgarvey, J. F.

1977-01-01

This paper discusses nonlinear stress-wave propagation in a perfectly flexible string obeying a quasilinear (rate-dependent) constitutive equation. Wave speeds and compatibility relations valid along various families of characteristics were determined. It was shown that the compatibility relations associated with the transverse as well as the longitudinal waves readily yield a physical interpretation when they are expressed in suitable variables and in vector form. Coding based on the present information was completed for the machine solution of a class of mixed initial- and boundary-value problems of practical interest. Computer simulation of the stress-wave interaction in the 40-foot lanyard in the Arcas 'Rocoz' system during deployment was carried out using a stress-strain relation for nylon at the strain rate of 30/second. A method for estimating the maximum tension and strain in a string during the initial loading phase is proposed.

Phase properties of elastic waves in systems constituted of adsorbed diatomic molecules on the (001) surface of a simple cubic crystal

NASA Astrophysics Data System (ADS)

Deymier, P. A.; Runge, K.

2018-03-01

A Green's function-based numerical method is developed to calculate the phase of scattered elastic waves in a harmonic model of diatomic molecules adsorbed on the (001) surface of a simple cubic crystal. The phase properties of scattered waves depend on the configuration of the molecules. The configurations of adsorbed molecules on the crystal surface such as parallel chain-like arrays coupled via kinks are used to demonstrate not only linear but also non-linear dependency of the phase on the number of kinks along the chains. Non-linear behavior arises for scattered waves with frequencies in the vicinity of a diatomic molecule resonance. In the non-linear regime, the variation in phase with the number of kinks is formulated mathematically as unitary matrix operations leading to an analogy between phase-based elastic unitary operations and quantum gates. The advantage of elastic based unitary operations is that they are easily realizable physically and measurable.

Effect of polydispersity, bimodality, and aspect ratio on the phase behavior of colloidal platelet suspensions

NASA Astrophysics Data System (ADS)

Martínez-Ratón, Yuri; Velasco, Enrique

2012-10-01

We use a fundamental-measure density functional for hard board-like polydisperse particles, in the restricted-orientation approximation, to explain the phase behaviour of platelet colloidal suspensions studied in recent experiments. In particular, we focus our attention on the behavior of the total packing fraction of the mixture, η, in the region of two-phase isotropic-nematic coexistence as a function of mean aspect ratio, polydispersity, and fraction of total volume γ occupied by the nematic phase. In our model, platelets are polydisperse in the square section, of side length σ, but have constant thickness L (and aspect ratio κ ≡ L/⟨σ⟩ < 1, with ⟨σ⟩ the mean side length). Good agreement between our theory and recent experiments is obtained by mapping the real system onto an effective one, with excluded volume interactions but with thicker particles (due to the presence of long-ranged repulsive interactions between platelets). The effect of polydispersity in both shape and particle size has been taken into account by using a size distribution function with an effective mean-square deviation that depends on both polydispersities. We also show that the bimodality of the size distribution function is required to correctly describe the huge two-phase coexistence gap and the nonlinearity of the function γ(η), two important features that these colloidal suspensions exhibit.

Evaluation of interaction dynamics of concurrent processes

NASA Astrophysics Data System (ADS)

Sobecki, Piotr; Białasiewicz, Jan T.; Gross, Nicholas

2017-03-01

The purpose of this paper is to present the wavelet tools that enable the detection of temporal interactions of concurrent processes. In particular, the determination of interaction coherence of time-varying signals is achieved using a complex continuous wavelet transform. This paper has used electrocardiogram (ECG) and seismocardiogram (SCG) data set to show multiple continuous wavelet analysis techniques based on Morlet wavelet transform. MATLAB Graphical User Interface (GUI), developed in the reported research to assist in quick and simple data analysis, is presented. These software tools can discover the interaction dynamics of time-varying signals, hence they can reveal their correlation in phase and amplitude, as well as their non-linear interconnections. The user-friendly MATLAB GUI enables effective use of the developed software what enables to load two processes under investigation, make choice of the required processing parameters, and then perform the analysis. The software developed is a useful tool for researchers who have a need for investigation of interaction dynamics of concurrent processes.

Generation of Caustics and Rogue Waves from Nonlinear Instability.

PubMed

Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W

2017-11-17

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Generation of Caustics and Rogue Waves from Nonlinear Instability

NASA Astrophysics Data System (ADS)

Safari, Akbar; Fickler, Robert; Padgett, Miles J.; Boyd, Robert W.

2017-11-01

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.