A Web Tool for Research in Nonlinear Optics

NASA Astrophysics Data System (ADS)

Prikhod'ko, Nikolay V.; Abramovsky, Viktor A.; Abramovskaya, Natalia V.; Demichev, Andrey P.; Kryukov, Alexandr P.; Polyakov, Stanislav P.

2016-02-01

This paper presents a project of developing the web platform called WebNLO for computer modeling of nonlinear optics phenomena. We discuss a general scheme of the platform and a model for interaction between the platform modules. The platform is built as a set of interacting RESTful web services (SaaS approach). Users can interact with the platform through a web browser or command line interface. Such a resource has no analogues in the field of nonlinear optics and will be created for the first time therefore allowing researchers to access high-performance computing resources that will significantly reduce the cost of the research and development process.

Time-Domain Finite Element Analysis of Nonlinear Breakdown Problems in High-Power-Microwave Devices and Systems

DTIC Science & Technology

2015-12-24

simulation of the electromagnetic- plasma interaction and the high-power microwave breakdown in air. Under the high pressure and high frequency condition of...the high-power air breakdown, the physical phenomenon is described using a nonlinearly coupled full-wave Maxwell and fluid plasma system. This...Challenges ........................................................................... 3 3.1.1 Plasma Fluid Model

Development and Breakdown of Goertler Vortices in High Speed Boundary Layers

NASA Technical Reports Server (NTRS)

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

2010-01-01

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

Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating

NASA Astrophysics Data System (ADS)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume

2018-03-01

The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.

Extreme Nonlinear Optics of High Intensity Laser Pulse Filamentation in Gases

DTIC Science & Technology

2016-05-12

of energy from femtosecond filaments. Published * absolute measurements of electronic, vibrational, and rotational nonlinear response in H2 and D2 ...coefficients in the fastest rotating molecules H2 and D2 , which can serve as a benchmark for theory of high field molecule interactions. One of the...17. Absolute measurement of the ultrafast nonlinear electronic and rovibrational response in H2 and D2 J. K. Wahlstrand, S. Zahedpour, Y.-H

Relativistic laser-plasma interactions in the quantum regime.

PubMed

Eliasson, Bengt; Shukla, P K

2011-04-01

We consider nonlinear interactions between a relativistically strong laser beam and a plasma in the quantum regime. The collective behavior of electrons is modeled by a Klein-Gordon equation, which is nonlinearly coupled with the electromagnetic wave through the Maxwell and Poisson equations. This allows us to study nonlinear interactions between arbitrarily large-amplitude electromagnetic waves and a quantum plasma. We have used our system of nonlinear equations to study theoretically the parametric instabilities involving stimulated Raman scattering and modulational instabilities. A model for quasi-steady-state propagating electromagnetic wave packets is also derived, and which shows possibility of localized solitary structures in a quantum plasma. Numerical simulations demonstrate collapse and acceleration of electrons in the nonlinear stage of the modulational instability, as well as possibility of the wake-field acceleration of electrons to relativistic speeds by short laser pulses at nanometer length scales. Our study is relevant for understanding the localization of intense electromagnetic pulses in a quantum plasma with extremely high electron densities and relatively low temperature.

Single-photon nonlinearities in the propagation of focused beams through dense atomic clouds

NASA Astrophysics Data System (ADS)

Wang, Yidan; Gorshkov, Alexey; Gullans, Michael

2017-04-01

We theoretically study single-photon nonlinearities realized when a highly focused Gaussian beam passes through a dense atomic cloud. In this system, strong dipole-dipole interactions arise between closely spaced atoms and significantly affect light propagation. We find that the highly focused Gaussian beam can be treated as an effective one-dimensional waveguide, which simplifies the calculation of photon transmission and correlation functions. The formalism we develop is also applicable to the case where additional atom-atom interactions, such as interactions between Rydberg atoms, are involved. This work was supported by the ARL, NSF PFC at the JQI, AFOSR, NSF PIF, ARO, and AFOSR MURI.

Comparing Numerical Spall Simulations with a Nonlinear Spall Formation Model

NASA Astrophysics Data System (ADS)

Ong, L.; Melosh, H. J.

2012-12-01

Spallation accelerates lightly shocked ejecta fragments to speeds that can exceed the escape velocity of the parent body. We present high-resolution simulations of nonlinear shock interactions in the near surface. Initial results show the acceleration of near-surface material to velocities up to 1.8 times greater than the peak particle velocity in the detached shock, while experiencing little to no shock pressure. These simulations suggest a possible nonlinear spallation mechanism to produce the high-velocity, low show pressure meteorites from other planets. Here we pre-sent the numerical simulations that test the production of spall through nonlinear shock interactions in the near sur-face, and compare the results with a model proposed by Kamegai (1986 Lawrence Livermore National Laboratory Report). We simulate near-surface shock interactions using the SALES_2 hydrocode and the Murnaghan equation of state. We model the shock interactions in two geometries: rectangular and spherical. In the rectangular case, we model a planar shock approaching the surface at a constant angle phi. In the spherical case, the shock originates at a point below the surface of the domain and radiates spherically from that point. The angle of the shock front with the surface is dependent on the radial distance of the surface point from the shock origin. We model the target as a solid with a nonlinear Murnaghan equation of state. This idealized equation of state supports nonlinear shocks but is tem-perature independent. We track the maximum pressure and maximum velocity attained in every cell in our simula-tions and compare them to the Hugoniot equations that describe the material conditions in front of and behind the shock. Our simulations demonstrate that nonlinear shock interactions in the near surface produce lightly shocked high-velocity material for both planar and cylindrical shocks. The spall is the result of the free surface boundary condi-tion, which forces a pressure gradient from the peak shock pressure to the zero pressure boundary. The nonlinear shock interactions occur where the pressure contours curve to accommodate the free surface. The material within this spall zone is ejected at speeds up to 1.8 km s-1 for an imposed pulse of 1 km s-1. Where the ejection velocities are highest, the maximum pressure attained in each cell is effectively zero. We compare our simulation results with a model for nonlinear shock interactions proposed by Kamegai (1986). This model recognizes that the material behind the shock is compressed and has a higher soundspeed than the mate-rial in front of the shock. As the rarefaction wave moves behind the shock, its increased velocity through the com-pressed material combines with the residual particle velocity behind the shock to "catch up" with the shock. This occurs in the near surface where the sum of the compressed sound speed and the residual particle velocity is greater than or equal to the shock velocity. Initial results for the spherical shocks qualitatively match the volume described by this model, but differ significantly in the quantitative slope of the curve defining the region of interaction. We continue to test the Kamegai model with high-resolution numerical simulations of shock interactions to determine its potential application to planetary spallation.

Problems in nonlinear acoustics: Pulsed finite amplitude sound beams, nonlinear acoustic wave propagation in a liquid layer, nonlinear effects in asymmetric cylindrical sound beams, effects of absorption on the interaction of sound beams, and parametric receiving arrays

NASA Astrophysics Data System (ADS)

Hamilton, Mark F.

1990-12-01

This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

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

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Perturbative and Ab-Initio Calculations of Electrical Susceptibilities of Atoms

NASA Astrophysics Data System (ADS)

Spott, Andrew

Perturbative nonlinear optics consists of many powerful predictive theoretical methods, including the perturbative series of observables related to the interaction of light with matter. The light intensity limits of such series have been studied in the past for highly nonlinear processes such as above threshold ionization and high harmonic generation. A more recent debate focuses on the limits of applicability of perturbation theory for the nonlinear electrical susceptibility and the nonlinear index of refraction of atoms, which are important parameters to study, for example, for filamentation of laser pulses in nonlinear media. In this thesis we analyze theoretical predictions for the electrical susceptibility of atoms for the transition from the perturbative to the nonperturbative intensity regime. To this end, we apply a numerical basis state method that allows us to perform respective calculations in the framework of perturbation theory as well as using ab-initio methods. The results let us identify the intensity at which the application of perturbation theory breaks down. Furthermore, we provide an analysis of the nonlinear susceptibility as a function of time during the interaction with the laser pulse and find that theoretical predictions are in good agreement with recent experimental data.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Nonlinearly stacked low noise turbofan stator

NASA Technical Reports Server (NTRS)

Schuster, William B. (Inventor); Nolcheff, Nick A. (Inventor); Gunaraj, John A. (Inventor); Kontos, Karen B. (Inventor); Weir, Donald S. (Inventor)

2009-01-01

A nonlinearly stacked low noise turbofan stator vane having a characteristic curve that is characterized by a nonlinear sweep and a nonlinear lean is provided. The stator is in an axial fan or compressor turbomachinery stage that is comprised of a collection of vanes whose highly three-dimensional shape is selected to reduce rotor-stator and rotor-strut interaction noise while maintaining the aerodynamic and mechanical performance of the vane. The nonlinearly stacked low noise turbofan stator vane reduces noise associated with the fan stage of turbomachinery to improve environmental compatibility.

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.)

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.

Temperature Induced Syllable Breaking Unveils Nonlinearly Interacting Timescales in Birdsong Motor Pathway

PubMed Central

Goldin, Matías A.; Alonso, Leandro M.; Alliende, Jorge A.; Goller, Franz; Mindlin, Gabriel B.

2013-01-01

The nature of telencephalic control over premotor and motor circuits is debated. Hypotheses range from complete usurping of downstream circuitry to highly interactive mechanisms of control. We show theoretically and experimentally, that telencephalic song motor control in canaries is consistent with a highly interactive strategy. As predicted from a theoretical model of respiratory control, mild cooling of a forebrain nucleus (HVC) led to song stretching, but further cooling caused progressive restructuring of song, consistent with the hypothesis that respiratory gestures are subharmonic responses to a timescale present in the output of HVC. This interaction between a life-sustaining motor function (respiration) and telencephalic song motor control suggests a more general mechanism of how nonlinear integration of evolutionarily new brain structures into existing circuitry gives rise to diverse, new behavior. PMID:23818988

Temperature induced syllable breaking unveils nonlinearly interacting timescales in birdsong motor pathway.

PubMed

Goldin, Matías A; Alonso, Leandro M; Alliende, Jorge A; Goller, Franz; Mindlin, Gabriel B

2013-01-01

The nature of telencephalic control over premotor and motor circuits is debated. Hypotheses range from complete usurping of downstream circuitry to highly interactive mechanisms of control. We show theoretically and experimentally, that telencephalic song motor control in canaries is consistent with a highly interactive strategy. As predicted from a theoretical model of respiratory control, mild cooling of a forebrain nucleus (HVC) led to song stretching, but further cooling caused progressive restructuring of song, consistent with the hypothesis that respiratory gestures are subharmonic responses to a timescale present in the output of HVC. This interaction between a life-sustaining motor function (respiration) and telencephalic song motor control suggests a more general mechanism of how nonlinear integration of evolutionarily new brain structures into existing circuitry gives rise to diverse, new behavior.

Experimental observation of multi-scale interactions among kink /tearing modes and high-frequency fluctuations in the HL-2A core NBI plasmas

NASA Astrophysics Data System (ADS)

Chen, W.; Jiang, M.; Xu, Y.; Shi, P. W.; Yu, L. M.; Ding, X. T.; Shi, Z. B.; Ji, X. Q.; Yu, D. L.; Li, Y. G.; Yang, Z. C.; Zhong, W. L.; Qiu, Z. Y.; Li, J. Q.; Dong, J. Q.; Yang, Q. W.; Liu, Yi.; Yan, L. W.; Xu, M.; Duan, X. R.

2017-11-01

Multi-scale interactions have been observed recently in the HL-2A core NBI plasmas, including the synchronous coupling between m/n=1/1 kink mode and m/n=2/1 tearing mode, nonlinear couplings of TAE/BAE and m/n=2/1 TM near q=2 surface, AITG/KBM/BAE and m/n=1/1 kink mode near q=1 surface, and between m/n=1/1 kink mode and high-frequency turbulence. Experimental results suggest that several couplings can exist simultaneously, Alfvenic fluctuations have an important contribution to the high-frequency turbulence spectra, and the couplings reveal the electromagnetic character. Multi-scale interactions via the nonlinear modulation process maybe enhance plasma transport and trigger sawtooth-crash onset.

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.

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

Study of large nonlinear change phase in Hibiscus Sabdariffa

NASA Astrophysics Data System (ADS)

Trejo-Durán, M.; Alvarado-Méndez, E.; Andrade-Lucio, J. A.; Rojas-Laguna, R.; Vázquez-Guevara, M. A.

2015-09-01

High intensities electromagnetic energy interacting with organic media gives rise to nonlinear optical effects. Hibiscus Sabdariffa is a flower whose concentrated solution presents interesting nonlinear optical properties. This organic material shows an important self-phase modulation with changes bigger than 2π. We present a diffraction ring patterns study of the Hibiscus Sabdariffa solution. Numerical results of transmittance, with refraction and simultaneous absorption, are shown.

Adaptive wavefront shaping for controlling nonlinear multimode interactions in optical fibres

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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.

Jet formation at the interaction of localized waves on the free surface of dielectric liquid in a tangential electric field

NASA Astrophysics Data System (ADS)

Kochurin, E. A.; Zubarev, N. M.

2018-01-01

Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid into a strip, the process of interaction of counter-propagating waves is numerically simulated. The nonlinear solitary waves on the surface can separately propagate along or against the direction of electric field without distortion. At the same time, the shape of the oppositely traveling waves can be distorted as the result of their interaction. In the problem under study, the nonlinearity leads to increasing the wave amplitudes and the duration of their interaction. This effect is inversely proportional to the fluid depth. In the shallow water limit, the tendency to the formation of a vertical liquid jet is observed.

Engineering high-order nonlinear dissipation for quantum superconducting circuits

NASA Astrophysics Data System (ADS)

Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

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.

Enhancing light-atom interactions via atomic bunching

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie L.; Gauthier, Daniel J.

2014-07-01

There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here we show theoretically that sub-Doppler-cooled two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonance saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all regimes of atomic bunching and simultaneously accounts for the backaction of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only limited regimes of atomic bunching. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices.

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.

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.

Periodic nonlinear waves resulting from the contact interaction of a crack

NASA Astrophysics Data System (ADS)

Lee, Sang Eon; Jin, Suyeong; Hong, Jung-Wuk

2017-09-01

When two different inputs of distinct low and high frequencies are applied to a medium, the linear responses are composed of waves of two dominant frequencies. However, microcracks such as fatigue cracks generate nonlinear waves by modulating the characteristics of the incident waves. Although this phenomenon has been observed and used to detect microcracks, the underlying principles have not been thoroughly elucidated. The hysteresis properties were introduced to describe the nonlinear relationship between the stress and strain to explain these phenomena [Van Den Abeele et al., Res. Nondestruct. Eval. 12, 17 (2000) and Nazarov et al., Acoust. Phys. 49, 344 (2003)]. The generation of harmonics was explained by superimposing stress-strain relations that vary with crack width and excitation magnitude. As the crack depth increases, the ratio of magnitudes of the second harmonic to the first harmonic increases, but the increment becomes smaller [Kawashima et al., Ultrasonics 40, 611 (2002)]. Here, we show that the waves affected by the contact motion of the crack surfaces cultivate the nonlinearity in waveforms, resulting in high frequency off-band signals. With the hypothesis that the clapping of cracks might generate nonlinear components close to the high excitation frequency, we prove that the generation of the high frequency off-band peaks is directly affected by the clapping contact interaction of the crack surfaces. The amount of energy transmitted is closely related to the size of the crack width and the magnitudes of low and high frequency excitations.

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Nonlinear acoustic spectroscopy of cracked flaws and disbonds: Fundamentals, techniques, and applications

NASA Astrophysics Data System (ADS)

Maev, R. Gr.; Solodov, I. Yu.

2000-05-01

Classical nonlinear acoustics of solids operates with distributed material nonlinearity related to unharmonicity of molecular interaction forces. Weakening of molecular bonds in a defect area or intermittent lack of elastic coupling between the faces of a vibrating crack or unbond ("clapping") results in anomalously high local contact acoustic nonlinearity (CAN). CAN properties and spectral features are different from those of the classical analog and important to develop new acoustic NDE techniques. Three approaches to nonlinear NDE methodology have been experimentally verified: low-frequency (hundreds of Hz) vibration technique, intermediate-frequency (hundreds of kHz) standing wave and high-frequency (tens of MHz) propagation modes. Low-frequency nonlinear contact vibrations revealed multiple sub- and super-harmonics generation featuring non-monotonous (sinx/x type) spectra. Parametric instability observed in resonator with a nonlinear contact leads to the output spectrum splitting up into successive sub-harmonics as the wave amplitude increases. High-frequency experiments demonstrated abnormal increases in the third harmonic amplitude: 3 or 4 order enhancement of the 3-ω nonlinear parameter was measured for the nonlinear contact. The CAN spectral features in both acoustic and vibration modes were used for nonlinear NDE of simulated and realistic flaws in glass, metal welds, etc. The sensitivities of the techniques are compared and their practical applicability assessed.

Nonlinear plasmonic imaging techniques and their biological applications

NASA Astrophysics Data System (ADS)

Deka, Gitanjal; Sun, Chi-Kuang; Fujita, Katsumasa; Chu, Shi-Wei

2017-01-01

Nonlinear optics, when combined with microscopy, is known to provide advantages including novel contrast, deep tissue observation, and minimal invasiveness. In addition, special nonlinearities, such as switch on/off and saturation, can enhance the spatial resolution below the diffraction limit, revolutionizing the field of optical microscopy. These nonlinear imaging techniques are extremely useful for biological studies on various scales from molecules to cells to tissues. Nevertheless, in most cases, nonlinear optical interaction requires strong illumination, typically at least gigawatts per square centimeter intensity. Such strong illumination can cause significant phototoxicity or even photodamage to fragile biological samples. Therefore, it is highly desirable to find mechanisms that allow the reduction of illumination intensity. Surface plasmon, which is the collective oscillation of electrons in metal under light excitation, is capable of significantly enhancing the local field around the metal nanostructures and thus boosting up the efficiency of nonlinear optical interactions of the surrounding materials or of the metal itself. In this mini-review, we discuss the recent progress of plasmonics in nonlinear optical microscopy with a special focus on biological applications. The advancement of nonlinear imaging modalities (including incoherent/coherent Raman scattering, two/three-photon luminescence, and second/third harmonic generations that have been amalgamated with plasmonics), as well as the novel subdiffraction limit imaging techniques based on nonlinear behaviors of plasmonic scattering, is addressed.

Modelization of highly nonlinear waves in coastal regions

NASA Astrophysics Data System (ADS)

Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre

2015-04-01

The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.

Verification of nonlinear dynamic structural test results by combined image processing and acoustic analysis

NASA Astrophysics Data System (ADS)

Tene, Yair; Tene, Noam; Tene, G.

1993-08-01

An interactive data fusion methodology of video, audio, and nonlinear structural dynamic analysis for potential application in forensic engineering is presented. The methodology was developed and successfully demonstrated in the analysis of heavy transportable bridge collapse during preparation for testing. Multiple bridge elements failures were identified after the collapse, including fracture, cracks and rupture of high performance structural materials. Videotape recording by hand held camcorder was the only source of information about the collapse sequence. The interactive data fusion methodology resulted in extracting relevant information form the videotape and from dynamic nonlinear structural analysis, leading to full account of the sequence of events during the bridge collapse.

Stochastic Convection Parameterizations

NASA Technical Reports Server (NTRS)

Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios

2012-01-01

computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts

Nonlinear quantum Rabi model in trapped ions

NASA Astrophysics Data System (ADS)

Cheng, Xiao-Hang; Arrazola, Iñigo; Pedernales, Julen S.; Lamata, Lucas; Chen, Xi; Solano, Enrique

2018-02-01

We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a blockade on the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We propose to use this blockade as a resource for the dissipative generation of high-number Fock states. Also, we compare the linear and nonlinear cases of the quantum Rabi model in the ultrastrong and deep strong-coupling regimes. Moreover, we propose a scheme to simulate the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red- and blue-sideband interactions in a single trapped ion, yielding applications as a dynamical quantum filter.

The dissipation of electromagnetic waves in plasmas

NASA Astrophysics Data System (ADS)

Basov, N. G.

The present anthology includes articles concerning the experimental study of the interaction of high power electromagnetic waves with collisionless plasmas and with electrons. Among the topics covered are the nonlinear dissipation of electromagnetic waves in inhomogeneous collisionless plasmas, the collisionless absorption of electromagnetic waves in plasmas and 'slow' nonlinear phenomena, the nonlinear effects of electron plasma waves propagating in an inhomogeneous plasma layer, and secondary-emission microwave discharges having large electron transit angles.

Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points

NASA Astrophysics Data System (ADS)

Choi, Youngsun; Hahn, Choloong; Yoon, Jae Woong; Song, Seok Ho; Berini, Pierre

2017-01-01

Time-asymmetric state-evolution properties while encircling an exceptional point are presently of great interest in search of new principles for controlling atomic and optical systems. Here, we show that encircling-an-exceptional-point interactions that are essentially reciprocal in the linear interaction regime make a plausible nonlinear integrated optical device architecture highly nonreciprocal over an extremely broad spectrum. In the proposed strategy, we describe an experimentally realizable coupled-waveguide structure that supports an encircling-an-exceptional-point parametric evolution under the influence of a gain saturation nonlinearity. Using an intuitive time-dependent Hamiltonian and rigorous numerical computations, we demonstrate strictly nonreciprocal optical transmission with a forward-to-backward transmission ratio exceeding 10 dB and high forward transmission efficiency (~100%) persisting over an extremely broad bandwidth approaching 100 THz. This predicted performance strongly encourages experimental realization of the proposed concept to establish a practical on-chip optical nonreciprocal element for ultra-short laser pulses and broadband high-density optical signal processing.

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint

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

Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan

2016-01-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

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

Pacini, Benjamin Robert; Mayes, Randall L.; Roettgen, Daniel R

2015-10-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

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).

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.

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

PubMed

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

2012-10-12

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

Nonlinear threshold effect in the Z-scan method of characterizing limiters for high-intensity laser light

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

Tereshchenko, S. A., E-mail: tsa@miee.ru; Savelyev, M. S.; Podgaetsky, V. M.

A threshold model is described which permits one to determine the properties of limiters for high-powered laser light. It takes into account the threshold characteristics of the nonlinear optical interaction between the laser beam and the limiter working material. The traditional non-threshold model is a particular case of the threshold model when the limiting threshold is zero. The nonlinear characteristics of carbon nanotubes in liquid and solid media are obtained from experimental Z-scan data. Specifically, the nonlinear threshold effect was observed for aqueous dispersions of nanotubes, but not for nanotubes in solid polymethylmethacrylate. The threshold model fits the experimental Z-scanmore » data better than the non-threshold model. Output characteristics were obtained that integrally describe the nonlinear properties of the optical limiters.« less

Numerical investigation of nonlinear interactions between multimodal guided waves and delamination in composite structures

NASA Astrophysics Data System (ADS)

Shen, Yanfeng

2017-04-01

This paper presents a numerical investigation of the nonlinear interactions between multimodal guided waves and delamination in composite structures. The elastodynamic wave equations for anisotropic composite laminate were formulated using an explicit Local Interaction Simulation Approach (LISA). The contact dynamics was modeled using the penalty method. In order to capture the stick-slip contact motion, a Coulomb friction law was integrated into the computation procedure. A random gap function was defined for the contact pairs to model distributed initial closures or openings to approximate the nature of rough delamination interfaces. The LISA procedure was coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized computation on powerful graphic cards. Several guided wave modes centered at various frequencies were investigated as the incident wave. Numerical case studies of different delamination locations across the thickness were carried out. The capability of different wave modes at various frequencies to trigger the Contact Acoustic Nonlinearity (CAN) was studied. The correlation between the delamination size and the signal nonlinearity was also investigated. Furthermore, the influence from the roughness of the delamination interfaces was discussed as well. The numerical investigation shows that the nonlinear features of wave delamination interactions can enhance the evaluation capability of guided wave Structural Health Monitoring (SHM) system. This paper finishes with discussion, concluding remarks, and suggestions for future work.

Interaction of ultrashort laser pulses and silicon solar cells under short circuit conditions

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

Mundus, M., E-mail: markus.mundus@ise.fraunhofer.de; Giesecke, J. A.; Fischer, P.

Ultrashort pulse lasers are promising tools for numerous measurement purposes. Among other benefits their high peak powers allow for efficient generation of wavelengths in broad spectral ranges and at spectral powers that are orders of magnitude higher than in conventional light sources. Very recently this has been exploited for the establishment of sophisticated measurement facilities for electrical characterization of photovoltaic (PV) devices. As the high peak powers of ultrashort pulses promote nonlinear optical effects they might also give rise to nonlinear interactions with the devices under test that possibly manipulate the measurement outcome. In this paper, we present a comprehensivemore » theoretical and experimental study of the nonlinearities affecting short circuit current (I{sub SC}) measurements of silicon (Si) solar cells. We derive a set of coupled differential equations describing the radiation-device interaction and discuss the nonlinearities incorporated in those. By a semi-analytical approach introducing a quasi-steady-state approximation and integrating a Green's function we solve the system of equations and obtain simulated I{sub SC} values. We validate the theoretical model by I{sub SC} ratios obtained from a double ring resonator setup capable for reproducible generation of various ultrashort pulse trains. Finally, we apply the model to conduct the most prominent comparison of I{sub SC} generated by ultrashort pulses versus continuous illumination. We conclude by the important finding that the nonlinearities induced by ultrashort pulses are negligible for the most common I{sub SC} measurements. However, we also find that more specialized measurements (e.g., of concentrating PV or Si-multijunction devices as well as highly localized electrical characterizations) will be biased by two-photon-absorption distorting the I{sub SC} measurement.« less

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.

Modal analysis and nonlinear characterization of an airborne power ultrasonic transducer with rectangular plate radiator.

PubMed

Andrés, R R; Acosta, V M; Lucas, M; Riera, E

2018-01-01

Some industrial processes like particle agglomeration or food dehydration among others can be enhanced by the use of power ultrasonic technologies. These technologies are based on an airborne power ultrasonic transducer (APUT) constituted by a pre-stressed Langevin-type transducer, a mechanical amplifier and an extensive plate radiator. In order to produce the desired effects in industrial processing, the transducer has to vibrate in an extensional mode driving an extensive radiator in the desired flexural mode with high amplitude displacements. Due to the generation of these high amplitude displacements in the radiator surfaces, non-linear effects like frequency shifts, hysteresis or modal interactions, among others, may be produced in the transducer behavior. When any nonlinear effect appears, when applying power, the stability and efficiency of this ultrasonic technology decreases, and the transducer may be damaged depending on the excitation power level and the nature of the nonlinearity. In this paper, an APUT with flat rectangular radiator is presented, as the active part of an innovative system with stepped reflectors. The nonlinear behavior of the APUT has been characterized numerically and experimentally in case of the modal analysis and experimentally in the case of dynamic analysis. According to the results obtained after the experiments, no modal interactions are expected, nor do other nonlinear effects. Copyright © 2017 Elsevier B.V. All rights reserved.

A nonlinear high temperature fracture mechanics basis for strainrange partitioning

NASA Technical Reports Server (NTRS)

Kitamura, Takayuki; Halford, Gary R.

1989-01-01

A direct link was established between Strainrange Partitioning (SRP) and high temperature fracture mechanics by deriving the general SRP inelastic strain range versus cyclic life relationships from high temperature, nonlinear, fracture mechanics considerations. The derived SRP life relationships are in reasonable agreement based on the experience of the SRP behavior of many high temperature alloys. In addition, fracture mechanics has served as a basis for derivation of the Ductility-Normalized SRP life equations, as well as for examination of SRP relations that are applicable to thermal fatigue life prediction. Areas of additional links between nonlinear fracture mechanics and SRP were identified for future exploration. These include effects of multiaxiality as well as low strain, nominally elastic, long life creep fatigue interaction.

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

Nonlinear cavity optomechanics with nanomechanical thermal fluctuations

PubMed Central

Leijssen, Rick; La Gala, Giada R.; Freisem, Lars; Muhonen, Juha T.; Verhagen, Ewold

2017-01-01

Although the interaction between light and motion in cavity optomechanical systems is inherently nonlinear, experimental demonstrations to date have allowed a linearized description in all except highly driven cases. Here, we demonstrate a nanoscale optomechanical system in which the interaction between light and motion is so large (single-photon cooperativity C0≈103) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement and radiation pressure backaction. Specifically, we measure an apparent optical linewidth that is dominated by thermo-mechanically induced frequency fluctuations over a wide temperature range, and show that in this regime thermal displacement measurements cannot be described by conventional analytical models. We perform a proof-of-concept demonstration of exploiting the nonlinearity to conduct sensitive quadratic readout of nanomechanical displacement. Finally, we explore how backaction in this regime affects the mechanical fluctuation spectra. PMID:28685755

Giant Kerr response of ultrathin gold films from quantum size effect.

PubMed

Qian, Haoliang; Xiao, Yuzhe; Liu, Zhaowei

2016-10-10

With the size of plasmonic devices entering into the nanoscale region, the impact of quantum physics needs to be considered. In the past, the quantum size effect on linear material properties has been studied extensively. However, the nonlinear aspects have not been explored much so far. On the other hand, much effort has been put into the field of integrated nonlinear optics and a medium with large nonlinearity is desirable. Here we study the optical nonlinear properties of a nanometre scale gold quantum well by using the z-scan method and nonlinear spectrum broadening technique. The quantum size effect results in a giant optical Kerr susceptibility, which is four orders of magnitude higher than the intrinsic value of bulk gold and several orders larger than traditional nonlinear media. Such high nonlinearity enables efficient nonlinear interaction within a microscopic footprint, making quantum metallic films a promising candidate for integrated nonlinear optical applications.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.

Bayesian dynamical systems modelling in the social sciences.

PubMed

Ranganathan, Shyam; Spaiser, Viktoria; Mann, Richard P; Sumpter, David J T

2014-01-01

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

Nonlinear vibration of a coupled high- Tc superconducting levitation system

NASA Astrophysics Data System (ADS)

Sugiura, T.; Inoue, T.; Ura, H.

2004-10-01

High- Tc superconducting levitation can be applied to electro-mechanical systems, such as flywheel energy storage and linear-drive transportation. Such a system can be modeled as a magnetically coupled system of many permanent magnets and high- Tc superconducting bulks. It is a multi-degree-of-freedom dynamical system coupled by nonlinear interaction between levitated magnets and superconducting bulks. This nonlinearly coupled system, with small damping due to no contact support, can easily show complicated phenomena of nonlinear dynamics. In mechanical design, it is important to evaluate this nonlinear dynamics, though it has not been well studied so far. This research deals with forced vibration of a coupled superconducting levitation system. As a simple modeling of a coupled system, a permanent magnet levitated above a superconducting bulk is placed between two fixed permanent magnets without contact. Frequency response of the levitated magnet under excitation of one of the fixed magnets was examined theoretically. The results show typical nonlinear vibration, such as jump, hysteresis, and parametric resonance, which were confirmed in our numerical analyses and experiments.

A Computational and Experimental Study of Nonlinear Aspects of Induced Drag

NASA Technical Reports Server (NTRS)

Smith, Stephen C.

1996-01-01

Despite the 80-year history of classical wing theory, considerable research has recently been directed toward planform and wake effects on induced drag. Nonlinear interactions between the trailing wake and the wing offer the possibility of reducing drag. The nonlinear effect of compressibility on induced drag characteristics may also influence wing design. This thesis deals with the prediction of these nonlinear aspects of induced drag and ways to exploit them. A potential benefit of only a few percent of the drag represents a large fuel savings for the world's commercial transport fleet. Computational methods must be applied carefully to obtain accurate induced drag predictions. Trefftz-plane drag integration is far more reliable than surface pressure integration, but is very sensitive to the accuracy of the force-free wake model. The practical use of Trefftz plane drag integration was extended to transonic flow with the Tranair full-potential code. The induced drag characteristics of a typical transport wing were studied with Tranair, a full-potential method, and A502, a high-order linear panel method to investigate changes in lift distribution and span efficiency due to compressibility. Modeling the force-free wake is a nonlinear problem, even when the flow governing equation is linear. A novel method was developed for computing the force-free wake shape. This hybrid wake-relaxation scheme couples the well-behaved nature of the discrete vortex wake with viscous-core modeling and the high-accuracy velocity prediction of the high-order panel method. The hybrid scheme produced converged wake shapes that allowed accurate Trefftz-plane integration. An unusual split-tip wing concept was studied for exploiting nonlinear wake interaction to reduced induced drag. This design exhibits significant nonlinear interactions between the wing and wake that produced a 12% reduction in induced drag compared to an equivalent elliptical wing at a lift coefficient of 0.7. The performance of the split-tip wing was also investigated by wing tunnel experiments. Induced drag was determined from force measurements by subtracting the estimated viscous drag, and from an analytical drag-decomposition method using a wake survey. The experimental results confirm the computational prediction.

Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

NASA Astrophysics Data System (ADS)

Dutykh, Denys; Hoefer, Mark; Mitsotakis, Dimitrios

2018-04-01

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order 4.

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.

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

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.

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

Pitch glide effect induced by a nonlinear string-barrier interaction

NASA Astrophysics Data System (ADS)

Kartofelev, Dmitri; Stulov, Anatoli; Välimäki, Vesa

2015-10-01

Interactions of a vibrating string with its supports and other spatially distributed barriers play a significant role in the physics of many stringed musical instruments. It is well known that the tone of the string vibrations is determined by the string supports, and that the boundary conditions of the string termination may cause a short-lasting initial fundamental frequency shifting. Generally, this phenomenon is associated with the nonlinear modulation of the stiff string tension. The aim of this paper is to study the initial frequency glide phenomenon that is induced only by the string-barrier interaction, apart from other possible physical causes, and without the interfering effects of dissipation and dispersion. From a numerical simulation perspective, this highly nonlinear problem may present various difficulties, not the least of which is the risk of numerical instability. We propose a numerically stable and a purely kinematic model of the string-barrier interaction, which is based on the travelling wave solution of the ideal string vibration. The model is capable of reproducing the motion of the vibrating string exhibiting the initial fundamental frequency glide, which is caused solely by the complex nonlinear interaction of the string with its termination. The results presented in this paper can expand our knowledge and understanding of the timbre evolution and the physical principles of sound generation of numerous stringed instruments, such as lutes called the tambura, sitar and biwa.

Concerted Mitigation of O···H and C(π)···H Interactions Prospects Sixfold Gain in Optical Nonlinearity of Ionic Stilbazolium Derivatives

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

Cole, Jacqueline M.; Lin, Tze-Chia; Edwards, Alison J.

2015-03-04

DAST (4-dimethylamino-N-methyl-4-stilbazolium tosylate) is the most commercially successful organic nonlinear optical (NLO) material for frequency-doubling, integrated optics, and THz wave applications. Its success is predicated on its high optical nonlinearity with concurrent sufficient thermal stability. Many chemical derivatives of DAST have therefore been developed to optimize their properties; yet, to date, none have surpassed the overall superiority of DAST for NLO photonic applications. This is perhaps because DAST is an ionic salt wherein its NLO-active cation is influenced by multiple types of subtle intermolecular forces that are hard to quantify, thus, making difficult the molecular engineering of better functioning DASTmore » derivatives. Here, we establish a model parameter, ηinter, that isolates the influence of intermolecular interactions on second-order optical nonlinearity in DAST and its derivatives, using second-harmonic generation (SHG) as a qualifier; by systematically mapping intercorrelations of all possible pairs of intermolecular interactions to ηinter, we uncover a relationship between concerted intermolecular interactions and SHG output. This correlation reveals that a sixfold gain in the intrinsic second-order NLO performance of DAST is possible, by eliminating the identified interactions. This prediction offers the first opportunity to systematically design next-generation DAST-based photonic device nanotechnology to realize such a prospect.« less

Dark Solitons in High Velocity Waveguide Polariton Fluids.

PubMed

Walker, P M; Tinkler, L; Royall, B; Skryabin, D V; Farrer, I; Ritchie, D A; Skolnick, M S; Krizhanovskii, D N

2017-09-01

We study exciton-polariton nonlinear optical fluids in the high momentum waveguide regime for the first time. We demonstrate the formation of dark solitons with the expected dependence of width on fluid density for both main classes of soliton-forming fluid defects. The results are well described by numerical modeling of the fluid propagation. We deduce a continuous wave nonlinearity more than ten times that on picosecond time scales, arising due to interaction with the exciton reservoir.

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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.

Nonlinear mode interaction in equal-leg angle struts susceptible to cellular buckling.

PubMed

Bai, L; Wang, F; Wadee, M A; Yang, J

2017-11-01

A variational model that describes the interactive buckling of a thin-walled equal-leg angle strut under pure axial compression is presented. A formulation combining the Rayleigh-Ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component. Solving the equations using numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weak-axis flexural buckling mode and the strong-axis flexural-torsional buckling mode for the first time-the resulting behaviour being highly unstable. Physical experiments conducted on 10 cold-formed steel specimens are presented and the results show good agreement with the variational model.

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

Foot and hip contributions to high frontal plane knee projection angle in athletes: a classification and regression tree approach.

PubMed

Bittencourt, Natalia F N; Ocarino, Juliana M; Mendonça, Luciana D M; Hewett, Timothy E; Fonseca, Sergio T

2012-12-01

Cross-sectional. To investigate predictors of increased frontal plane knee projection angle (FPKPA) in athletes. The underlying mechanisms that lead to increased FPKPA are likely multifactorial and depend on how the musculoskeletal system adapts to the possible interactions between its distal and proximal segments. Bivariate and linear analyses traditionally employed to analyze the occurrence of increased FPKPA are not sufficiently robust to capture complex relationships among predictors. The investigation of nonlinear interactions among biomechanical factors is necessary to further our understanding of the interdependence of lower-limb segments and resultant dynamic knee alignment. The FPKPA was assessed in 101 athletes during a single-leg squat and in 72 athletes at the moment of landing from a jump. The investigated predictors were sex, hip abductor isometric torque, passive range of motion (ROM) of hip internal rotation (IR), and shank-forefoot alignment. Classification and regression trees were used to investigate nonlinear interactions among predictors and their influence on the occurrence of increased FPKPA. During single-leg squatting, the occurrence of high FPKPA was predicted by the interaction between hip abductor isometric torque and passive hip IR ROM. At the moment of landing, the shank-forefoot alignment, abductor isometric torque, and passive hip IR ROM were predictors of high FPKPA. In addition, the classification and regression trees established cutoff points that could be used in clinical practice to identify athletes who are at potential risk for excessive FPKPA. The models captured nonlinear interactions between hip abductor isometric torque, passive hip IR ROM, and shank-forefoot alignment.

Nanoscale light–matter interactions in atomic cladding waveguides

PubMed Central

Stern, Liron; Desiatov, Boris; Goykhman, Ilya; Levy, Uriel

2013-01-01

Alkali vapours, such as rubidium, are being used extensively in several important fields of research such as slow and stored light nonlinear optics quantum computation, atomic clocks and magnetometers. Recently, there is a growing effort towards miniaturizing traditional centimetre-size vapour cells. Owing to the significant reduction in device dimensions, light–matter interactions are greatly enhanced, enabling new functionalities due to the low power threshold needed for nonlinear interactions. Here, taking advantage of the mature platform of silicon photonics, we construct an efficient and flexible platform for tailored light–vapour interactions on a chip. Specifically, we demonstrate light–matter interactions in an atomic cladding waveguide, consisting of a silicon nitride nano-waveguide core with a rubidium vapour cladding. We observe the efficient interaction of the electromagnetic guided mode with the rubidium cladding and show that due to the high confinement of the optical mode, the rubidium absorption saturates at powers in the nanowatt regime. PMID:23462991

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

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.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

NASA Astrophysics Data System (ADS)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

All-optical tunable dual Fano resonance in nonlinear metamaterials in optical communication range

NASA Astrophysics Data System (ADS)

Zhou, Yi; Hu, Xiaoyong; Li, Chong; Yang, Hong; Gong, Qihuang

2018-01-01

Low-power, ultra-fast all-optical tunable dual Fano resonance was realized in a metamaterial coated with a non-linear nanocomposite layer composed of gold nanoparticle-doped polycrystalline barium strontium titanate and multilayer tungsten disulphide microsheets. A high non-linear refractive index of -2.148 × 10-11 m2/W was achieved in the nanocomposite material that originated in the non-linearity enhancement associated with the quantum confinement effect, the local-field enhancement effect, and reinforced interactions between photons and the multilayer tungsten disulphide microsheets. An ultra-low threshold pump intensity of 600 kW/cm2 was obtained. An ultra-fast response time of 25.4 ps was maintained because of the fast relaxation dynamics of the bound electrons in the nanoscale polycrystalline barium strontium titanate grains. The large third-order non-linear responses of the metamaterial were confirmed with a high third harmonic generation conversion efficiency of 5.4 × 10-5. This work may help to pave the way towards realization of ultra-high-speed information processing chips and multifunctional integrated photonic devices based on metamaterials.

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

NASA Astrophysics Data System (ADS)

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

2015-03-01

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

Generalized nonlinear Schrödinger equation and ultraslow optical solitons in a cold four-state atomic system.

PubMed

Hang, Chao; Huang, Guoxiang; Deng, L

2006-03-01

We investigate the influence of high-order dispersion and nonlinearity on the propagation of ultraslow optical solitons in a lifetime broadened four-state atomic system under a Raman excitation. Using a standard method of multiple-scales we derive a generalized nonlinear Schrödinger equation and show that for realistic physical parameters and at the pulse duration of 10(-6)s, the effects of third-order linear dispersion, nonlinear dispersion, and delay in nonlinear refractive index can be significant and may not be considered as perturbations. We provide exact soliton solutions for the generalized nonlinear Schrödinger equation and demonstrate that optical solitons obtained may still have ultraslow propagating velocity. Numerical simulations on the stability and interaction of these ultraslow optical solitons in the presence of linear and differential absorptions are also presented.

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.

Modeling dynamic interactions and coherence between marine zooplankton and fishes linked to environmental variability

NASA Astrophysics Data System (ADS)

Liu, Hui; Fogarty, Michael J.; Hare, Jonathan A.; Hsieh, Chih-hao; Glaser, Sarah M.; Ye, Hao; Deyle, Ethan; Sugihara, George

2014-03-01

The dynamics of marine fishes are closely related to lower trophic levels and the environment. Quantitatively understanding ecosystem dynamics linking environmental variability and prey resources to exploited fishes is crucial for ecosystem-based management of marine living resources. However, standard statistical models typically grounded in the concept of linear system may fail to capture the complexity of ecological processes. We have attempted to model ecosystem dynamics using a flexible, nonparametric class of nonlinear forecasting models. We analyzed annual time series of four environmental indices, 22 marine copepod taxa, and four ecologically and commercially important fish species during 1977 to 2009 on Georges Bank, a highly productive and intensively studied area of the northeast U.S. continental shelf ecosystem. We examined the underlying dynamic features of environmental indices and copepods, quantified the dynamic interactions and coherence with fishes, and explored the potential control mechanisms of ecosystem dynamics from a nonlinear perspective. We found: (1) the dynamics of marine copepods and environmental indices exhibiting clear nonlinearity; (2) little evidence of complex dynamics across taxonomic levels of copepods; (3) strong dynamic interactions and coherence between copepods and fishes; and (4) the bottom-up forcing of fishes and top-down control of copepods coexisting as target trophic levels vary. These findings highlight the nonlinear interactions among ecosystem components and the importance of marine zooplankton to fish populations which point to two forcing mechanisms likely interactively regulating the ecosystem dynamics on Georges Bank under a changing environment.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

Interactive Augmentation of Voice Quality and Reduction of Breath Airflow in the Soprano Voice.

PubMed

Rothenberg, Martin; Schutte, Harm K

2016-11-01

In 1985, at a conference sponsored by the National Institutes of Health, Martin Rothenberg first described a form of nonlinear source-tract acoustic interaction mechanism by which some sopranos, singing in their high range, can use to reduce the total airflow, to allow holding the note longer, and simultaneously enrich the quality of the voice, without straining the voice. (M. Rothenberg, "Source-Tract Acoustic Interaction in the Soprano Voice and Implications for Vocal Efficiency," Fourth International Conference on Vocal Fold Physiology, New Haven, Connecticut, June 3-6, 1985.) In this paper, we describe additional evidence for this type of nonlinear source-tract interaction in some soprano singing and describe an analogous interaction phenomenon in communication engineering. We also present some implications for voice research and pedagogy. Copyright © 2016 The Voice Foundation. Published by Elsevier Inc. All rights reserved.

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).

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.

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.

Simulation of Shock-Shock Interaction in Parsec-Scale Jets

NASA Astrophysics Data System (ADS)

Fromm, Christian M.; Perucho, Manel; Ros, Eduardo; Mimica, Petar; Savolainen, Tuomas; Lobanov, Andrei P.; Zensus, J. Anton

The analysis of the radio light curves of the blazar CTA 102 during its 2006 flare revealed a possible interaction between a standing shock wave and a traveling one. In order to better understand this highly non-linear process, we used a relativistic hydrodynamic code to simulate the high energy interaction and its related emission. The calculated synchrotron emission from these simulations showed an increase in turnover flux density, Sm, and turnover frequency, νm, during the interaction and decrease to its initial values after the passage of the traveling shock wave.

Terahertz pulse induced intervalley scattering in photoexcited GaAs.

PubMed

Su, F H; Blanchard, F; Sharma, G; Razzari, L; Ayesheshim, A; Cocker, T L; Titova, L V; Ozaki, T; Kieffer, J-C; Morandotti, R; Reid, M; Hegmann, F A

2009-06-08

Nonlinear transient absorption bleaching of intense few-cycle terahertz (THz) pulses is observed in photoexcited GaAs using opticalpump--THz-probe techniques. A simple model of the electron transport dynamics shows that the observed nonlinear response is due to THz-electric- field-induced intervalley scattering over sub-picosecond time scales as well as an increase in the intravalley scattering rate attributed to carrier heating. Furthermore, the nonlinear nature of the THz pulse transmission at high peak fields leads to a measured terahertz conductivity in the photoexcited GaAs that deviates significantly from the Drude behavior observed at low THz fields, emphasizing the need to explore nonlinear THz pulse interactions with materials in the time domain.

Nonlinear waveguide optics and photonic crystal fibers.

PubMed

Knight, J C; Skryabin, D V

2007-11-12

Focus Serial: Frontiers of Nonlinear Optics

Pump-probe nonlinear phase dispersion spectroscopy.

PubMed

Robles, Francisco E; Samineni, Prathyush; Wilson, Jesse W; Warren, Warren S

2013-04-22

Pump-probe microscopy is an imaging technique that delivers molecular contrast of pigmented samples. Here, we introduce pump-probe nonlinear phase dispersion spectroscopy (PP-NLDS), a method that leverages pump-probe microscopy and spectral-domain interferometry to ascertain information from dispersive and resonant nonlinear effects. PP-NLDS extends the information content to four dimensions (phase, amplitude, wavelength, and pump-probe time-delay) that yield unique insight into a wider range of nonlinear interactions compared to conventional methods. This results in the ability to provide highly specific molecular contrast of pigmented and non-pigmented samples. A theoretical framework is described, and experimental results and simulations illustrate the potential of this method. Implications for biomedical imaging are discussed.

Pump-probe nonlinear phase dispersion spectroscopy

PubMed Central

Robles, Francisco E.; Samineni, Prathyush; Wilson, Jesse W.; Warren, Warren S.

2013-01-01

Pump-probe microscopy is an imaging technique that delivers molecular contrast of pigmented samples. Here, we introduce pump-probe nonlinear phase dispersion spectroscopy (PP-NLDS), a method that leverages pump-probe microscopy and spectral-domain interferometry to ascertain information from dispersive and resonant nonlinear effects. PP-NLDS extends the information content to four dimensions (phase, amplitude, wavelength, and pump-probe time-delay) that yield unique insight into a wider range of nonlinear interactions compared to conventional methods. This results in the ability to provide highly specific molecular contrast of pigmented and non-pigmented samples. A theoretical framework is described, and experimental results and simulations illustrate the potential of this method. Implications for biomedical imaging are discussed. PMID:23609646

Generation of high-field narrowband terahertz radiation by counterpropagating plasma wakefields

NASA Astrophysics Data System (ADS)

Timofeev, I. V.; Annenkov, V. V.; Volchok, E. P.

2017-10-01

It is found that nonlinear interaction of plasma wakefields driven by counterpropagating laser or particle beams can efficiently generate high-power electromagnetic radiation at the second harmonic of the plasma frequency. Using a simple analytical theory and particle-in-cell simulations, we show that this phenomenon can be attractive for producing high-field ( ˜10 MV/cm) tunable terahertz radiation with a narrow line width. For laser drivers produced by existing petawatt-class systems, this nonlinear process opens the way to the generation of gigawatt, multi-millijoule terahertz pulses which are not presently available for any other generating schemes.

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.

Optical Chirality in Nonlinear Optics: Application to High Harmonic Generation.

PubMed

Neufeld, Ofer; Cohen, Oren

2018-03-30

Optical chirality (OC)-one of the fundamental quantities of electromagnetic fields-corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

Optical Chirality in Nonlinear Optics: Application to High Harmonic Generation

NASA Astrophysics Data System (ADS)

Neufeld, Ofer; Cohen, Oren

2018-03-01

Optical chirality (OC)—one of the fundamental quantities of electromagnetic fields—corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

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.

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.

Laser-induced generation of surface periodic structures in media with nonlinear diffusion

NASA Astrophysics Data System (ADS)

Zhuravlev, V. M.; Zolotovskii, I. O.; Korobko, D. A.; Morozov, V. M.; Svetukhin, V. V.; Yavtushenko, I. O.; Yavtushenko, M. S.

2017-12-01

A model of fast formation of high-contrast periodic structure appearing on a semiconductor surface under action of laser radiation is proposed. The process of growing a surface structure due to the interaction surface plasmon- polaritons excited on nonequilibrium electrons with incident laser radiation are considered in the framework of a medium with nonlinear diffusion of nonequilibrium carriers (defects). A resonance effect of superfast pico- and subpicosecond amplification of the plasmon-polariton structure generated on the surface, the realization of which can result in a high-contrast defect lattice.

Pre-launch simulation experiment of microwave-ionosphere nonlinear interaction rocket experiment in the space plasma chamber

NASA Astrophysics Data System (ADS)

Kaya, N.; Tsutsui, M.; Matsumoto, H.; Kimura, I.

1980-09-01

A pre-flight test experiment of a microwave-ionosphere nonlinear interaction rocket experiment (MINIX) has been carried out in a space plasma simulation chamber. Though the first rocket experiment ended up in failure because of a high voltage trouble, interesting results are observed in the pre-flight experiment. A significant microwave heating of plasma up to 300% temperature increase is observed. Strong excitations of plasma waves by the transmitted microwaves in the VLF and HF range are observed as well. These microwave effects may have to be taken into account in solar power satellite projects in the future.

Vector rectangular-shape laser based on reduced graphene oxide interacting with a long fiber taper.

PubMed

Gao, Lei; Zhu, Tao; Huang, Wei; Zeng, Jing

2014-10-01

A vector dual-wavelength rectangular-shape laser (RSL) based on a long fiber taper deposited with reduced graphene oxide is proposed, where nonlinearity is enhanced due to a large evanescent-field-interacting length and strong field confinement of an 8 mm fiber taper with a waist diameter of 4 μm. Graphene flakes are deposited uniformly on the taper waist with light pressure effect, so this structure guarantees both excellent saturable absorption and high nonlinearity. The RSL with a repetition rate of 7.9 MHz shows fast polarization switching in two orthogonal polarization directions, and temporal and spectral characteristics are investigated.

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

PubMed Central

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

2014-01-01

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

Nonlinear terms in storm surge predictions: Effect of tide and shelf geometry with case study from Hurricane Rita

NASA Astrophysics Data System (ADS)

Rego, JoãO. L.; Li, Chunyan

2010-06-01

This study applied the finite volume coastal ocean model (FVCOM) to the storm surge induced by Hurricane Rita along the Louisiana-Texas coast. The model was calibrated for tides and validated with observed water levels. Peak water levels were shown to be lower than expected for a landfall at high tide. For low- and high-tide landfalls, nonlinear effects due to tide-surge coupling were constructive and destructive to total storm tide, respectively, and their magnitude reached up to 70% of the tidal amplitude in the Rita application. Tide-surge interaction was further examined using a standard hurricane under idealized scenarios to evaluate the effects of various shelf geometries, tides, and landfall timings (relative to tide). Nonlinearity was important between landfall position and locations within 2.5 × radius of maximum winds. On an idealized wide continental shelf, nonlinear effects reached up to 80% of the tidal amplitude with an S2 tide and up to 47% with a K1 tide. Increasing average depths by 4 m reduced nonlinear effects to 41% of the tidal amplitude; increasing the slope by a factor of 3 produced nonlinearities of just 26% of tide (both with a K1 tide). The nonlinear effect was greatest for landfalls at low tide, followed by landfalls at high tide and then by landfalls at midebb or midflood.

Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding

PubMed Central

Tajima, Satohiro; Yanagawa, Toru; Fujii, Naotaka; Toyoizumi, Taro

2015-01-01

Brain-wide interactions generating complex neural dynamics are considered crucial for emergent cognitive functions. However, the irreducible nature of nonlinear and high-dimensional dynamical interactions challenges conventional reductionist approaches. We introduce a model-free method, based on embedding theorems in nonlinear state-space reconstruction, that permits a simultaneous characterization of complexity in local dynamics, directed interactions between brain areas, and how the complexity is produced by the interactions. We demonstrate this method in large-scale electrophysiological recordings from awake and anesthetized monkeys. The cross-embedding method captures structured interaction underlying cortex-wide dynamics that may be missed by conventional correlation-based analysis, demonstrating a critical role of time-series analysis in characterizing brain state. The method reveals a consciousness-related hierarchy of cortical areas, where dynamical complexity increases along with cross-area information flow. These findings demonstrate the advantages of the cross-embedding method in deciphering large-scale and heterogeneous neuronal systems, suggesting a crucial contribution by sensory-frontoparietal interactions to the emergence of complex brain dynamics during consciousness. PMID:26584045

Optical pump-probe microscopy for biomedicine and art conservation

NASA Astrophysics Data System (ADS)

Fischer, Martin

2013-03-01

Nonlinear optical microscopy can provide contrast in highly heterogeneous media and a wide range of applications has emerged, primarily in biology, medicine, and materials science. Compared to linear microscopy methods, the localized nature of nonlinear interactions leads to high spatial resolution, optical sectioning, and larger possible imaging depth in scattering media. However, nonlinear contrast (other than fluorescence, harmonic generation or CARS) is generally difficult to measure because it is overwhelmed by the large background of detected illumination light. This background can be suppressed by using femtosecond pulse or pulse train shaping to encode nonlinear interactions in background-free regions of the frequency spectrum. We have developed this shaping technology to study novel intrinsic structural and molecular contrast in biological tissue, generally using less power than a laser pointer. For example we have recently been able to sensitively measure detailed transient absorption dynamics of melanin sub-types in a variety of skin lesions, showing clinically relevant differences of melanin type and distribution between cancerous and benign tissue.[1] Recently we have also applied this technology to paint samples and to historic artwork in order to provide detailed, depth-resolved pigment identification. Initial studies in different inorganic and organic pigments have shown a rich and pigment-specific nonlinear absorption signature.[2] Some pigments, for example lapis lazuli (natural ultramarine), even show marked differences in signal depending on its geographic origin and on age, demonstrating the potential of this technique to determine authenticity, provenance, technology of manufacture, or state of preservation of historic works of art.

Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report

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

Cai, Xiao-Chuan; Keyes, David; Yang, Chao

2014-09-29

The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementationmore » since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.« less

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.

Semiconductor Nonlinear Dynamics Study by Broadband Terahertz Spectroscopy

NASA Astrophysics Data System (ADS)

Ho, I.-Chen

Semiconductor nonlinearity in the terahertz (THz) frequency range has been attracting considerable attention due to the recent development of high-power semiconductor-based nanodevices. However, the underlying physics concerning carrier dynamics in the presence of high-field THz transients is still obscure. This thesis introduces an ultrafast, time-resolved THz pump/THz probe approach to the study of semiconductor properties in the nonlinear regime. The carrier dynamics regarding two mechanisms, intervalley scattering and impact ionization, is observed for doped InAs on a sub-picosecond time scale. In addition, polaron modulation driven by intense THz pulses is experimentally and theoretically investigated. The observed polaron dynamics verifies the interaction between energetic electrons and a phonon field. In contrast to previous work which reports optical phonon responses, acoustic phonon modulations are addressed in this study. A further understanding of the intense field interacting with solid materials will accelerate the development of semiconductor devices. This thesis starts with the design and performance of a table-top THz spectrometer which has the advantages of ultra-broad bandwidth (one order higher bandwidth compared to a conventional ZnTe sensor) and high electric field strength (>100 kV/cm). Unlike the conventional THz time-domain spectroscopy, the spectrometer integrates a novel THz air-biased-coherent-detection (THz-ABCD) technique and utilizes selected gases as THz emitters and sensors. In comparison with commonly used electro-optic (EO) crystals or photoconductive (PC) dipole antennas, the gases have the benefits of no phonon absorption as existing in EO crystals and no carrier life time limitation as observed in PC dipole antennas. The newly development THz-ABCD spectrometer with a strong THz field strength capability provides a platform for various research topics especially on the nonlinear carrier dynamics of semiconductors. Two mechanisms, electron intervalley scattering and impact ionization of InAs crystals, are observed under the excitation of intense THz field on a sub-picosecond time scale. These two competing mechanisms are demonstrated by changing the impurity doping type of the semiconductors and varying the strength of the THz field. Another investigation of nonlinear carrier dynamics is the observation of coherent polaron oscillation in n-doped semiconductors excited by intense THz pulses. Through modulations of surface reflection with a THz pump/THz probe technique, this work experimentally verifies the interaction between energetic electrons and a phonon field, which has been theoretically predicted by previous publications, and shows that this interaction applies for the acoustic phonon modes. Usually, two transverse acoustic (2TA) phonon responses are inactive in infrared measurement, while they are detectable in second-order Raman spectroscopy. The study of polaron dynamics, with nonlinear THz spectroscopy (in the far-infrared range), provides a unique method to diagnose the overtones of 2TA phonon responses of semiconductors, and therefore incorporates the abilities of both infrared and Raman spectroscopy. This work presents a new milestone in wave-matter interaction and seeks to benefit the industrial applications in high power, small scale devices.

Two-dimensional nonlinear finite element analysis of well damage due to reservoir compaction, well-to-well interactions, and localization on weak layers

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

Hilbert, L.B. Jr.; Fredrich, J.T.; Bruno, M.S.

1996-05-01

In this paper the authors present the results of a coupled nonlinear finite element geomechanics model for reservoir compaction and well-to-well interactions for the high-porosity, low strength diatomite reservoirs of the Belridge field near Bakersfield, California. They show that well damage and failures can occur under the action of two distinct mechanisms: shear deformations induced by pore compaction, and subsidence, and shear deformations due to well-to-well interactions during production or water injection. They show such casting damage or failure can be localized to weak layers that slide or slip under shear due to subsidence. The magnitude of shear displacements andmore » surface subsidence agree with field observations.« less

Conservation laws, bilinear forms and solitons for a fifth-order nonlinear Schrödinger equation for the attosecond pulses in an optical fiber

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

Chai, Jun; Tian, Bo, E-mail: tian_bupt@163.com; Zhen, Hui-Ling

Under investigation in this paper is a fifth-order nonlinear Schrödinger equation, which describes the propagation of attosecond pulses in an optical fiber. Based on the Lax pair, infinitely-many conservation laws are derived. With the aid of auxiliary functions, bilinear forms, one-, two- and three-soliton solutions in analytic forms are generated via the Hirota method and symbolic computation. Soliton velocity varies linearly with the coefficients of the high-order terms. Head-on interaction between the bidirectional two solitons and overtaking interaction between the unidirectional two solitons as well as the bound state are depicted. For the interactions among the three solitons, two head-onmore » and one overtaking interactions, three overtaking interactions, an interaction between a bound state and a single soliton and the bound state are displayed. Graphical analysis shows that the interactions between the two solitons are elastic, and interactions among the three solitons are pairwise elastic. Stability analysis yields the modulation instability condition for the soliton solutions.« less

Nonlinear acoustics experimental characterization of microstructure evolution in Inconel 617

NASA Astrophysics Data System (ADS)

Yao, Xiaochu; Liu, Yang; Lissenden, Cliff J.

2014-02-01

Inconel 617 is a candidate material for the intermediate heat exchanger in a very high temperature reactor for the next generation nuclear power plant. This application will require the material to withstand fatigue-ratcheting interaction at temperatures up to 950°C. Therefore nondestructive evaluation and structural health monitoring are important capabilities. Acoustic nonlinearity (which is quantified in terms of a material parameter, the acoustic nonlinearity parameter, β) has been proven to be sensitive to microstructural changes in material. This research develops a robust experimental procedure to track the evolution of damage precursors in laboratory tested Inconel 617 specimens using ultrasonic bulk waves. The results from the acoustic non-linear tests are compared with stereoscope surface damage results. Therefore, the relationship between acoustic nonlinearity and microstructural evaluation can be clearly demonstrated for the specimens tested.

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.

Algebra of Majorana doubling.

PubMed

Lee, Jaehoon; Wilczek, Frank

2013-11-27

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

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.

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.

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.

Device and method for imaging of non-linear and linear properties of formations surrounding a borehole

DOEpatents

Johnson, Paul A; Tencate, James A; Le Bas, Pierre-Yves; Guyer, Robert; Vu, Cung Khac; Skelt, Christopher

2013-11-05

In some aspects of the disclosure, a method and an apparatus is disclosed for investigating material surrounding the borehole. The method includes generating a first low frequency acoustic wave within the borehole, wherein the first low frequency acoustic wave induces a linear and a nonlinear response in one or more features in the material that are substantially perpendicular to a radius of the borehole; directing a first sequence of high frequency pulses in a direction perpendicularly with respect to the longitudinal axis of the borehole into the material contemporaneously with the first acoustic wave; and receiving one or more second high frequency pulses at one or more receivers positionable in the borehole produced by an interaction between the first sequence of high frequency pulses and the one or more features undergoing linear and nonlinear elastic distortion due to the first low frequency acoustic wave to investigate the material surrounding the borehole.

Numerical simulation of stability and stability control of high speed compressible rotating couette flow

NASA Technical Reports Server (NTRS)

Biringen, Sedat; Hatay, Ferhat F.

1993-01-01

The nonlinear temporal evolution of disturbances in compressible flow between infinitely long, concentric cylinders is investigated through direct numerical simulations of the full, three-dimensional Navier-Stokes and energy equations. Counter-rotating cylinders separated by wide gaps are considered with supersonic velocities of the inner cylinder. Initially, the primary disturbance grows exponentially in accordance with linear stability theory. As the disturbances evolve, higher harmonics and subharmonics are generated in a cascading order eventually reaching a saturation state. Subsequent highly nonlinear stages of the evolution are governed by the interaction of the disturbance modes, particularly the axial subharmonics. Nonlinear evolution of the disturbance field is characterized by the formation of high-shear layers extending from the inner cylinder towards the center of the gap in the form of jets similar to the ejection events in transitional and turbulent wall-bounded shear flows.

High-order interactions observed in multi-task intrinsic networks are dominant indicators of aberrant brain function in schizophrenia

PubMed Central

Plis, Sergey M; Sui, Jing; Lane, Terran; Roy, Sushmita; Clark, Vincent P; Potluru, Vamsi K; Huster, Rene J; Michael, Andrew; Sponheim, Scott R; Weisend, Michael P; Calhoun, Vince D

2013-01-01

Identifying the complex activity relationships present in rich, modern neuroimaging data sets remains a key challenge for neuroscience. The problem is hard because (a) the underlying spatial and temporal networks may be nonlinear and multivariate and (b) the observed data may be driven by numerous latent factors. Further, modern experiments often produce data sets containing multiple stimulus contexts or tasks processed by the same subjects. Fusing such multi-session data sets may reveal additional structure, but raises further statistical challenges. We present a novel analysis method for extracting complex activity networks from such multifaceted imaging data sets. Compared to previous methods, we choose a new point in the trade-off space, sacrificing detailed generative probability models and explicit latent variable inference in order to achieve robust estimation of multivariate, nonlinear group factors (“network clusters”). We apply our method to identify relationships of task-specific intrinsic networks in schizophrenia patients and control subjects from a large fMRI study. After identifying network-clusters characterized by within- and between-task interactions, we find significant differences between patient and control groups in interaction strength among networks. Our results are consistent with known findings of brain regions exhibiting deviations in schizophrenic patients. However, we also find high-order, nonlinear interactions that discriminate groups but that are not detected by linear, pair-wise methods. We additionally identify high-order relationships that provide new insights into schizophrenia but that have not been found by traditional univariate or second-order methods. Overall, our approach can identify key relationships that are missed by existing analysis methods, without losing the ability to find relationships that are known to be important. PMID:23876245

HAARP-based Investigations of Lightning-induced Nonlinearities within the D-Region Ionosphere

NASA Astrophysics Data System (ADS)

Moore, R. C.

2015-12-01

It is well-documented that energetic lightning can produce fantastical events with the lower ionosphere. Although the High-frequency Active Auroral Research Program (HAARP) transmitter is not as powerful as lightning, it can be used to investigate the nonlinear interactions that occur within the lower ionosphere, many of which also occur during lightning-induced ionospheric events. This paper presents the best experimental results obtained during D-region modification experiments performed by the University of Florida at the HAARP observatory between 2007 and 2014, including ELF/VLF wave generation experiments, wave-wave mixing experiments, and cross-modulation experiments. We emphasize the physical processes important for lightning-ionosphere interactions that can be directly investigated using HAARP.

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.

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.

Quantitative Assessment of Fatigue Damage Accumulation in Wavy Slip Metals from Acoustic Harmonic Generation

NASA Technical Reports Server (NTRS)

Cantrell, John H.

2006-01-01

A comprehensive, analytical treatment is presented of the microelastic-plastic nonlinearities resulting from the interaction of a stress perturbation with dislocation substructures (veins and persistent slip bands) and cracks that evolve during high-cycle fatigue of wavy slip metals. The nonlinear interaction is quantified by a material (acoustic) nonlinearity parameter beta extracted from acoustic harmonic generation measurements. The contribution to beta from the substructures is obtained from the analysis of Cantrell [Cantrell, J. H., 2004, Proc. R. Soc. London A, 460, 757]. The contribution to beta from cracks is obtained by applying the Paris law for crack propagation to the Nazarov-Sutin crack nonlinearity equation [Nazarov, V. E., and Sutin, A. M., 1997, J. Acoust. Soc. Am. 102, 3349]. The nonlinearity parameter resulting from the two contributions is predicted to increase monotonically by hundreds of percent during fatigue from the virgin state to fracture. The increase in beta during the first 80-90 percent of fatigue life is dominated by the evolution of dislocation substructures, while the last 10-20 percent is dominated by crack growth. The model is applied to the fatigue of aluminium alloy 2024-T4 in stress-controlled loading at 276MPa for which experimental data are reported. The agreement between theory and experiment is excellent.

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.

Connective stability of nonlinear matrix systems

NASA Technical Reports Server (NTRS)

Siljak, D. D.

1974-01-01

Consideration of stability under structural perturbations of free dynamic systems described by the differential equation dx/dt = A(t,x)x, where the matrix A(t,x) has time-varying nonlinear elements. The concept of 'connective stability' is introduced to study the structural properties of competitive-cooperative nonlinear matrix systems. It is shown that stability reliability in such systems is high and that they remain stable despite time-varying (including 'on-off') interaction among individual agents present in the system. The results obtained can be used to study stability aspects of mathematical models arising in as diverse fields as economics, biology, arms races, and transistor circuits.

Nonlinear harmonic generation in distributed optical klystrons

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

H.P. Freund; George R. Neil

2001-12-01

A distributed optical klystron has the potential for dramatically shortening the total interaction length in high-gain free-electron lasers (INP 77-59, Novosibirsk, 1977; Nucl. Instr. and Meth A 304 (1991) 463) in comparison to a single-wiggler-segment configuration. This shortening can be even more dramatic if a nonlinear harmonic generation mechanism is used to reach the desired wavelength. An example operating at a 4.5{angstrom} fundamental and a 1.5{angstrom} harmonic is discussed.

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.

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.

Dynamic of Langmuir and Ion-Sound Waves in Type 3 Solar Radio Sources

NASA Technical Reports Server (NTRS)

Robinson, P. A.; Willes, A. J.; Cairns, I. H.

1993-01-01

The evolution of Langmuir and ion-sound waves in type 3 sources is investigated, incorporating linear growth, linear damping, and nonlinear electrostatic decay. Improved estimates are obtained for the wavenumber range of growing waves and the nonlinear coupling coefficient for the decay process. The resulting prediction for the electrostatic decay threshold is consistent with the observed high-field cutoff in the Langmuir field distribution. It is shown that the conditions in the solar wind do not allow a steady state to be attained; rather, bursty linear and nonlinear interactions take place, consistent with the highly inhomogeneous and impulsive waves actually observed. Nonlinear growth is found to be fast enough to saturate the growth of the parent Langmuir waves in the available interaction time. The resulting levels of product Langmuir and ion-sound waves are estimated theoretically and shown to be consistent with in situ ISEE 3 observations of type 3 events at 1 AU. Nonlinear interactions slave the growth and decay of product sound waves to that of the product Langmuir waves. The resulting probability distribution of ion-sound field strengths is predicted to have a flat tail extending to a high-field cutoff. This prediction is consistent with statistics derived here from ISEE 3 observations. Agreement is also found between the frequencies of the observed waves and predictions for the product S waves. The competing processes of nonlinear wave collapse and quasilinear relaxation are discussed, and it is concluded that neither is responsible for the saturation of Langmuir growth. When wave and beam inhomogeneities are accounted for, arguments from quasi-linear relaxation yield an upper bound on the Langmuir fields that is too high to be relevant. Nor are the criteria for direct wave collapse of the beam-driven waves met, consistent with earlier simulation results that imply that this process is not responsible for saturation of the beam instability. Indeed, even if the highest observed Langmuir fields are assumed to he part of a long-wavelength 'condensate' produced via electrostatic decay, they still fall short of the relevant requirements for wave collapse. The most stringent requirement for collapse is that collapsing wave packets not be disrupted by ambient density fluctuations in the solar wind. Fields of several mV m(exp -1) extending over several hundred km would be needed to satisfy this requirement; at 1 AU such fields are rare at best.

Triple tailored nonlinear dispersion of dressed four- and six-wave mixing

NASA Astrophysics Data System (ADS)

Sun, Yanyong; Wang, Zhiguo; Zhang, Zhaoyang; Gu, Bingling; Wang, Kun; Yang, Gaoguo; Zhang, Yanpeng

2018-06-01

We investigate the spectral signals and spatial images of a probe transmission signal, four-wave mixing (FWM), and six-wave mixing (SWM) under double dressing effects in an inverted Y-type system. Especially, we get the triple tailored nonlinear dispersion (about 60 MHz) of the dressed FWM and SWM through the interaction between electromagnetically induced transparency (EIT) windows and the Kerr nonlinearity. Moreover, SWM and dressed FWM with narrow linewidth are obtained through the tailoring of the three EIT windows, which is much narrower than the EIT. In addition, we first elaborate the modulation effect from the self-Kerr coefficient of FWM on the spot. We also investigate the spatial characteristics (defocusing, shifting, and splitting) of FWM and SWM induced by tailored self-Kerr and cross-Kerr effects among the relative fields. Such spatial shifting, splitting induced by the tailored nonlinear dispersion can be used for a higher contrast and high speed switch as well as a high resolution router.

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

Nonlinear damping of oblique whistler mode waves through Landau resonance

NASA Astrophysics Data System (ADS)

Hsieh, Y.; Omura, Y.

2017-12-01

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

Simulation of linear and nonlinear Landau damping of lower hybrid waves

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

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

2013-06-15

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

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.

Efficient quantum computing using coherent photon conversion.

PubMed

Langford, N K; Ramelow, S; Prevedel, R; Munro, W J; Milburn, G J; Zeilinger, A

2011-10-12

Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting systems with extremely strong intrinsic nonlinearities. Furthermore, exploiting higher-order nonlinearities with multiple pump fields yields a mechanism for multiparty mediation of the complex, coherent dynamics.

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.

Plasma interactions with large spacecraft

NASA Technical Reports Server (NTRS)

Sagalyn, Rita C.; Maynard, Nelson C.

1986-01-01

Space is playing a rapidly expanding role in the conduct of the Air Force mission. Larger, more complex, high-power space platforms are planned and military astronauts will provide a new capability in spacecraft servicing. Interactions of operational satellites with the environment have been shown to degrade space sensors and electronics and to constrain systems operations. The environmental interaction effects grow nonlinearly with increasing size and power. Quantification of the interactions and development of mitigation techniques for systems-limiting interactions is essential to the success of future Air Force space operations.

Evidence of nonlinear interaction between quasi 2 day wave and quasi-stationary wave

NASA Astrophysics Data System (ADS)

Gu, Sheng-Yang; Liu, Han-Li; Li, Tao; Dou, Xiankang; Wu, Qian; Russell, James M.

2015-02-01

The nonlinear interaction between the westward quasi 2 day wave (QTDW) with zonal wave number s = 3 (W3) and stationary planetary wave with s = 1 (SPW1) is first investigated using both Thermosphere, Ionosphere, and Mesosphere Electric Dynamics (TIMED) satellite observations and the thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM) simulations. A QTDW with westward s = 2 (W2) is identified in the mesosphere and lower thermosphere (MLT) region in TIMED/Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature and TIMED/TIMED Doppler Imager (TIDI) wind observations during 2011/2012 austral summer period, which coincides with a strong SPW1 episode at high latitude of the northern winter hemisphere. The temperature perturbation of W2 QTDW reaches a maximum amplitude of ~8 K at ~30°S and ~88 km in the Southern Hemisphere, with a smaller amplitude in the Northern Hemisphere at similar latitude and minimum amplitude at the equator. The maximum meridional wind amplitude of the W2 QTDW is observed to be ~40 m/s at 95 km in the equatorial region. The TIME-GCM is utilized to simulate the nonlinear interactions between W3 QTDW and SPW1 by specifying both W3 QTDW and SPW1 perturbations at the lower model boundary. The model results show a clear W2 QTDW signature in the MLT region, which agrees well with the TIMED/SABER temperature and TIMED/TIDI horizontal wind observations. We conclude that the W2 QTDW during the 2011/2012 austral summer period results from the nonlinear interaction between W3 QTDW and SPW1.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

Nonlinear Delta-f Simulations of Collective Effects in Intense Charged Particle Beams

NASA Astrophysics Data System (ADS)

Qin, Hong

2002-11-01

A nonlinear delta-f particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code, the nonlinear delta-f method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next- generation accelerators and storage rings, such as the Spallation Neutron Source, and heavy ion fusion drivers. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring (PSR) experiment at Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles of less than 0.25collective processes in high-intensity beams, such as anisotropy-driven instabilities, collective eigenmode excitations for perturbations about stable beam equilibria, and the Darwin model for fully electromagnetic perturbations will also be discussed.

Nonlinear analysis of a relativistic beam-plasma cyclotron instability

NASA Technical Reports Server (NTRS)

Sprangle, P.; Vlahos, L.

1986-01-01

A self-consistent set of nonlinear and relativistic wave-particle equations are derived for a magnetized beam-plasma system interacting with electromagnetic cyclotron waves. In particular, the high-frequency cyclotron mode interacting with a streaming and gyrating electron beam within a background plasma is considered in some detail. This interaction mode may possibly find application as a high-power source of coherent short-wavelength radiation for laboratory devices. The background plasma, although passive, plays a central role in this mechanism by modifying the dielectric properties in which the magnetized electron beam propagates. For a particular choice of the transverse beam velocity (i.e., the speed of light divided by the relativistic mass factor), the interaction frequency equals the nonrelativistic electron cyclotron frequency times the relativistic mass factor. For this choice of transverse beam velocity the detrimental effects of a longitudinal beam velocity spread is virtually removed. Power conversion efficiencies in excess of 18 percent are both analytically calculated and obtained through numerical simulations of the wave-particle equations. The quality of the electron beam, degree of energy and pitch angle spread, and its effect on the beam-plasma cyclotron instability is studied.

An energy balance model exploration of the impacts of interactions between surface albedo, cloud cover and water vapor on polar amplification

NASA Astrophysics Data System (ADS)

Södergren, A. Helena; McDonald, Adrian J.; Bodeker, Gregory E.

2017-11-01

We examine the effects of non-linear interactions between surface albedo, water vapor and cloud cover (referred to as climate variables) on amplified warming of the polar regions, using a new energy balance model. Our simulations show that the sum of the contributions to surface temperature changes due to any variable considered in isolation is smaller than the temperature changes from coupled feedback simulations. This non-linearity is strongest when all three climate variables are allowed to interact. Surface albedo appears to be the strongest driver of this non-linear behavior, followed by water vapor and clouds. This is because increases in longwave radiation absorbed by the surface, related to increases in water vapor and clouds, and increases in surface absorbed shortwave radiation caused by a decrease in surface albedo, amplify each other. Furthermore, our results corroborate previous findings that while increases in cloud cover and water vapor, along with the greenhouse effect itself, warm the polar regions, water vapor also significantly warms equatorial regions, which reduces polar amplification. Changes in surface albedo drive large changes in absorption of incoming shortwave radiation, thereby enhancing surface warming. Unlike high latitudes, surface albedo change at low latitudes are more constrained. Interactions between surface albedo, water vapor and clouds drive larger increases in temperatures in the polar regions compared to low latitudes. This is in spite of the fact that, due to a forcing, cloud cover increases at high latitudes and decreases in low latitudes, and that water vapor significantly enhances warming at low latitudes.

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.

Comparison of Control Approaches in Genetic Regulatory Networks by Using Stochastic Master Equation Models, Probabilistic Boolean Network Models and Differential Equation Models and Estimated Error Analyzes

NASA Astrophysics Data System (ADS)

Caglar, Mehmet Umut; Pal, Ranadip

2011-03-01

Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.

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.

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.

Study of non-linear deformation of vocal folds in simulations of human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2014-11-01

Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

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

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

NASA Astrophysics Data System (ADS)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

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.

Generation of Optical Vortices by Nonlinear Inverse Thomson Scattering at Arbitrary Angle Interactions

NASA Astrophysics Data System (ADS)

Taira, Yoshitaka; Katoh, Masahiro

2018-06-01

We theoretically verify that optical vortices carrying orbital angular momentum are generated in various astrophysical situations via nonlinear inverse Thomson scattering. Arbitrary angle collisions between relativistic electrons and circularly polarized strong electromagnetic waves are treated. We reveal that the higher harmonic components of scattered photons carry well-defined orbital angular momentum under a specific condition that the Lorentz factor of the electron is much larger than the field strength parameter of the electromagnetic wave. Our study indicates that optical vortices in a wide frequency range from radio waves to gamma-rays are naturally generated in environments where high-energy electrons interact with circularly polarized strong electromagnetic waves at various interaction angles. Optical vortices should be a new multi-messenger member carrying information concerning the physical circumstances of their sources, e.g., the magnetic and radiation fields. Moreover, their interactions with matter via their orbital angular momenta may play an important role in the evolution of matter in the universe.

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.

Spectral long-range interaction of temporal incoherent solitons.

PubMed

Xu, Gang; Garnier, Josselin; Picozzi, Antonio

2014-02-01

We study the interaction of temporal incoherent solitons sustained by a highly noninstantaneous (Raman-like) nonlinear response. The incoherent solitons exhibit a nonmutual interaction, which can be either attractive or repulsive depending on their relative initial distance. The analysis reveals that incoherent solitons exhibit a long-range interaction in frequency space, which is in contrast with the expected spectral short-range interaction described by the usual approach based on the Raman-like spectral gain curve. Both phenomena of anomalous interaction and spectral long-range behavior of incoherent solitons are described in detail by a long-range Vlasov equation.

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Spectroscopic and theoretical study of the charge transfer interaction effect on the vibrational modes and nonlinear optical properties in L-asparaginium nitrate crystal

NASA Astrophysics Data System (ADS)

Elleuch, Nabil; Abid, Younes; Feki, Habib

2016-09-01

Single crystals of L-asparaginium nitrate (LAsnN) were grown by slow evaporation technique. To confirm the crystalline nature of the obtained compound, samples were the subject of an XRPD. The density functional theory (DFT) computations were carried out at B3LYP/6-31G (d) level to reach the optimized geometry, the vibrational spectra and the NLO properties. The excellent agreement between simulated and observed vibrational spectra led to a reliable vibrational assignment. To demonstrate the various charge transfer interactions that stabilize the compound and led to the high nonlinear optical activity, NBO analysis was performed. Also, owing to the hydrogen bond formation, a lowering in the HOMO-LUMO energy gap is noticed. Moreover, as a result of the charge transfer interactions, the symmetry of the nitrate ions was lost and some forbidden modes were excited.

Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint

NASA Technical Reports Server (NTRS)

Bullock, S. J.; Peterson, L. D.

1994-01-01

The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.

Nonlinear silicon photonics

NASA Astrophysics Data System (ADS)

Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.

2017-09-01

Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.

Establishing nonlinearity thresholds with ultraintense X-ray pulses

NASA Astrophysics Data System (ADS)

Szlachetko, Jakub; Hoszowska, Joanna; Dousse, Jean-Claude; Nachtegaal, Maarten; Błachucki, Wojciech; Kayser, Yves; Sà, Jacinto; Messerschmidt, Marc; Boutet, Sebastien; Williams, Garth J.; David, Christian; Smolentsev, Grigory; van Bokhoven, Jeroen A.; Patterson, Bruce D.; Penfold, Thomas J.; Knopp, Gregor; Pajek, Marek; Abela, Rafael; Milne, Christopher J.

2016-09-01

X-ray techniques have evolved over decades to become highly refined tools for a broad range of investigations. Importantly, these approaches rely on X-ray measurements that depend linearly on the number of incident X-ray photons. The advent of X-ray free electron lasers (XFELs) is opening the ability to reach extremely high photon numbers within ultrashort X-ray pulse durations and is leading to a paradigm shift in our ability to explore nonlinear X-ray signals. However, the enormous increase in X-ray peak power is a double-edged sword with new and exciting methods being developed but at the same time well-established techniques proving unreliable. Consequently, accurate knowledge about the threshold for nonlinear X-ray signals is essential. Herein we report an X-ray spectroscopic study that reveals important details on the thresholds for nonlinear X-ray interactions. By varying both the incident X-ray intensity and photon energy, we establish the regimes at which the simplest nonlinear process, two-photon X-ray absorption (TPA), can be observed. From these measurements we can extract the probability of this process as a function of photon energy and confirm both the nature and sub-femtosecond lifetime of the virtual intermediate electronic state.

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Nonlinear Optical Interactions in Plasmas at JILA

NASA Astrophysics Data System (ADS)

Dollar, F.; Hickstein, D. D.; Popmintchev, D.; Becker, A.; Ellis, J.; Hernandez-Garcia, C.; Jaron-Becker, A.; Popmintchev, T.; Xiong, W.; Murnane, M. M.; Kapteyn, H. C.; Dukovic, G.; Jimenez, J.; Palm, B.; Schnitzenbaumer, K.; Perez-Hernandez, J.; Gaeta, A.; Gao, X.; Shim, B.; Plaja, L.; Levis, R.; Tarazkar, M.; Foord, M. E.; Gaffney, J. A.; Libby, S. B.

2014-10-01

We present data from two recent experiments. First, we demonstrate direct observations of localized light absorption in a single nanoparticle irradiated by a strong femtosecond laser field. By imaging the photoion momentum distribution resulting from plasma formation in a laser-irradiated nanostructure, we map the spatial location of the highly localized plasma and thereby image the nanoscale light absorption. Secondly, we show the high linear and nonlinear UV refractive indices of both neutral atoms and ions compensate for plasma dispersion, even in multiply-ionized gases. The experimental work was primarily funded by DOE Grant Number: DE-SC0008803, the DARPA PULSE program, and ARO W911NF-12-1-0436.

Ultra-low-power hybrid light–matter solitons

PubMed Central

Walker, P. M.; Tinkler, L.; Skryabin, D. V.; Yulin, A.; Royall, B.; Farrer, I.; Ritchie, D. A.; Skolnick, M. S.; Krizhanovskii, D. N.

2015-01-01

New functionalities in nonlinear optics will require systems with giant optical nonlinearity as well as compatibility with photonic circuit fabrication techniques. Here we introduce a platform based on strong light–matter coupling between waveguide photons and quantum-well excitons. On a sub-millimetre length scale we generate picosecond bright temporal solitons at a pulse energy of only 0.5 pJ. From this we deduce a nonlinear refractive index three orders of magnitude larger than in any other ultrafast system. We study both temporal and spatio-temporal nonlinear effects and observe dark–bright spatio-temporal polariton solitons. Theoretical modelling of soliton formation in the strongly coupled system confirms the experimental observations. These results show the promise of our system as a high speed, low power, integrated platform for physics and devices based on strong interactions between photons. PMID:26400748

Ultra-low-power hybrid light-matter solitons.

PubMed

Walker, P M; Tinkler, L; Skryabin, D V; Yulin, A; Royall, B; Farrer, I; Ritchie, D A; Skolnick, M S; Krizhanovskii, D N

2015-09-24

New functionalities in nonlinear optics will require systems with giant optical nonlinearity as well as compatibility with photonic circuit fabrication techniques. Here we introduce a platform based on strong light-matter coupling between waveguide photons and quantum-well excitons. On a sub-millimetre length scale we generate picosecond bright temporal solitons at a pulse energy of only 0.5 pJ. From this we deduce a nonlinear refractive index three orders of magnitude larger than in any other ultrafast system. We study both temporal and spatio-temporal nonlinear effects and observe dark-bright spatio-temporal polariton solitons. Theoretical modelling of soliton formation in the strongly coupled system confirms the experimental observations. These results show the promise of our system as a high speed, low power, integrated platform for physics and devices based on strong interactions between photons.

Advances in the Application of High-order Techniques in Simulation of Multi-disciplinary Phenomena

NASA Astrophysics Data System (ADS)

Gaitonde, D. V.; Visbal, M. R.

2003-03-01

This paper describes the development of a comprehensive high-fidelity algorithmic framework to simulate the three-dimensional fields associated with multi-disciplinary physics. A wide range of phenomena is considered, from aero-acoustics and turbulence to electromagnetics, non-linear fluid-structure interactions, and magnetogasdynamics. The scheme depends primarily on "spectral-like," up to sixth-order accurate compact-differencing and up to tenth-order filtering techniques. The tightly coupled procedure suppresses numerical instabilities commonly encountered with high-order methods on non-uniform meshes, near computational boundaries or in the simulation of nonlinear dynamics. Particular emphasis is placed on developing the proper metric evaluation procedures for three-dimensional moving and curvilinear meshes so that the advantages of higher-order schemes are retained in practical calculations. A domain-decomposition strategy based on finite-sized overlap regions and interface boundary treatments enables the development of highly scalable solvers. The utility of the method to simulate problems governed by widely disparate governing equations is demonstrated with several examples encompassing vortex dynamics, wave scattering, electro-fluid plasma interactions, and panel flutter.

Kinetic theory of turbulence for parallel propagation revisited: Low-to-intermediate frequency regime

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

Yoon, Peter H., E-mail: yoonp@umd.edu; School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701

2015-09-15

A previous paper [P. H. Yoon, “Kinetic theory of turbulence for parallel propagation revisited: Formal results,” Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. Inmore » the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.« less

Nonscanning Moiré deflectometry for measurement of nonlinear refractive index and absorption coefficient of liquids.

PubMed

Farahani, Shahrzad Shahrabi; Madanipour, Khosro; Koohian, Ata

2017-05-01

In this work, a nonscanning measurement technique is presented for determining the nonlinear refractive index and absorption coefficient of liquid media based on Moiré deflectometry. In the proposed method two lasers are used: a low power, wide beam as probe and a high power with specific wavelength as a pump. Interaction of the pump laser beam with the nonlinear sample changes the refractive index, which leads to change in convergence/divergence of the collimated incident probe laser beam. The induced deflection is monitored by Moiré deflectometry. If the pump laser has a Gaussian intensity profile, the refractive index profile of the sample is Gaussian, too. Measuring the deflection angle of the probe beam by Moiré fringes deflection, and by using the inverse Abel transform integral, the refractive index profile and nonlinear refractive index can be determined. This method is fast, easy, and insensitive to environmental noise and allows real-time measurement. Also, the refractive index profile of the interacted medium with pump laser can be achieved by this technique. As a liquid sample, a DCJ dye in water solution was studied. The value of nonlinear refractive index, n₂, and absorption coefficient, α, were obtained -2.54×10^-4  cm² w^-1 and 1.368  cm^-1, respectively.

A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects

PubMed Central

De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.

2012-01-01

Background While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. Methods In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. Results We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. Conclusions A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal Interactive Simulation) for general use. PMID:22629108

Nonlinear Terahertz Absorption of Graphene Plasmons.

PubMed

Jadidi, Mohammad M; König-Otto, Jacob C; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin

2016-04-13

Subwavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, subwavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a terahertz pump-terahertz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by 2 orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results. The model shows that the observed strong linearity is caused by an unexpected red shift of plasmon resonance together with a broadening and weakening of the resonance caused by the transient increase in electron temperature. The model further predicts that even greater resonant enhancement of the nonlinear response can be expected in high-mobility graphene, suggesting that nonlinear graphene plasmonic devices could be promising candidates for nonlinear optical processing.

Internal resonance of an elastic body levitated above high-Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Kokuzawa, T.; Toshihiko, S.; Yoshizawa, M.

2010-06-01

In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.

The vibration behavior of railway track at high frequencies under multiple preloads and wheel interactions

PubMed

Wu; Thompson

2000-09-01

The track foundation is preloaded by multiple wheel loads due to the train weight and, as the pad and ballast are nonlinear, their stiffness depends upon the preload in them. Due to the influence of these resilient components of the track, the track vibration is affected by the wheel loads. It is also affected by the wheel/rail interactions. In this article the preloads in the pad and ballast are calculated by considering the nonlinear properties of the track foundation, and thus the preloaded pad and ballast stiffnesses are determined. The vibration properties are explored for the track under multiple wheel loads and multiple wheel/rail interactions by comparing the results from different track models with and without these effects. It is found that the point receptance of the track is reduced and the vibration decay rate is enhanced at low frequencies due to the wheel loads. The effects of the wheel/rail interactions are most significant for frequencies 400-2000 Hz. Because of the wheel/rail interactions, the point receptance fluctuates and the vibration decay is enhanced in the regions around the wheels.

Physics of Alfvén waves and energetic particles in burning plasmas

NASA Astrophysics Data System (ADS)

Chen, Liu; Zonca, Fulvio

2016-01-01

Dynamics of shear Alfvén waves and energetic particles are crucial to the performance of burning fusion plasmas. This article reviews linear as well as nonlinear physics of shear Alfvén waves and their self-consistent interaction with energetic particles in tokamak fusion devices. More specifically, the review on the linear physics deals with wave spectral properties and collective excitations by energetic particles via wave-particle resonances. The nonlinear physics deals with nonlinear wave-wave interactions as well as nonlinear wave-energetic particle interactions. Both linear as well as nonlinear physics demonstrate the qualitatively important roles played by realistic equilibrium nonuniformities, magnetic field geometries, and the specific radial mode structures in determining the instability evolution, saturation, and, ultimately, energetic-particle transport. These topics are presented within a single unified theoretical framework, where experimental observations and numerical simulation results are referred to elucidate concepts and physics processes.

Ghost Dark Energy with Non-Linear Interaction Term

NASA Astrophysics Data System (ADS)

Ebrahimi, E.

2016-06-01

Here we investigate ghost dark energy (GDE) in the presence of a non-linear interaction term between dark matter and dark energy. To this end we take into account a general form for the interaction term. Then we discuss about different features of three choices of the non-linear interacting GDE. In all cases we obtain equation of state parameter, w D = p/ ρ, the deceleration parameter and evolution equation of the dark energy density parameter (Ω D ). We find that in one case, w D cross the phantom line ( w D < -1). However in two other classes w D can not cross the phantom divide. The coincidence problem can be solved in these models completely and there exist good agreement between the models and observational values of w D , q. We study squared sound speed {vs2}, and find that for one case of non-linear interaction term {vs2} can achieves positive values at late time of evolution.

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

Engineering non-linear resonator mode interactions in circuit QED by continuous driving: Manipulation of a photonic quantum memory

NASA Astrophysics Data System (ADS)

Reagor, Matthew; Pfaff, Wolfgang; Heeres, Reinier; Ofek, Nissim; Chou, Kevin; Blumoff, Jacob; Leghtas, Zaki; Touzard, Steven; Sliwa, Katrina; Holland, Eric; Albert, Victor V.; Frunzio, Luigi; Devoret, Michel H.; Jiang, Liang; Schoelkopf, Robert J.

2015-03-01

Recent advances in circuit QED have shown great potential for using microwave resonators as quantum memories. In particular, it is possible to encode the state of a quantum bit in non-classical photonic states inside a high-Q linear resonator. An outstanding challenge is to perform controlled operations on such a photonic state. We demonstrate experimentally how a continuous drive on a transmon qubit coupled to a high-Q storage resonator can be used to induce non-linear dynamics of the resonator. Tailoring the drive properties allows us to cancel or enhance non-linearities in the system such that we can manipulate the state stored in the cavity. This approach can be used to either counteract undesirable evolution due to the bare Hamiltonian of the system or, ultimately, to perform logical operations on the state encoded in the cavity field. Our method provides a promising pathway towards performing universal control for quantum states stored in high-coherence resonators in the circuit QED platform.

The influence of filtering and downsampling on the estimation of transfer entropy

PubMed Central

Florin, Esther; von Papen, Michael; Timmermann, Lars

2017-01-01

Transfer entropy (TE) provides a generalized and model-free framework to study Wiener-Granger causality between brain regions. Because of its nonparametric character, TE can infer directed information flow also from nonlinear systems. Despite its increasing number of applications in neuroscience, not much is known regarding the influence of common electrophysiological preprocessing on its estimation. We test the influence of filtering and downsampling on a recently proposed nearest neighborhood based TE estimator. Different filter settings and downsampling factors were tested in a simulation framework using a model with a linear coupling function and two nonlinear models with sigmoid and logistic coupling functions. For nonlinear coupling and progressively lower low-pass filter cut-off frequencies up to 72% false negative direct connections and up to 26% false positive connections were identified. In contrast, for the linear model, a monotonic increase was only observed for missed indirect connections (up to 86%). High-pass filtering (1 Hz, 2 Hz) had no impact on TE estimation. After low-pass filtering interaction delays were significantly underestimated. Downsampling the data by a factor greater than the assumed interaction delay erased most of the transmitted information and thus led to a very high percentage (67–100%) of false negative direct connections. Low-pass filtering increases the number of missed connections depending on the filters cut-off frequency. Downsampling should only be done if the sampling factor is smaller than the smallest assumed interaction delay of the analyzed network. PMID:29149201

Nonlinear Whistler Wave Physics in the Radiation Belts

NASA Astrophysics Data System (ADS)

Crabtree, Chris

2016-10-01

Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data suggest that these weak turbulence processes may be playing a role in saturating the nonlinear instability.

Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality

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

Kong Qian; Department of Physics, Shanghai University, Shanghai 200444; Wang, Q.

2010-07-15

We investigate theoretically the interaction of dark solitons in materials with a spatially nonlocal nonlinearity. In particular we do this analytically and for arbitrary degree of nonlocality. We employ the variational technique to show that nonlocality induces an attractive force in the otherwise repulsive soliton interaction.

Localization of intense electromagnetic waves in a relativistically hot plasma.

PubMed

Shukla, P K; Eliasson, B

2005-02-18

We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schro dinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.

Evaluation of the interaction between hydroxyapatite and bisphosphonate by nonlinear capillary electrochromatography.

PubMed

Kong, Deying; Chen, Zilin

2017-05-01

Bisphosphonates are a class of chemical compounds used to treat diseases caused by increased bone resorption. Zoledronate is a third-generation bisphosphonate drug. Hydroxyapatite is main mineral constituent of bones, which can be bound by bisphosphonates in vivo. In this work, we report a method of nonlinear capillary electrochromatography for study on the interaction between hydroxyapatite and bisphosphonate. Hydroxyapatite was modified on the inner wall of capillary by a biomimetic-mineralization method. Then nonlinear chromatography was used to fit and analyze the interaction between zoledronate and hydroxyapatite. The association rate constants of zoledronate in hydroxyapatite-modified capillary and bare capillary are 642.3 and 195/M/min, respectively. This indicates that there is strong binding interactions and affinity between zoledronate and hydroxyapatite. Besides, the interaction between zoledronate and hydroxyapatite was confirmed further by ultraviolet spectroscopy. The method of nonlinear capillary electrochromatography provides a fast and effect approach for studying of bone metabolism disease by evaluation of interaction between hydroxyapatite and bisphosphonates. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification

PubMed Central

Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.

2016-01-01

The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. PMID:27108814

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.

PubMed

Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A

2016-04-29

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

Nonlinear Fano-Resonant Dielectric Metasurfaces

DOE PAGES

Yang, Yuanmu; Wang, Wenyi; Boulesbaa, Abdelaziz; ...

2015-10-26

Strong nonlinear light matter interaction is highly sought-after for a variety of applications including lasing and all-optical light modulation. Recently, resonant plasmonic structures have been considered promising candidates for enhancing nonlinear optical processes due to their ability to greatly enhance the optical near-field; however, their small mode volumes prevent the inherently large nonlinear susceptibility of the metal from being efficiently exploited. We present an alternative approach that utilizes a Fano-resonant silicon metasurface. The metasurface results in strong near-field enhancement within the volume of the silicon resonator while minimizing two photon absorption. Here, we measure a third harmonic generation enhancement factormore » of 1.5 105 with respect to an unpatterned silicon film and an absolute conversion efficiency of 1.2 10 6 with a peak pump intensity of 3.2 GW cm 2. The enhanced nonlinearity, combined with a sharp linear transmittance spectrum, results in transmission modulation with a modulation depth of 36%. Finally, the modulation mechanism is studied by pump probe experiments« less

Nonlinear Interactions Between Shear Alfvén waves on LaPD

NASA Astrophysics Data System (ADS)

Brugman, B.; Carter, T. A.; Pribyl, P.; Dorland, W.; Quataert, E.

2003-10-01

Turbulent energy cascades may play a major role in many astrophysical phenomenon, such as accretion disks, as well as in terrestrial plasmas, as related to turbulent cross field transport. Existing theories have yet to be rigorously compared with experimental results and instead have relied on indirect measurements from astrophysics and solar probes. The turbulent interaction between counter propagating shear Alfvén waves and the interaction of Alfvén waves launched into a reflecting cavity represent two practical experiments relevant to the study of such cascades. These experiments will be conducted on the LaPD and the results compared to those calculated using the GS2 code, which makes use of the gyrokinetic approximation. Due to the effects of Landau damping it is believed that high amplitude Alfvén waves must be launched in order for nonlinear processes to be measurable; several means of launching such waves will be employed. The first method will employ the use of antenna launched Alfvén waves and the second will make use of waves launched by a source instability native to LaPD (J. E. Maggs, G. Morales, PRL, In Press). It is believed that both of these schemes will be capable of generating waves of sufficient magnitude to probe the nonlinear interactions of interest. Initial measurements show signs of nonlinear effects when shear Alfvén waves, generated by instabilities in the LaPD source, are launched into a closed cavity. These effects are manifested as coupling between a low frequency wave and the launched wave, as indicated by the creation of side bands centered on the frequency of the launched wave. Further measurements of this effect and wave sources will be presented.

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.

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.

Short-term effects of meteorological factors on hand, foot and mouth disease among children in Shenzhen, China: Non-linearity, threshold and interaction.

PubMed

Zhang, Zhen; Xie, Xu; Chen, Xiliang; Li, Yuan; Lu, Yan; Mei, Shujiang; Liao, Yuxue; Lin, Hualiang

2016-01-01

Various meteorological factors have been associated with hand, foot and mouth disease (HFMD) among children; however, fewer studies have examined the non-linearity and interaction among the meteorological factors. A generalized additive model with a log link allowing Poisson auto-regression and over-dispersion was applied to investigate the short-term effects daily meteorological factors on children HFMD with adjustment of potential confounding factors. We found positive effects of mean temperature and wind speed, the excess relative risk (ERR) was 2.75% (95% CI: 1.98%, 3.53%) for one degree increase in daily mean temperature on lag day 6, and 3.93% (95% CI: 2.16% to 5.73%) for 1m/s increase in wind speed on lag day 3. We found a non-linear effect of relative humidity with thresholds with the low threshold at 45% and high threshold at 85%, within which there was positive effect, the ERR was 1.06% (95% CI: 0.85% to 1.27%) for 1 percent increase in relative humidity on lag day 5. No significant effect was observed for rainfall and sunshine duration. For the interactive effects, we found a weak additive interaction between mean temperature and relative humidity, and slightly antagonistic interaction between mean temperature and wind speed, and between relative humidity and wind speed in the additive models, but the interactions were not statistically significant. This study suggests that mean temperature, relative humidity and wind speed might be risk factors of children HFMD in Shenzhen, and the interaction analysis indicates that these meteorological factors might have played their roles individually. Copyright © 2015 Elsevier B.V. All rights reserved.

Experimental quantification of nonlinear time scales in inertial wave rotating turbulence

NASA Astrophysics Data System (ADS)

Yarom, Ehud; Salhov, Alon; Sharon, Eran

2017-12-01

We study nonlinearities of inertial waves in rotating turbulence. At small Rossby numbers the kinetic energy in the system is contained in helical inertial waves with time dependence amplitudes. In this regime the amplitude variations time scales are slow compared to wave periods, and the spectrum is concentrated along the dispersion relation of the waves. A nonlinear time scale was extracted from the width of the spectrum, which reflects the intensity of nonlinear wave interactions. This nonlinear time scale is found to be proportional to (U.k ) -1, where k is the wave vector and U is the root-mean-square horizontal velocity, which is dominated by large scales. This correlation, which indicates the existence of turbulence in which inertial waves undergo weak nonlinear interactions, persists only for small Rossby numbers.

Nonlinear Bubble Dynamics And The Effects On Propagation Through Near-Surface Bubble Layers

NASA Astrophysics Data System (ADS)

Leighton, Timothy G.

2004-11-01

Nonlinear bubble dynamics are often viewed as the unfortunate consequence of having to use high acoustic pressure amplitudes when the void fraction in the near-surface oceanic bubble layer is great enough to cause severe attenuation (e.g. >50 dB/m). This is seen as unfortunate since existing models for acoustic propagation in bubbly liquids are based on linear bubble dynamics. However, the development of nonlinear models does more than just allow quantification of the errors associated with the use of linear models. It also offers the possibility of propagation modeling and acoustic inversions which appropriately incorporate the bubble nonlinearity. Furthermore, it allows exploration and quantification of possible nonlinear effects which may be exploited. As a result, high acoustic pressure amplitudes may be desirable even in low void fractions, because they offer opportunities to gain information about the bubble cloud from the nonlinearities, and options to exploit the nonlinearities to enhance communication and sonar in bubbly waters. This paper presents a method for calculating the nonlinear acoustic cross-sections, scatter, attenuations and sound speeds from bubble clouds which may be inhomogeneous. The method allows prediction of the time dependency of these quantities, both because the cloud may vary and because the incident acoustic pulse may have finite and arbitrary time history. The method can be readily adapted for bubbles in other environments (e.g. clouds of interacting bubbles, sediments, structures, in vivo, reverberant conditions etc.). The possible exploitation of bubble acoustics by marine mammals, and for sonar enhancement, is explored.

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

PubMed

Rademacher, Georg; Warm, Stefan; Petermann, Klaus

2015-01-12

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

Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

NASA Astrophysics Data System (ADS)

Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.

2005-03-01

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

Experimental study of isolas in nonlinear systems featuring modal interactions

PubMed Central

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

2018-01-01

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

Influence of nonlinear detuning at plasma wavebreaking threshold on backward Raman compression of non-relativistic laser pulses

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Fraiman, G. M.; Jia, Q.; Fisch, N. J.

2018-06-01

Taking into account the nonlinear dispersion of the plasma wave, the fluid equations for the three-wave (Raman) interaction in plasmas are derived. It is found that, in some parameter regimes, the nonlinear detuning resulting from the plasma wave dispersion during Raman compression limits the plasma wave amplitude to noticeably below the generally recognized wavebreaking threshold. Particle-in-cell simulations confirm the theoretical estimates. For weakly nonlinear dispersion, the detuning effect can be counteracted by pump chirping or, equivalently, by upshifting slightly the pump frequency, so that the frequency-upshifted pump interacts with the seed at the point where the plasma wave enters the nonlinear stage.

Shoaling of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.C.; Butman, B.; Pineda, J.

2008-01-01

The shoaling of the nonlinear internal tide in Massachusetts Bay is studied with a fully nonlinear and nonhydrostatic model. The results are compared with current and temperature observations obtained during the August 1998 Massachusetts Bay Internal Wave Experiment and observations from a shorter experiment which took place in September 2001. The model shows how the approaching nonlinear undular bore interacts strongly with a shoaling bottom, offshore of where KdV theory predicts polarity switching should occur. It is shown that the shoaling process is dominated by nonlinearity, and the model results are interpreted with the aid of a two-layer nonlinear but hydrostatic model. After interacting with the shoaling bottom, the undular bore emerges on the shallow shelf inshore of the 30-m isobath as a nonlinear internal tide with a range of possible shapes, all of which are found in the available observational record. Copyright 2008 by the American Geophysical Union.

Laser cutting of ultra-thin glasses based on a nonlinear laser interaction effect

NASA Astrophysics Data System (ADS)

Chen, Jian; Wu, Zhouling

2013-07-01

Glass panel substrates have been widely used in consumer electronics such as in flat panel TVs, laptops, and cell phones. With the advancement in the industry, the glass substrates are becoming thinner and stronger for reduced weight and volume, which brings great challenges for traditional mechanical processes in terms of cut quality, yield, and throughput. Laser glass cutting provides a non-contact process with minimum impact and superior quality compared to the mechanical counterparts. In this paper, we presented recent progresses in advanced laser processing of ultra-thin glass substrates, especially laser-cutting of ultra-thin glasses by a high power laser through a nonlinear interaction effect. Our results indicate that this technique has great potential of application for mass production of ultra-thin glass substrates.

Optical pulse generation in a transistor laser via intra-cavity photon-assisted tunneling and excess base carrier redistribution

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

Feng, M.; Iverson, E. W.; Wang, C. Y.

2015-11-02

For a direct-gap semiconductor (e.g., a p-n junction), photon-assisted tunneling is known to exhibit a high nonlinear absorption. In a transistor laser, as discussed here, the coherent photons generated at the quantum well interact with the collector junction field and “assist” electron tunneling from base to collector, thus resulting in the nonlinear modulation of the laser and the realization of optical pulse generation. 1 and 2 GHz optical pulses are demonstrated in the transistor laser using collector voltage control.

Probing Atomic Dynamics and Structures Using Optical Patterns

NASA Astrophysics Data System (ADS)

Schmittberger, Bonnie L.; Gauthier, Daniel J.

2015-05-01

Pattern formation is a widely studied phenomenon that can provide fundamental insights into nonlinear systems. Emergent patterns in cold atoms are of particular interest in condensed matter physics and quantum information science because one can relate optical patterns to spatial structures in the atoms. In our experimental system, we study multimode optical patterns generated from a sample of cold, thermal atoms. We observe this nonlinear optical phenomenon at record low input powers due to the highly nonlinear nature of the spatial bunching of atoms in an optical lattice. We present a detailed study of the dynamics of these bunched atoms during optical pattern formation. We show how small changes in the atomic density distribution affect the symmetry of the generated patterns as well as the nature of the nonlinearity that describes the light-atom interaction. We gratefully acknowledge the financial support of the National Science Foundation through Grant #PHY-1206040.

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.

Sensitivity analysis and nonlinearity assessment of steam cracking furnace process

NASA Astrophysics Data System (ADS)

Rosli, M. N.; Sudibyo, Aziz, N.

2017-11-01

In this paper, sensitivity analysis and nonlinearity assessment of cracking furnace process are presented. For the sensitivity analysis, the fractional factorial design method is employed as a method to analyze the effect of input parameters, which consist of four manipulated variables and two disturbance variables, to the output variables and to identify the interaction between each parameter. The result of the factorial design method is used as a screening method to reduce the number of parameters, and subsequently, reducing the complexity of the model. It shows that out of six input parameters, four parameters are significant. After the screening is completed, step test is performed on the significant input parameters to assess the degree of nonlinearity of the system. The result shows that the system is highly nonlinear with respect to changes in an air-to-fuel ratio (AFR) and feed composition.

Evolution of cooperation on complex networks with synergistic and discounted group interactions

NASA Astrophysics Data System (ADS)

Zhou, Lei; Li, Aming; Wang, Long

2015-06-01

In the real world individuals often engage in group interactions and their payoffs are determined by many factors, including the typical nonlinear interactions, i.e., synergy and discounting. Previous literatures assume that individual payoffs are either synergistically enhanced or discounted with the additional cooperators. Such settings ignore the interplay of these two factors, which is in sharp contrast with the fact that they ubiquitously coexist. Here we investigate how the coexistence and periodical switching of synergistic and discounted group interactions affect the evolution of cooperation on various complex networks. We show that scale-free networks facilitate the emergence of cooperation in terms of fixation probability for group interactions. With nonlinear interactions the heterogeneity of the degree acts as a double-edged sword: below the neutral drift it is the best for cooperation while above the neutral drift it instead provides the least opportunity for cooperators to be fixed. The advantages of the heterogeneity fade as interactive attributes switch between synergy and discounting, which suggests that the heterogeneity of population structures cannot favor cooperators in group interactions even with simple nonlinear interactions. Nonetheless, scale-free networks always guarantee cooperators the fastest rate of fixation. Our work implies that even very simple nonlinear group interactions could greatly shape the fixation probability and fixation time of cooperators in structured populations indicated by complex networks.

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

Getting off the Straight and Narrow: Exploiting Non-Linear, Interactive Narrative Structures in Digital Stories for Language Teaching

ERIC Educational Resources Information Center

Prosser, Andrew

2014-01-01

Digital storytelling is already used extensively in language education. Web documentaries, particularly in terms of design and narrative structure, provide an extension of the digital storytelling concept, specifically in terms of increased interactivity. Using a model of interactive, non-linear storytelling, originally derived from computer game…

Change of nonlinear acoustics in ASME grade 122 steel welded joint during creep

NASA Astrophysics Data System (ADS)

Ohtani, Toshihiro; Honma, Takumi; Ishii, Yutaka; Tabuchi, Masaaki; Hongo, Hiromichi; Hirao, Masahiko

2016-02-01

In this paper, we described the changes of two nonlinear acoustic characterizations; resonant frequency shift and three-wave interaction, with electromagnetic acoustic resonance (EMAR) throughout the creep life in the welded joints of ASME Grade 122, one of high Cr ferritic heat resisting steels. EMAR was a combination of the resonant acoustic technique with a non-contact electromagnetic acoustic transducer (EMAT). These nonlinear acoustic parameters decreased from the start to 50% of creep life. After slightly increased, they rapidly increased from 80% of creep life to rupture. We interpreted these phenomena in terms of dislocation recovery, recrystallization, and restructuring related to the initiation and growth of creep void, with support from the SEM and TEM observation.

Joint Entropy for Space and Spatial Frequency Domains Estimated from Psychometric Functions of Achromatic Discrimination

PubMed Central

Silveira, Vladímir de Aquino; Souza, Givago da Silva; Gomes, Bruno Duarte; Rodrigues, Anderson Raiol; Silveira, Luiz Carlos de Lima

2014-01-01

We used psychometric functions to estimate the joint entropy for space discrimination and spatial frequency discrimination. Space discrimination was taken as discrimination of spatial extent. Seven subjects were tested. Gábor functions comprising unidimensionalsinusoidal gratings (0.4, 2, and 10 cpd) and bidimensionalGaussian envelopes (1°) were used as reference stimuli. The experiment comprised the comparison between reference and test stimulithat differed in grating's spatial frequency or envelope's standard deviation. We tested 21 different envelope's standard deviations around the reference standard deviation to study spatial extent discrimination and 19 different grating's spatial frequencies around the reference spatial frequency to study spatial frequency discrimination. Two series of psychometric functions were obtained for 2%, 5%, 10%, and 100% stimulus contrast. The psychometric function data points for spatial extent discrimination or spatial frequency discrimination were fitted with Gaussian functions using the least square method, and the spatial extent and spatial frequency entropies were estimated from the standard deviation of these Gaussian functions. Then, joint entropy was obtained by multiplying the square root of space extent entropy times the spatial frequency entropy. We compared our results to the theoretical minimum for unidimensional Gábor functions, 1/4π or 0.0796. At low and intermediate spatial frequencies and high contrasts, joint entropy reached levels below the theoretical minimum, suggesting non-linear interactions between two or more visual mechanisms. We concluded that non-linear interactions of visual pathways, such as the M and P pathways, could explain joint entropy values below the theoretical minimum at low and intermediate spatial frequencies and high contrasts. These non-linear interactions might be at work at intermediate and high contrasts at all spatial frequencies once there was a substantial decrease in joint entropy for these stimulus conditions when contrast was raised. PMID:24466158

Joint entropy for space and spatial frequency domains estimated from psychometric functions of achromatic discrimination.

PubMed

Silveira, Vladímir de Aquino; Souza, Givago da Silva; Gomes, Bruno Duarte; Rodrigues, Anderson Raiol; Silveira, Luiz Carlos de Lima

2014-01-01

We used psychometric functions to estimate the joint entropy for space discrimination and spatial frequency discrimination. Space discrimination was taken as discrimination of spatial extent. Seven subjects were tested. Gábor functions comprising unidimensionalsinusoidal gratings (0.4, 2, and 10 cpd) and bidimensionalGaussian envelopes (1°) were used as reference stimuli. The experiment comprised the comparison between reference and test stimulithat differed in grating's spatial frequency or envelope's standard deviation. We tested 21 different envelope's standard deviations around the reference standard deviation to study spatial extent discrimination and 19 different grating's spatial frequencies around the reference spatial frequency to study spatial frequency discrimination. Two series of psychometric functions were obtained for 2%, 5%, 10%, and 100% stimulus contrast. The psychometric function data points for spatial extent discrimination or spatial frequency discrimination were fitted with Gaussian functions using the least square method, and the spatial extent and spatial frequency entropies were estimated from the standard deviation of these Gaussian functions. Then, joint entropy was obtained by multiplying the square root of space extent entropy times the spatial frequency entropy. We compared our results to the theoretical minimum for unidimensional Gábor functions, 1/4π or 0.0796. At low and intermediate spatial frequencies and high contrasts, joint entropy reached levels below the theoretical minimum, suggesting non-linear interactions between two or more visual mechanisms. We concluded that non-linear interactions of visual pathways, such as the M and P pathways, could explain joint entropy values below the theoretical minimum at low and intermediate spatial frequencies and high contrasts. These non-linear interactions might be at work at intermediate and high contrasts at all spatial frequencies once there was a substantial decrease in joint entropy for these stimulus conditions when contrast was raised.

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.

Nonlinear Optical Interactions in Semiconductors.

DTIC Science & Technology

1985-12-10

Physique du Solide et Energie Solaire We had on-going interaction with Dr. Christian Verie on the growth of high quality narrow-gap semiconductor crystals...The band gap energy of the semiconductor decreases with increasing temperature. Consequently, the absorption of light in the energy region of the...gas and, more importantly, will modulate the electron energy at the difference frequency, wI - 02" Under ordinary circumstances such an energy (or

Multiphoton excitation and high-harmonics generation in topological insulator.

PubMed

Avetissian, H K; Avetissian, A K; Avchyan, B R; Mkrtchian, G F

2018-05-10

Multiphoton interaction of coherent electromagnetic radiation with 2D metallic carriers confined on the surface of the 3D topological insulator is considered. A microscopic theory describing the nonlinear interaction of a strong wave and metallic carriers with many-body Coulomb interaction is developed. The set of integrodifferential equations for the interband polarization and carrier occupation distribution is solved numerically. Multiphoton excitation of Fermi-Dirac sea of 2D massless carriers is considered for a THz pump wave. It is shown that in the moderately strong pump wave field along with multiphoton interband/intraband transitions the intense radiation of high harmonics takes place.

Multiphoton excitation and high-harmonics generation in topological insulator

NASA Astrophysics Data System (ADS)

Avetissian, H. K.; Avetissian, A. K.; Avchyan, B. R.; Mkrtchian, G. F.

2018-05-01

Multiphoton interaction of coherent electromagnetic radiation with 2D metallic carriers confined on the surface of the 3D topological insulator is considered. A microscopic theory describing the nonlinear interaction of a strong wave and metallic carriers with many-body Coulomb interaction is developed. The set of integrodifferential equations for the interband polarization and carrier occupation distribution is solved numerically. Multiphoton excitation of Fermi–Dirac sea of 2D massless carriers is considered for a THz pump wave. It is shown that in the moderately strong pump wave field along with multiphoton interband/intraband transitions the intense radiation of high harmonics takes place.

Routine Discovery of Complex Genetic Models using Genetic Algorithms

PubMed Central

Moore, Jason H.; Hahn, Lance W.; Ritchie, Marylyn D.; Thornton, Tricia A.; White, Bill C.

2010-01-01

Simulation studies are useful in various disciplines for a number of reasons including the development and evaluation of new computational and statistical methods. This is particularly true in human genetics and genetic epidemiology where new analytical methods are needed for the detection and characterization of disease susceptibility genes whose effects are complex, nonlinear, and partially or solely dependent on the effects of other genes (i.e. epistasis or gene-gene interaction). Despite this need, the development of complex genetic models that can be used to simulate data is not always intuitive. In fact, only a few such models have been published. We have previously developed a genetic algorithm approach to discovering complex genetic models in which two single nucleotide polymorphisms (SNPs) influence disease risk solely through nonlinear interactions. In this paper, we extend this approach for the discovery of high-order epistasis models involving three to five SNPs. We demonstrate that the genetic algorithm is capable of routinely discovering interesting high-order epistasis models in which each SNP influences risk of disease only through interactions with the other SNPs in the model. This study opens the door for routine simulation of complex gene-gene interactions among SNPs for the development and evaluation of new statistical and computational approaches for identifying common, complex multifactorial disease susceptibility genes. PMID:20948983

The mechanism by which nonlinearity sustains turbulence in plane Couette flow

NASA Astrophysics Data System (ADS)

Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.

2018-04-01

Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

Squeezed-light generation in a nonlinear planar waveguide with a periodic corrugation

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

Perina, Jan Jr.; Haderka, Ondrej; Sibilia, Concita

Two-mode nonlinear interaction (second-harmonic and second-subharmonic generation) in a planar waveguide with a small periodic corrugation at the surface is studied. Scattering of the interacting fields on the corrugation leads to constructive interference that enhances the nonlinear process provided that all the interactions are phase matched. Conditions for the overall phase matching are found. Compared with a perfectly quasi-phase-matched waveguide, better values of squeezing as well as higher intensities are reached under these conditions. Procedure for finding optimum values of parameters for squeezed-light generation is described.

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 interactions between electromagnetic waves and electron plasma oscillations in quantum plasmas.

PubMed

Shukla, P K; Eliasson, B

2007-08-31

We consider nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in a dense quantum plasma, taking into account the electron density response in the presence of the relativistic ponderomotive force and mass increase in the CPEM wave fields. The dynamics of the CPEM waves and EPOs is governed by the two coupled nonlinear Schrödinger equations and Poisson's equation. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave pipes in the electron density hole that is associated with a positive potential distribution in our dense plasma. The relevance of our investigation to the next generation intense laser-solid density plasma interaction experiments is discussed.

Numerical model for the weakly nonlinear propagation of sound through turbulence

NASA Technical Reports Server (NTRS)

Lipkens, Bart; Blanc-Benon, Philippe

1994-01-01

When finite amplitude (or intense) sound, such as a sonic boom, propagates through a turbulent atmosphere, the propagation is strongly affected by the turbulence. The interaction between sound and turbulence has mostly been studied as a linear phenomenon, i.e., the nonlinear behavior of the intense sound has been neglected. It has been shown that turbulence has an effect on the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. Peak pressure and rise time are important factors that determine the loudness of the sonic boom when heard outdoors. However, the interaction between turbulence and nonlinear effects has mostly not been included in propagation studies of sonic booms. It is therefore important to investigate the influence of acoustical nonlinearity on the interaction of intense sound with turbulence.

Observation of nonlinear optical interactions of ultralow levels of light in a tapered optical nanofiber embedded in a hot rubidium vapor.

PubMed

Spillane, S M; Pati, G S; Salit, K; Hall, M; Kumar, P; Beausoleil, R G; Shahriar, M S

2008-06-13

We report the observation of low-light level optical interactions in a tapered optical nanofiber (TNF) embedded in a hot rubidium vapor. The small optical mode area plays a significant role in the optical properties of the hot vapor Rb-TNF system, allowing nonlinear optical interactions with nW level powers even in the presence of transit-time dephasing rates much larger than the intrinsic linewidth. We demonstrate nonlinear absorption and V-type electromagnetically induced transparency with cw powers below 10 nW, comparable to the best results in any Rb-optical waveguide system. The good performance and flexibility of the Rb-TNF system makes it a very promising candidate for ultralow power resonant nonlinear optical applications.

Nonlinear magnetoelectric effects at high magnetic field amplitudes in composite multiferroics

NASA Astrophysics Data System (ADS)

Fetisov, L. Y.; Burdin, D. A.; Ekonomov, N. A.; Chashin, D. V.; Zhang, J.; Srinivasan, G.; Fetisov, Y. K.

2018-04-01

Magnetoelectric effects (ME) in ferromagnetic-ferroelectric layered composites arise due to magnetostriction and piezoelectric effect in the ferroic phases and are mediated by mechanical strain. The ME coupling strength in such composites could be measured by electrical response to an applied ac magnetic field h and a bias magnetic field H. The coupling, in general, is linear for small ac field amplitudes, but one expects nonlinear ME interactions for high field strengths since the dependence of magnetostriction λ on magnetic fields is nonlinear. Here we report on nonlinear voltage response of a composite of ferromagnetic Metglas and piezoelectric lanthanum gallium tantalate (langatate) subjected to an ac and a bias magnetic fields, resulting in the generation of voltages at harmonics of the frequency of h. The dependences of the ME voltage of the first four harmonics on the magnetic fields for H  =  0–20 Oe and h  =  0–50 Oe were measured. Up to a hundred harmonics were observed in the voltage versus frequency spectra and was indicative of high nonlinearity of the ME coupling in the multiferroic structure. It is shown that for h smaller than the saturation magnetic field H S for magnetostriction in the ferromagnetic layer, the amplitudes of the ME voltages are proportional to the derivatives of λ with respect to H and show a power-law dependence on the pumping field amplitude A n (H) ~ λ (n)(H)h n . We discuss a procedure for estimating the amplitudes of the harmonics for large pumping fields h, on the order of H S. The nonlinear ME effects in the composites are of interest for application in signal processing devices and highly sensitive magnetic field sensors.

Nondestructive Evaluation of Metal Fatigue Using Nonlinear Acoustics

NASA Technical Reports Server (NTRS)

Cantrell, John H., Jr.

2008-01-01

Safe-life and damage-tolerant design philosophies of high performance structures have driven the development of various methods to evaluate nondestructively the accumulation of damage in such structures resulting from cyclic loading. Although many techniques have proven useful, none has been able to provide an unambiguous, quantitative assessment of damage accumulation at each stage of fatigue from the virgin state to fracture. A method based on nonlinear acoustics is shown to provide such a means to assess the state of metal fatigue. The salient features of an analytical model are presented of the microelastic-plastic nonlinearities resulting from the interaction of an acoustic wave with fatigue-generated dislocation substructures and cracks that predictably evolve during the metal fatigue process. The interaction is quantified by the material (acoustic) nonlinearity parameter extracted from acoustic harmonic generation measurements. The parameters typically increase monotonically by several hundred percent over the fatigue life of the metal, thus providing a unique measure of the state of fatigue. Application of the model to aluminum alloy 2024-T4, 410Cb stainless steel, and IN100 nickel-base superalloy specimens fatigued using different loading conditions yields good agreement between theory and experiment. Application of the model and measurement technique to the on-site inspection of steam turbine blades is discussed.

Turbulence of electrostatic electron cyclotron harmonic waves observed by Ogo 5.

NASA Technical Reports Server (NTRS)

Oya, H.

1972-01-01

Analysis of VLF emissions that have been observed near 3/2, 5/2, and 7/2 f sub H by Ogo 5 in the magnetosphere (f sub H is the electron cyclotron frequency) in the light of the mechanism used for the diffuse plasma resonance f sub Dn observed by Alouette 2 and Isis 1. The VLF emission is considered to be generated by nonlinear coupling mechanisms in certain portions of the observation as the f sub Dn is enhanced by its association with nonlinear wave-particle interaction of the electrostatic electron cyclotron harmonic wave, including the instability due to the nonlinear inverse Landau damping mechanism in the turbulence. The difference between the two observations is in the excitation mechanism of the turbulence; the turbulence in the plasma trough detected by Ogo 5 is due to natural origins, whereas the ionospheric topside sounder makes the plasma wave turbulence artificially by submitting strong stimulation pulses. Electron density values in the plasma trough are deduced by applying the f sub Dn-f sub N/f sub H relationship obtained from the Alouette 2 experiment as well as by applying the condition for the wave-particle nonlinear interactions. The electron density values reveal good agreement with the ion density values observed simultaneously by the highly sensitive ion mass spectrometer.

How safe is gamete micromanipulation by laser tweezers?

NASA Astrophysics Data System (ADS)

Koenig, Karsten; Tromberg, Bruce J.; Tadir, Yona; Berns, Michael W.

1998-04-01

Laser tweezers, used as novel sterile micromanipulation tools of living cells, are employed in laser-assisted in vitro fertilization (IVF). For example, controlled spermatozoa transport with 1064 nm tweezers to human egg cells has been performed in European clinics in cases of male infertility. The interaction of approximately 100 mW near infrared (NIR) trapping beams at MW/cm2 intensity with human gametes results in low mean less than 2 K temperature increases and less than 100 pN trapping forces. Therefore, photothermal or photomechanical induced destructive effects appear unlikely. However, the high photon flux densities may induce simultaneous absorption of two NIR photons resulting in nonlinear interactions. These nonlinear interactions imply non-resonant two-photon excitation of endogenous cellular chromophores. In the case of less than 800 nm tweezers, UV- like damage effects may occur. The destructive effect is amplified when multimode cw lasers are used as tweezer sources due to longitudinal mode-beating effects and partial mode- locking. Spermatozoa damage within seconds using 760 nm traps due to formation of unstable ps pulses in a cw Ti:Sa ring laser is demonstrated. We recommend the use of greater than or equal to 800 nm traps for optical gamete micromanipulation. To our opinion, further basic studies on the influence of nonlinear effects of laser tweezers on human gamete are necessary.

A Multiscale Nested Modeling Framework to Simulate the Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves

DTIC Science & Technology

2015-09-30

We aim at understanding the impact of tidal , seasonal, and mesoscale variability of the internal wave field and how it influences the surface waves ...Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves

Phase-space topography characterization of nonlinear ultrasound waveforms.

PubMed

Dehghan-Niri, Ehsan; Al-Beer, Helem

2018-03-01

Fundamental understanding of ultrasound interaction with material discontinuities having closed interfaces has many engineering applications such as nondestructive evaluation of defects like kissing bonds and cracks in critical structural and mechanical components. In this paper, to analyze the acoustic field nonlinearities due to defects with closed interfaces, the use of a common technique in nonlinear physics, based on a phase-space topography construction of ultrasound waveform, is proposed. The central idea is to complement the "time" and "frequency" domain analyses with the "phase-space" domain analysis of nonlinear ultrasound waveforms. A nonlinear time series method known as pseudo phase-space topography construction is used to construct equivalent phase-space portrait of measured ultrasound waveforms. Several nonlinear models are considered to numerically simulate nonlinear ultrasound waveforms. The phase-space response of the simulated waveforms is shown to provide different topographic information, while the frequency domain shows similar spectral behavior. Thus, model classification can be substantially enhanced in the phase-space domain. Experimental results on high strength aluminum samples show that the phase-space transformation provides a unique detection and classification capabilities. The Poincaré map of the phase-space domain is also used to better understand the nonlinear behavior of ultrasound waveforms. It is shown that the analysis of ultrasound nonlinearities is more convenient and informative in the phase-space domain than in the frequency domain. Copyright © 2017 Elsevier B.V. All rights reserved.

APPLIED OPTICS. Overcoming Kerr-induced capacity limit in optical fiber transmission.

PubMed

Temprana, E; Myslivets, E; Kuo, B P-P; Liu, L; Ataie, V; Alic, N; Radic, S

2015-06-26

Nonlinear optical response of silica imposes a fundamental limit on the information transfer capacity in optical fibers. Communication beyond this limit requires higher signal power and suppression of nonlinear distortions to prevent irreversible information loss. The nonlinear interaction in silica is a deterministic phenomenon that can, in principle, be completely reversed. However, attempts to remove the effects of nonlinear propagation have led to only modest improvements, and the precise physical mechanism preventing nonlinear cancellation remains unknown. We demonstrate that optical carrier stability plays a critical role in canceling Kerr-induced distortions and that nonlinear wave interaction in silica can be substantially reverted if optical carriers possess a sufficient degree of mutual coherence. These measurements indicate that fiber information capacity can be notably increased over previous estimates. Copyright © 2015, American Association for the Advancement of Science.

Uranium(IV) Interaction with Aqueous/Solid Interfaces Studied by Nonlinear Optics

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

Geiger, Franz

2015-03-27

This is the Final Technical Report for "Uranium(IV) Interaction with Aqueous/Solid Interfaces Studied by Nonlinear Optics", by Franz M. Geiger, PI, from Northwestern University, IL, USA, Grant Number SC0004101 and/or DE-PS02-ER09-07.

Establishing nonlinearity thresholds with ultraintense X-ray pulses

DOE PAGES

Szlachetko, Jakub; Hoszowska, Joanna; Dousse, Jean-Claude; ...

2016-09-13

X-ray techniques have evolved over decades to become highly refined tools for a broad range of investigations. Importantly, these approaches rely on X-ray measurements that depend linearly on the number of incident X-ray photons. The advent of X-ray free electron lasers (XFELs) is opening the ability to reach extremely high photon numbers within ultrashort X-ray pulse durations and is leading to a paradigm shift in our ability to explore nonlinear X-ray signals. However, the enormous increase in X-ray peak power is a double-edged sword with new and exciting methods being developed but at the same time well-established techniques proving unreliable.more » Consequently, accurate knowledge about the threshold for nonlinear X-ray signals is essential. Here in this paper we report an X-ray spectroscopic study that reveals important details on the thresholds for nonlinear X-ray interactions. By varying both the incident X-ray intensity and photon energy, we establish the regimes at which the simplest nonlinear process, two-photon X-ray absorption (TPA), can be observed. From these measurements we can extract the probability of this process as a function of photon energy and confirm both the nature and sub-femtosecond lifetime of the virtual intermediate electronic state.« less

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

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.

Nonlinear modeling of wave-topography interactions, shear instabilities and shear induced wave breaking using vortex method

NASA Astrophysics Data System (ADS)

Guha, Anirban

2017-11-01

Theoretical studies on linear shear instabilities as well as different kinds of wave interactions often use simple velocity and/or density profiles (e.g. constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Moreover, such simple profiles provide a minimal model to obtain a mechanistic understanding of shear instabilities. Here we have extended this minimal paradigm into nonlinear domain using vortex method. Making use of unsteady Bernoulli's equation in presence of linear shear, and extending Birkhoff-Rott equation to multiple interfaces, we have numerically simulated the interaction between multiple fully nonlinear waves. This methodology is quite general, and has allowed us to simulate diverse problems that can be essentially reduced to the minimal system with interacting waves, e.g. spilling and plunging breakers, stratified shear instabilities (Holmboe, Taylor-Caulfield, stratified Rayleigh), jet flows, and even wave-topography interaction problem like Bragg resonance. We found that the minimal models capture key nonlinear features (e.g. wave breaking features like cusp formation and roll-ups) which are observed in experiments and/or extensive simulations with smooth, realistic profiles.

A quantum description of linear, and non-linear optical interactions in arrays of plasmonic nanoparticles

NASA Astrophysics Data System (ADS)

Arabahmadi, Ehsan; Ahmadi, Zabihollah; Rashidian, Bizhan

2018-06-01

A quantum theory for describing the interaction of photons and plasmons, in one- and two-dimensional arrays is presented. Ohmic losses and inter-band transitions are not considered. We use macroscopic approach, and quantum field theory methods including S-matrix expansion, and Feynman diagrams for this purpose. Non-linear interactions are also studied, and increasing the probability of such interactions, and its application are also discussed.

Causal inference in nonlinear systems: Granger causality versus time-delayed mutual information

NASA Astrophysics Data System (ADS)

Li, Songting; Xiao, Yanyang; Zhou, Douglas; Cai, David

2018-05-01

The Granger causality (GC) analysis has been extensively applied to infer causal interactions in dynamical systems arising from economy and finance, physics, bioinformatics, neuroscience, social science, and many other fields. In the presence of potential nonlinearity in these systems, the validity of the GC analysis in general is questionable. To illustrate this, here we first construct minimal nonlinear systems and show that the GC analysis fails to infer causal relations in these systems—it gives rise to all types of incorrect causal directions. In contrast, we show that the time-delayed mutual information (TDMI) analysis is able to successfully identify the direction of interactions underlying these nonlinear systems. We then apply both methods to neuroscience data collected from experiments and demonstrate that the TDMI analysis but not the GC analysis can identify the direction of interactions among neuronal signals. Our work exemplifies inference hazards in the GC analysis in nonlinear systems and suggests that the TDMI analysis can be an appropriate tool in such a case.

Studies of central interactions of Si ions at 14.5 x A GeV/c in Au and Cu

NASA Astrophysics Data System (ADS)

Eiseman, S. E.; Etkin, A.; Foley, K. J.; Hackenburg, R. W.; Longacre, R. S.; Love, W. A.; Morris, T. W.; Platner, E. D.; Saulys, A. C.; Lindenbaum, S. J.

Understanding the growth and saturation of parametric instabilities in laser-produced plasmas requires knowledge of the nonlinear properties of the instabilities and their interaction with each other. Nonlinear behavior of parametric instabilities, which are usually associated with unique optical features, were evidenced in numerous experiments on a variety of laser facilities. Four examples of nonlinear behavior in laser-produced plasmas are discussed: nonlinear stimulated Brillouin scattering spectra, suppression of stimulated Raman scattering by stimulated Brillouin scattering, the parametric decay instability and the onset of turbulence, and the transition to bursting behavior of the two-plasmon decay instability. Experiments are discussed that demonstrate the nonlinear effects which occur as a consequence.

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

PubMed

Balzani, Daniel; Deparis, Simone; Fausten, Simon; Forti, Davide; Heinlein, Alexander; Klawonn, Axel; Quarteroni, Alfio; Rheinbach, Oliver; Schröder, Joerg

2016-10-01

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

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.

Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

The existence of electron-acoustic shock waves and their interactions in a non-Maxwellian plasma with q-nonextensive distributed electrons

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

Han, Jiu-Ning; He, Yong-Lin; Han, Zhen-Hai

2013-07-15

We present a theoretical investigation for the nonlinear interaction between electron-acoustic shock waves in a nonextensive two-electron plasma. The interaction is governed by a pair of Korteweg-de Vries-Burgers equations. We focus on studying the colliding effects on the propagation of shock waves, more specifically, we have studied the effects of plasma parameters, i.e., the nonextensive parameter q, the “hot” to “cold” electron number density ratio α, and the normalized electron kinematic viscosity η{sub 0} on the trajectory changes (phase shifts) of shock waves. It is found that there are trajectory changes (phase shifts) for both colliding shock waves in themore » present plasma system. We also noted that the nonlinearity has no decisive effect on the trajectory changes, the occurrence of trajectory changes may be due to the combined role played by the dispersion and dissipation of the nonlinear structure. Our theoretical study may be beneficial to understand the propagation and interaction of nonlinear electrostatic waves and may brings a possibility to develop the nonlinear theory of electron-acoustic waves in astrophysical plasma systems.« less

PREFACE: Ultrafast biophotonics Ultrafast biophotonics

NASA Astrophysics Data System (ADS)

Gu, Min; Reid, Derryck; Ben-Yakar, Adela

2010-08-01

The use of light to explore biology can be traced to the first observations of tissue made with early microscopes in the mid-seventeenth century, and has today evolved into the discipline which we now know as biophotonics. This field encompasses a diverse range of activities, each of which shares the common theme of exploiting the interaction of light with biological material. With the rapid advancement of ultrafast optical technologies over the last few decades, ultrafast lasers have increasingly found applications in biophotonics, to the extent that the distinctive new field of ultrafast biophotonics has now emerged, where robust turnkey ultrafast laser systems are facilitating cutting-edge studies in the life sciences to take place in everyday laboratories. The broad spectral bandwidths, precision timing resolution, low coherence and high peak powers of ultrafast optical pulses provide unique opportunities for imaging and manipulating biological systems. Time-resolved studies of bio-molecular dynamics exploit the short pulse durations from such lasers, while other applications such as optical coherence tomography benefit from the broad optical bandwidths possible by using super-continuum generation and additionally allowing for high speed imaging with speeds as high as 47 000 scans per second. Continuing progress in laser-system technology is accelerating the adoption of ultrafast techniques across the life sciences, both in research laboratories and in clinical applications, such as laser-assisted in situ keratomileusis (LASIK) eye surgery. Revolutionizing the field of optical microscopy, two-photon excitation fluorescence (TPEF) microscopy has enabled higher spatial resolution with improved depth penetration into biological specimens. Advantages of this nonlinear optical process include: reduced photo-interactions, allowing for extensive imaging time periods; simultaneously exciting multiple fluorescent molecules with only one excitation wavelength; and reduced chromatic aberration effects. These extensive advantages have led to further exploration of nonlinear processes including second-harmonic generation (SHG) microscopy and third-harmonic generation (THG) microscopy. Second-harmonic generation has provided biologists with an extremely powerful tool for generating contrast in biological imaging, with the additional benefit of non-invasive three-dimensional imaging. The recent popularity of THG microscopy is largely due to the fact that three-dimensional imaging is achievable without the need for any labels, but rather relying on the intrinsic properties of the biological specimen itself. This optical nonlinear technique has attracted much attention recently from the biological community due to its non-invasive capabilities. Users of ultrafast lasers in the biological and medical fields are becoming a fast-growing community, employing pulse-shaping microscopy, resolution-enhancing microscopy techniques, linear and nonlinear micro-spectroscopy, functional deep-tissue imaging, optical coherence tomography, nonlinear fluorescence microscopy, molecular imaging and control, harmonic microscopy and femtosecond lifetime imaging, for cutting-edge research concerning the interaction of light with biological dynamics. The adaptability of ultrafast lasers to interact with a large array of materials through nonlinear excitation has enabled precise control of laser fluence allowing for highly localized material interactions, permitting micro-structured fabricated surfaces. The resultant multi-dimensional fabricated micro-structures are capable of replicating and/or manipulating microenvironments for controlled cell biology. In this special issue of Journal of Optics readers have a chance to view a collection of new contributions to the growing research field of ultrafast biophotonics. They are presented with recent advances in ultrafast technology applied to biological and medical investigations, where topics include advances in the visualization and identification of photo-reaction dynamics of biological functions under relevant physiological conditions, theoretically proposed imaging designs for obtaining super-resolved optical sectioned images in single exposures and fabricated micro-structured surfaces for biological micro-environments. We hope the collection will stimulate innovative new research in this growing field by showcasing new techniques for the visualization and manipulation of complex biological systems using linear and and nonlinear optical processes. Professor Min Gu would like to acknowledge Dr Betty Kouskousis for her contribution and support towards this editorial.

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.; Sandham, N. D.; Hadjadj, A.; Kwak, Dochan (Technical Monitor)

2000-01-01

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

NASA Astrophysics Data System (ADS)

Manfredi, Sabato

2016-06-01

Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.

High Power, Pulsed, RF Generation from Nonlinear Lumped Element Transmission Lines (NLETLs)

DTIC Science & Technology

2011-02-05

specific to solitons. including both overtaking and head on collision interactions and the Fermi- Pasta -Ulam recurrence phenomenon [50]. Contributions by...simulation has indicated the initiation of this curious effect. The Fernii- Pasta -Ulain recurrence phenomena, whereby a sinusoidal excitation applied to a

Bayesian parameter estimation for nonlinear modelling of biological pathways.

PubMed

Ghasemi, Omid; Lindsey, Merry L; Yang, Tianyi; Nguyen, Nguyen; Huang, Yufei; Jin, Yu-Fang

2011-01-01

The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems. Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.

Transfer of dipolar gas through the discrete localized mode.

PubMed

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

2013-12-01

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

Controlling modal interactions in lasers for frequency selection and power enhancement

NASA Astrophysics Data System (ADS)

Ge, Li

2015-03-01

The laser is an out-of-equilibrium non-linear wave system where the interplay of the cavity geometry and non-linear wave interactions determines the self-organized oscillation frequencies and the associated spatial field patterns. Using the correspondence between nonlinear and linear systems, we propose a simple and systematic method to achieve selective excitation of lasing modes that would have been dwarfed by more dominant ones. The key idea is incorporating the control of modal interaction into the spatial pump profile. Our proposal is most valuable in the regime of spatially and spectrally overlapping modes, which can lead to a significant enhancement of laser power as well.

Features of the Paired Soliton Interactions Within the Framework of the Gardner Equation

NASA Astrophysics Data System (ADS)

Shurgalina, E. G.

2018-02-01

We study the dynamics of the two-soliton interaction within the framework of a completely integrable model, namely, the Gardner equation with negative cubic nonlinearity, which admits the existence of a limiting soliton. The features of the soliton interaction with participation of a thick soliton are demonstrated. Special attention is paid to the nonlinear-interaction influence on the wave-field moments, which determine the skewness and the kurtosis in the theory of turbulence.

A Lattice-Boltzmann model to simulate diffractive nonlinear ultrasound beam propagation in a dissipative fluid medium

NASA Astrophysics Data System (ADS)

Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan

2012-12-01

Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is presented.

Analytical and Computational Modeling of Mechanical Waves in Microscale Granular Crystals: Nonlinearity and Rotational Dynamics

NASA Astrophysics Data System (ADS)

Wallen, Samuel P.

Granular media are one of the most common, yet least understood forms of matter on earth. The difficulties in understanding the physics of granular media stem from the fact that they are typically heterogeneous and highly disordered, and the grains interact via nonlinear contact forces. Historically, one approach to reducing these complexities and gaining new insight has been the study of granular crystals, which are ordered arrays of similarly-shaped particles (typically spheres) in Hertzian contact. Using this setting, past works explored the rich nonlinear dynamics stemming from contact forces, and proposed avenues where such granular crystals could form designer, dynamically responsive materials, which yield beneficial functionality in dynamic regimes. In recent years, the combination of self-assembly fabrication methods and laser ultrasonic experimental characterization have enabled the study of granular crystals at microscale. While our intuition may suggest that these microscale granular crystals are simply scaled-down versions of their macroscale counterparts, in fact, the relevant physics change drastically; for example, short-range adhesive forces between particles, which are negligible at macroscale, are several orders of magnitude stronger than gravity at microscale. In this thesis, we present recent advances in analytical and computational modeling of microscale granular crystals, in particular concerning the interplay of nonlinearity, shear interactions, and particle rotations, which have previously been either absent, or included separately at macroscale. Drawing inspiration from past works on phononic crystals and nonlinear lattices, we explore problems involving locally-resonant metamaterials, nonlinear localized modes, amplitude-dependent energy partition, and other rich dynamical phenomena. This work enhances our understanding of microscale granular media, which may find applicability in fields such as ultrasonic wave tailoring, signal processing, shock and vibration mitigation, and powder processing.

Different responses of influenza epidemic to weather factors among Shanghai, Hong Kong, and British Columbia.

PubMed

Wang, Xi-Ling; Yang, Lin; He, Dai-Hai; Chiu, Alice Py; Chan, Kwok-Hung; Chan, King-Pan; Zhou, Maigeng; Wong, Chit-Ming; Guo, Qing; Hu, Wenbiao

2017-06-01

Weather factors have long been considered as key sources for regional heterogeneity of influenza seasonal patterns. As influenza peaks coincide with both high and low temperature in subtropical cities, weather factors may nonlinearly or interactively affect influenza activity. This study aims to assess the nonlinear and interactive effects of weather factors with influenza activity and compare the responses of influenza epidemic to weather factors in two subtropical regions of southern China (Shanghai and Hong Kong) and one temperate province of Canada (British Columbia). Weekly data on influenza activity and weather factors (i.e., mean temperature and relative humidity (RH)) were obtained from pertinent government departments for the three regions. Absolute humidity (AH) was measured by vapor pressure (VP), which could be converted from temperature and RH. Generalized additive models were used to assess the exposure-response relationship between weather factors and influenza virus activity. Interactions of weather factors were further assessed by bivariate response models and stratification analyses. The exposure-response curves of temperature and VP, but not RH, were consistent among three regions/cities. Bivariate response model revealed a significant interactive effect between temperature (or VP) and RH (P < 0.05). Influenza peaked at low temperature or high temperature with high RH. Temperature and VP are important weather factors in developing a universal model to explain seasonal outbreaks of influenza. However, further research is needed to assess the association between weather factors and influenza activity in a wider context of social and environmental conditions.

Nanomaterial-enhanced frequency combs (Conference Presentation)

NASA Astrophysics Data System (ADS)

Armani, Andrea M.; Castro-Beltran, Rigoberto; Diep, Vinh; Gungor, Eda; Shen, Xiaoqin; Soltani, Soheil

2017-02-01

Optical cavities are able to confine and store specific wavelengths of light, acting as optical amplifiers at those wavelengths. Because the amount of amplification is directly related to the cavity quality factor (Q) (or the cavity finesse), frequency comb research has focused on high-Q and ultra-high Q microcavities fabricated from a range of materials using a variety of methods. In all cases, the comb generation relies on a nonlinear process known as parametric frequency conversion which is based on a third order nonlinear interaction and which results in four wave mixing (FWM). Clearly, this approach requires significant optical power, which was the original motivation for using ultra-high-Q cavities. In fact, the majority of research to date has focused on pursuing increasingly high Q factors. However, another strategy is to improve the nonlinearity of the resonator through intelligently designing materials for this application. In the present work, a suite of nanomaterials (organic and inorganic) have been intelligently designed with the explicit purpose to enhance the nonlinearity of the resonator and reducing the threshold for frequency comb generation in the near-IR. The nanomaterials do not change the structure of the comb and only act to reduce the comb threshold. The silica microcavity is used as a testbed for initial demonstration and verification purposes. However, the fundamental strategy is translatable to other whispering gallery mode cavities.

Nonlinear Internal Wave Interaction in the China Seas

NASA Technical Reports Server (NTRS)

Liu, Antony K.; Hsu, Ming-K.

1998-01-01

This project researched the nonlinear wave interactions in the East China Sea, and the South China Sea, using Synthetic Aperture Radar (SAR) images. The complicated nature of the internal wave field, including the generation mechanisms, was studied, and is discussed. Discussion of wave-wave interactions in the East China Sea, the area of the China Sea northeast of Taiwan, and the Yellow Sea is included.

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.

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.

Swarming behaviors in multi-agent systems with nonlinear dynamics

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

Yu, Wenwu, E-mail: wenwuyu@gmail.com; School of Electrical and Computer Engineering, RMIT University, Melbourne VIC 3001; Chen, Guanrong

2013-12-15

The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agentmore » is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.« less

Numerical calculation of nonlinear ultrashort laser pulse propagation in transparent Kerr media

NASA Astrophysics Data System (ADS)

Arnold, Cord L.; Heisterkamp, Alexander; Ertmer, Wolfgang; Lubatschowski, Holger

2005-03-01

In the focal region of tightly focused ultrashort laser pulses, sufficient high intensities to initialize nonlinear ionization processes are easily achieved. Due to these nonlinear ionization processes, mainly multiphoton ionization and cascade ionization, free electrons are generated in the focus resulting in optical breakdown. A model including both nonlinear pulse propagation and plasma generation is used to calculate numerically the interaction of ultrashort pulses with their self-induced plasma in the vicinity of the focus. The model is based on a (3+1)-dimensional nonlinear Schroedinger equation describing the pulse propagation coupled to a system of rate equations covering the generation of free electrons. It is applicable to any transparent Kerr medium, whose linear and nonlinear optical parameters are known. Numerical calculations based on this model are used to understand nonlinear side effects, such as streak formation, occurring in addition to optical breakdown during short pulse refractive eye surgeries like fs-LASIK. Since the optical parameters of water are a good first-order approximation to those of corneal tissue, water is used as model substance. The free electron density distribution induced by focused ultrashort pulses as well as the pulses spatio-temporal behavior are studied in the low-power regime around the critical power for self-focusing.

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.

New Representation of Bearings in LS-DYNA

NASA Technical Reports Server (NTRS)

Carney, Kelly S.; Howard, Samuel A.; Miller, Brad A.; Benson, David J.

2014-01-01

Non-linear, dynamic, finite element analysis is used in various engineering disciplines to evaluate high-speed, dynamic impact and vibration events. Some of these applications require connecting rotating to stationary components. For example, bird impacts on rotating aircraft engine fan blades are a common analysis performed using this type of analysis tool. Traditionally, rotating machines utilize some type of bearing to allow rotation in one degree of freedom while offering constraints in the other degrees of freedom. Most times, bearings are modeled simply as linear springs with rotation. This is a simplification that is not necessarily accurate under the conditions of high-velocity, high-energy, dynamic events such as impact problems. For this reason, it is desirable to utilize a more realistic non-linear force-deflection characteristic of real bearings to model the interaction between rotating and non-rotating components during dynamic events. The present work describes a rolling element bearing model developed for use in non-linear, dynamic finite element analysis. This rolling element bearing model has been implemented in LS-DYNA as a new element, *ELEMENT_BEARING.

Linear and nonlinear dynamics of isospectral granular chains

NASA Astrophysics Data System (ADS)

Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

2017-04-01

We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

Nonlinear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.

1972-01-01

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

Bright-dark and dark-dark solitons for the coupled cubic-quintic nonlinear Schrödinger equations in a twin-core nonlinear optical fiber

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Liu, Lei; Chai, Han-Peng

2017-11-01

In this paper, we investigate the coupled cubic-quintic nonlinear Schrödinger equations, which can describe the effects of quintic nonlinearity on the ultrashort optical soliton pulse propagation in a twin-core nonlinear optical fiber. Through the Kadomtsev-Petviashvili hierarchy reduction, we present the bright-dark and dark-dark soliton solutions in terms of the Grammian for such equations. With the help of analytic and graphic analysis, head-on and overtaking elastic interactions between the two solitons are presented, as well as the bound-state solitons. Particularly, we find the inelastic interaction between the bright-dark two solitons. One of the electromagnetic fields presents the V-shape profile, while the other one presents the Y-shape profile.

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.

Leaderless consensus for the fractional-order nonlinear multi-agent systems under directed interaction topology

NASA Astrophysics Data System (ADS)

Bai, Jing; Wen, Guoguang; Rahmani, Ahmed

2018-04-01

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems' convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems' stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

Giant nonlinear response at a plasmonic nanofocus drives efficient four-wave mixing

NASA Astrophysics Data System (ADS)

Nielsen, Michael P.; Shi, Xingyuan; Dichtl, Paul; Maier, Stefan A.; Oulton, Rupert F.

2017-12-01

Efficient optical frequency mixing typically must accumulate over large interaction lengths because nonlinear responses in natural materials are inherently weak. This limits the efficiency of mixing processes owing to the requirement of phase matching. Here, we report efficient four-wave mixing (FWM) over micrometer-scale interaction lengths at telecommunications wavelengths on silicon. We used an integrated plasmonic gap waveguide that strongly confines light within a nonlinear organic polymer. The gap waveguide intensifies light by nanofocusing it to a mode cross-section of a few tens of nanometers, thus generating a nonlinear response so strong that efficient FWM accumulates over wavelength-scale distances. This technique opens up nonlinear optics to a regime of relaxed phase matching, with the possibility of compact, broadband, and efficient frequency mixing integrated with silicon photonics.

On the tidal interaction between protoplanets and the primordial solar nebula. II - Self-consistent nonlinear interaction

NASA Technical Reports Server (NTRS)

Lin, D. N. C.; Papaloizou, J.

1986-01-01

A method to analyze the full nonlinear response and physical processes associated with the tidal interaction between a binary system and a thin disk in the steady state is presented. Using this approach, density wave propagation, induced by tidal interaction, may be studied for a wide range of sound speeds and viscosities. The effect of self-gravity may also be incorporated. The results of several calculations relevant to the tidal interaction between a protoplanet and the primordial solar nebula are also presented.

AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, 4th, Cleveland, OH, Sept. 21-23, 1992, Technical Papers. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

1992-01-01

The papers presented at the symposium cover aerodynamics, design applications, propulsion systems, high-speed flight, structures, controls, sensitivity analysis, optimization algorithms, and space structures applications. Other topics include helicopter rotor design, artificial intelligence/neural nets, and computational aspects of optimization. Papers are included on flutter calculations for a system with interacting nonlinearities, optimization in solid rocket booster application, improving the efficiency of aerodynamic shape optimization procedures, nonlinear control theory, and probabilistic structural analysis of space truss structures for nonuniform thermal environmental effects.

All-optical control of group velocity dispersion in tellurite photonic crystal fibers.

PubMed

Liu, Lai; Tian, Qijun; Liao, Meisong; Zhao, Dan; Qin, Guanshi; Ohishi, Yasutake; Qin, Weiping

2012-12-15

We demonstrate all-optical control of group velocity dispersion (GVD) via optical Kerr effect in highly nonlinear tellurite photonic crystal fibers. The redshift of the zero-dispersion wavelength is over 307 nm, measured by soliton self-frequency shift cancellation, when the pump peak power of a 1.56 μm femtosecond fiber laser is increased to 11.6 kW. The all-optical control of GVD not only offers a new platform for constructing all-optical-control photonic devices but also promises a new class of experiments in nonlinear fiber optics and light-matter interactions.

Instantaneous Frequency Analysis on Nonlinear EMIC Emissions: Arase Observation

NASA Astrophysics Data System (ADS)

Shoji, M.; Yoshizumi, M.; Omura, Y.; Kasaba, Y.; Ishisaka, K.; Matsuda, S.; Kasahara, Y.; Yagitani, S.; Matsuoka, A.; Teramoto, M.; Takashima, T.; Shinohara, I.

2017-12-01

In the inner magnetosphere, electromagnetic ion cyclotron (EMIC) waves cause nonlinear interactions with energetic protons. The waves drastically modify the proton distribution function, resulting in the particle loss in the radiation belt. Arase spacecraft, launched in late 2016, observed a nonlinear EMIC falling tone emission in the high magnetic latitude (MLAT) region of the inner magnetosphere. The wave growth with sub-packet structures of the falling tone emission is found by waveform data from PWE/EFD instrument. The evolution of the instantaneous frequency of the electric field of the EMIC falling tone emission is analyzed by Hilbert-Huang transform (HHT). We find several sub-packets with rising frequency in the falling tone wave. A self-consistent hybrid simulation suggested the complicate frequency evolution of the EMIC sub-packet emissions in the generation region. The intrinsic mode functions of Arase data derived from HHT are compared with the simulation data. The origin of the falling tone emission in the high MLAT region is also discussed.

Observation of three-photon bound states in a quantum nonlinear medium

NASA Astrophysics Data System (ADS)

Liang, Qi-Yu; Venkatramani, Aditya V.; Cantu, Sergio H.; Nicholson, Travis L.; Gullans, Michael J.; Gorshkov, Alexey V.; Thompson, Jeff D.; Chin, Cheng; Lukin, Mikhail D.; Vuletić, Vladan

2018-02-01

Bound states of massive particles, such as nuclei, atoms, or molecules, constitute the bulk of the visible world around us. By contrast, photons typically only interact weakly. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. Photon correlation and conditional phase measurements reveal the distinct bunching and phase features associated with three-photon and two-photon bound states. Such photonic trimers and dimers possess shape-preserving wave functions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are described by an effective field theory of Rydberg-induced photon-photon interactions. These observations demonstrate the ability to realize and control strongly interacting quantum many-body states of light.

Quasisubharmonic vibrations in metal plates excited by high-power ultrasonic pulses

NASA Astrophysics Data System (ADS)

Chen, Zhao-jiang; Zhang, Shu-yi; Zheng, Kai; Kuo, Pao-kuang

2009-07-01

Strongly nonlinear vibration phenomena in metal plates excited by high-power ultrasonic pulses in different conditions are studied experimentally and theoretically. The experimental conditions for generating quasisubharmonics and subharmonics are found and discussed. The plate vibrations are characterized by waveforms, frequency spectra, pseudostate portraits, and Poincaré maps. Then, a three-degree-of-freedom vibroimpact-dynamic model is presented to explore the generation mechanisms of the quasisubharmonic and subharmonic vibrations in the plates. According to the model, the intermittent contact-impact forces caused by the interactions between the transducer horn tip and the plate are considered as the main source for generating the complex nonlinear vibration in the plate. The numerical calculation results can explain reasonably the observed experimental phenomena.

Designing Adaptive Low Dissipative High Order Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, B.; Parks, John W. (Technical Monitor)

2002-01-01

Proper control of the numerical dissipation/filter to accurately resolve all relevant multiscales of complex flow problems while still maintaining nonlinear stability and efficiency for long-time numerical integrations poses a great challenge to the design of numerical methods. The required type and amount of numerical dissipation/filter are not only physical problem dependent, but also vary from one flow region to another. This is particularly true for unsteady high-speed shock/shear/boundary-layer/turbulence/acoustics interactions and/or combustion problems since the dynamics of the nonlinear effect of these flows are not well-understood. Even with extensive grid refinement, it is of paramount importance to have proper control on the type and amount of numerical dissipation/filter in regions where it is needed.

Enhancement of laser power-efficiency by control of spatial hole burning interactions

NASA Astrophysics Data System (ADS)

Ge, Li; Malik, Omer; Türeci, Hakan E.

2014-11-01

The laser is an out-of-equilibrium nonlinear wave system where the interplay of the cavity geometry and nonlinear wave interactions mediated by the gain medium determines the self-organized oscillation frequencies and the associated spatial field patterns. In the steady state, a constant energy flux flows through the laser from the pump to the far field, with the ratio of the total output power to the input power determining the power-efficiency. Although nonlinear wave interactions have been modelled and well understood since the early days of laser theory, their impact on the power-efficiency of a laser system is poorly understood. Here, we show that spatial hole burning interactions generally decrease the power-efficiency. We then demonstrate how spatial hole burning interactions can be controlled by a spatially tailored pump profile, thereby boosting the power-efficiency, in some cases by orders of magnitude.

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

NASA Astrophysics Data System (ADS)

Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

2018-02-01

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

FOREWORD: Workshop on Large Amplitude Waves and Fields in Plasmas, sponsored by the Commission of the European Communities

NASA Astrophysics Data System (ADS)

Bingham, R.; De Angelis, U.; Shukla, P. K.; Stenflo, L.

1990-01-01

During the last decade considerable progress has been made in the area of nonlinear plasma wave phenomena and their applications. In order to exhibit the present state-of-art in this field, a one-week (22-26 May) workshop on Large Amplitude Waves and Fields was organized at the International Centre for Theoretical Physics (ICTP), Trieste, Italy, during the bi-yearly activity of the Spring College on Plasma Physics (15 May-9 June, 1989). Most of the invited lectures are published in this Topical Issue of Physica Scripta so that scientists working, or who want to enter the field of nonlinear plasma wave theory, can find out what has been achieved and what are the current research trends in this area. The material included here consists of general plasma wave theory, results of computer simulations, and experimental verifications. Without going into any detail, we shall just highlight the topics and the general features of the lectures contained in these proceedings. Various aspects of the excitation, propagation and interaction of nonlinear waves in plasmas are reviewed. Their relevance to plasma-based beat wave accelerators, short pulse laser and particle beam wake-field accelerators, plasma lenses, laser fusion and ionospheric modification experiments is discussed. Some introductory lectures present the general physics of nonlinear plasma waves including the saturation mechanisms and wave breaking conditions for both non-relativistic and relativistic nonlinearities. Three wave and four wave processes which include stimulated Raman, Brillouin and Compton scattering, modulational instabilities, self-focusing and collapse of the waves are discussed, emphasizing the important effects due to the relativistic electron mass variation and ponderomotive force. Detailed numerical studies of the interaction of high frequency plasma waves with low frequency density fluctuations described by the Zakharov equations show the localization of the high frequency field in density cavities and their burn-out resulting in very strong turbulence. Remarkable agreement between the simulations and ionospheric modification experiments have been demonstrated. The articles presented also attempted to correlate the theories of parametric instabilities with experimental observations. The properties of plasma lenses used for focusing of high energy particle beams is also presented as part of the uses of the nonlinear plasmas. Self-organisation of plasmas resulting in coherent nonlinear structures and particle diffusion processes are reported. On the experimental side the nonlinear optics of plasmas as a new area of research has been reviewed. This is becoming an important area for research since it treats the plasma from the outset as a nonlinear medium. Experimental observations of phase conjugation of electromagnetic signals demonstrate once again the importance of the nonlinearities inherent in the interaction of large amplitude waves with plasmas. Finally the importance of turbulence in space plasmas is emphasized in a discussion of the auroral phenomenon, presenting the plasma physicists point of view on this topic. The workshop, attended by scientists from all over the world, stimulated a great deal of lively discussions about the theoretical foundations, experimental observations and interpretations together with computer simulation results on the physics of nonlinear plasma wave phenomena. The workshop was made possible by the kind support of Professors A Salam, L Bertocchi and M Hassan. We are grateful to them for giving us the opportunity to organize the workshop within the activities of the Spring College on Plasma Physics. Thanks are also due to the ICTP and the European Economic Community (EEC) for providing partial financial support. Finally, our most cordial thanks are extended to the invited speakers for coming to Trieste delivering excellent talks and enhancing the activity of the Spring College.

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.

Finite element analysis of hysteresis effects in piezoelectric transducers

NASA Astrophysics Data System (ADS)

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

2000-06-01

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

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.

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.

Three-dimensional instability of standing waves

NASA Astrophysics Data System (ADS)

Zhu, Qiang; Liu, Yuming; Yue, Dick K. P.

2003-12-01

We investigate the three-dimensional instability of finite-amplitude standing surface waves under the influence of gravity. The analysis employs the transition matrix (TM) approach and uses a new high-order spectral element (HOSE) method for computation of the nonlinear wave dynamics. HOSE is an extension of the original high-order spectral method (HOS) wherein nonlinear wave wave and wave body interactions are retained up to high order in wave steepness. Instead of global basis functions in HOS, however, HOSE employs spectral elements to allow for complex free-surface geometries and surface-piercing bodies. Exponential convergence of HOS with respect to the total number of spectral modes (for a fixed number of elements) and interaction order is retained in HOSE. In this study, we use TM-HOSE to obtain the stability of general three-dimensional perturbations (on a two-dimensional surface) on two classes of standing waves: plane standing waves in a rectangular tank; and radial/azimuthal standing waves in a circular basin. For plane standing waves, we confirm the known result of two-dimensional side-bandlike instability. In addition, we find a novel three-dimensional instability for base flow of any amplitude. The dominant component of the unstable disturbance is an oblique (standing) wave oriented at an arbitrary angle whose frequency is close to the (nonlinear) frequency of the original standing wave. This finding is confirmed by direct long-time simulations using HOSE which show that the nonlinear evolution leads to classical Fermi Pasta Ulam recurrence. For the circular basin, we find that, beyond a threshold wave steepness, a standing wave (of nonlinear frequency Omega) is unstable to three-dimensional perturbations. The unstable perturbation contains two dominant (standing-wave) components, the sum of whose frequencies is close to 2Omega. From the cases we consider, the critical wave steepness is found to generally decrease/increase with increasing radial/azimuthal mode number of the base standing wave. Finally, we show that the instability we find for both two- and three-dimensional standing waves is a result of third-order (quartet) resonance.

Canonical Descriptions of High Intensity Laser-Plasma Interaction

NASA Astrophysics Data System (ADS)

Le Cornu, B. J.

The problem of laser-plasma interaction has been studied extensively in the context of inertial confinement fusion (ICF). These studies have focussed on effects like the nonlinear force, self-focusing, Rayleigh- Taylor instabilities, stimulated Brillouin scattering and stimulated Raman scattering observed in ICF schemes. However, there remains a large discrepancy between theory and experiment in the context of nuclear fusion schemes. Several authors have attempted to gain greater understanding of the physics involved by the application of standard or 'canonical' methods used in Lagrangian and Hamiltonian mechanics to the problem of plasma physics. This thesis presents a new canonical description of laser-plasma interaction based on the Podolsky Lagrangian. Finite self-energy of charged particles, incroporation of high-frequency effects and an ability to quantise are the main advantages of this new model. The nature of the Podolsky constant is also analysed in the context of plasma physics, specifically in terms of the plasma dispersion relation. A new gauge invariant expression of the energy-momentum tensor for any gauge invariant Lagrangian dependent on second order derivatives is derived for the first time. Finally, the transient and nontransient expressions of the nonlinear ponderomotive force in laser-plasma interaction are discussed and shown to be closely approximated by a canonical derivation of the electromagnetic Lagrangian, a fact that seems to have been missed in the literature.

Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

PubMed

Si, Wenjie; Dong, Xunde; Yang, Feifei

2018-03-01

This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

Knowledge Driven Image Mining with Mixture Density Mercer Kernels

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Oza, Nikunj

2004-01-01

This paper presents a new methodology for automatic knowledge driven image mining based on the theory of Mercer Kernels; which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. In that high dimensional feature space, linear clustering, prediction, and classification algorithms can be applied and the results can be mapped back down to the original image space. Thus, highly nonlinear structure in the image can be recovered through the use of well-known linear mathematics in the feature space. This process has a number of advantages over traditional methods in that it allows for nonlinear interactions to be modelled with only a marginal increase in computational costs. In this paper, we present the theory of Mercer Kernels, describe its use in image mining, discuss a new method to generate Mercer Kernels directly from data, and compare the results with existing algorithms on data from the MODIS (Moderate Resolution Spectral Radiometer) instrument taken over the Arctic region. We also discuss the potential application of these methods on the Intelligent Archive, a NASA initiative for developing a tagged image data warehouse for the Earth Sciences.

Knowledge Driven Image Mining with Mixture Density Mercer Kernals

NASA Technical Reports Server (NTRS)

Srivastava, Ashok N.; Oza, Nikunj

2004-01-01

This paper presents a new methodology for automatic knowledge driven image mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly infinite dimensional feature space. In that high dimensional feature space, linear clustering, prediction, and classification algorithms can be applied and the results can be mapped back down to the original image space. Thus, highly nonlinear structure in the image can be recovered through the use of well-known linear mathematics in the feature space. This process has a number of advantages over traditional methods in that it allows for nonlinear interactions to be modelled with only a marginal increase in computational costs. In this paper we present the theory of Mercer Kernels; describe its use in image mining, discuss a new method to generate Mercer Kernels directly from data, and compare the results with existing algorithms on data from the MODIS (Moderate Resolution Spectral Radiometer) instrument taken over the Arctic region. We also discuss the potential application of these methods on the Intelligent Archive, a NASA initiative for developing a tagged image data warehouse for the Earth Sciences.

Experimental characterization and modeling of non-linear coupling of the LHCD power on Tore Supra

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

Preynas, M.; Goniche, M.; Hillairet, J.

2014-02-12

To achieve steady state operation on future tokamaks, in particular on ITER, the unique capability of a LHCD system to efficiently drive off-axis non-inductive current is needed. In this context, it is of prime importance to study and master the coupling of LH wave to the core plasma at high power density (tens of MW/m{sup 2}). In some specific conditions, deleterious effects on the LHCD coupling are sometimes observed on Tore Supra. At high power the waves may modify the edge parameters that change the wave coupling properties in a non-linear manner. In this way, dedicated LHCD experiments have beenmore » performed using the LHCD system of Tore Supra, composed of two different conceptual designs of launcher: the Fully Active Multijunction (FAM) and the new Passive Active Multijunction (PAM) antennas. A nonlinear interaction between the electron density and the electric field has been characterized in a thin plasma layer in front of the two LHCD antennas. The resulting dependence of the power reflection coefficient with the LHCD power, leading occasionally to trips in the output power, is not predicted by the standard linear theory of the LH wave coupling. Therefore, it is important to investigate and understand the possible origin of such non-linear effects in order to avoid their possible deleterious consequences. The PICCOLO-2D code, which self-consistently treats the wave propagation in the antenna vicinity and its interaction with the local edge plasma density, is used to simulate Tore Supra discharges. The simulation reproduces very well the occurrence of a non-linear behavior in the coupling observed in the LHCD experiments. The important differences and trends between the FAM and the PAM antennas, especially a larger increase in RC for the FAM, are also reproduced by the PICCOLO-2D simulation. The working hypothesis of the contribution of the ponderomotive effect in the non-linear observations of LHCD coupling is therefore validated through this comprehensive modeling for the first time on the FAM and PAM antennas on Tore Supra.« less

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

NASA Astrophysics Data System (ADS)

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

2014-11-01

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

Nanosecond-pulse-controlled higher-order sideband comb in a GaAs optomechanical disk resonator in the non-perturbative regime

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

Xiong, Hao, E-mail: haoxiong1217@gmail.com; Si, Liu-Gang, E-mail: siliugang@gmail.com; Lü, Xin-You

2014-10-15

We propose an interesting scheme for tunable high-order sideband comb generation by utilizing ultrastrong optomechanical interaction in a GaAs optomechanical disk resonator beyond the perturbative approximation. We analyze the nonlinear nature of the optomechanical interaction, and give a full description of the non-perturbative effects. It is shown, within the non-perturbative regime, that high-order sideband comb with large intensities can be realized and controlled in a GaAs optomechanical disk resonator with experimentally achievable system parameters, and the non-perturbative regime leads to rich and nontrivial behavior.

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.

Electromagnetic-continuum-induced nonlinearity

NASA Astrophysics Data System (ADS)

Matsko, Andrey B.; Vyatchanin, Sergey P.

2018-05-01

A nonrelativistic Hamiltonian describing interaction between a mechanical degree of freedom and radiation pressure is commonly used as an ultimate tool for studying system behavior in optomechanics. This Hamiltonian is derived from the equation of motion of a mechanical degree of freedom and the optical wave equation with time-varying boundary conditions. We show that this approach is deficient for studying higher-order nonlinear effects in an open resonant optomechanical system. Optomechanical interaction induces a large mechanical nonlinearity resulting from a strong dependence of the power of the light confined in the optical cavity on the mechanical degrees of freedom of the cavity due to coupling with electromagnetic continuum. This dissipative nonlinearity cannot be inferred from the standard Hamiltonian formalism.

Strongly interacting photons in asymmetric quantum well via resonant tunneling.

PubMed

Sun, H; Fan, S L; Feng, X L; Wu, C F; Gong, S Q; Huang, G X; Oh, C H

2012-04-09

We propose an asymmetric quantum well structure to realize strong interaction between two slow optical pulses. The essential idea is the combination of the advantages of inverted-Y type scheme and resonant tunneling. We analytically demonstrate that giant cross-Kerr nonlinearity can be achieved with vanishing absorptions. Owing to resonant tunneling, the contributions of the probe and signal cross-Kerr nonlinearities to total nonlinear phase shift vary from destructive to constrictive, leading to nonlinear phase shift on order of π at low light level. In this structure, the scheme is inherent symmetric for the probe and signal pulses. Consequently, the condition of group velocity matching can be fulfilled with appropriate initial electron distribution.

Hidden symmetry and nonlinear paraxial atom optics

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

Impens, Francois

2009-12-15

A hidden symmetry of the nonlinear wave equation is exploited to analyze the propagation of paraxial and uniform atom-laser beams in time-independent and quadratic transverse potentials with cylindrical symmetry. The quality factor and the paraxial ABCD formalism are generalized to account exactly for mean-field interaction effects in such beams. Using an approach based on moments, these theoretical tools provide a simple yet exact picture of the interacting beam profile evolution. Guided atom laser experiments are discussed. This treatment addresses simultaneously optical and atomic beams in a unified manner, exploiting the formal analogy between nonlinear optics, nonlinear paraxial atom optics, andmore » the physics of two-dimensional Bose-Einstein condensates.« less

NLOphoric multichromophoric auxiliary methoxy aided triphenylamine D-π-A chromophores - Spectroscopic and computational studies

NASA Astrophysics Data System (ADS)

Erande, Yogesh; Kothavale, Shantaram; Sreenath, Mavila C.; Chitrambalam, Subramaniyan; Joe, Isaac H.; Sekar, Nagaiyan

2017-11-01

Molecules containing methoxy supported triphenylamine as strong electron-donor and dicyanovinyl as electron-acceptor groups interacting via isophorone as a configurationally locked polyene π-conjugated bridge are studied for their nonlinear optical properties. The photophysical study of examined chromophores in non-polar and polar solvents suggest that they exhibit strong emission solvatochromism and significant charge transfer characteristics supported by Lippert-Mataga plots and Generalised Mulliken Hush analysis. Linear and nonlinear optical properties as well as electronic properties measured by spectroscopic methods and cyclic voltametry and supported by DFT calculation were used to elucidate the structure property relationships. All three chromophores exhibit very high thermal stabilities with the decomposition temperatures higher than 340°C. The vibrational motions play very important role in determining the overall NLO response styryl chromophores which was established by DFT study. Dye 3 with maximum nonlinear optical susceptibility among three D-π-A systems proves that the multibranched push-pull chromophores exhibit a higher third order nonlinear susceptibility and justifies the design strategy.

Multi-dimensional high order essentially non-oscillatory finite difference methods in generalized coordinates

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

1992-01-01

The nonlinear stability of compact schemes for shock calculations is investigated. In recent years compact schemes were used in various numerical simulations including direct numerical simulation of turbulence. However to apply them to problems containing shocks, one has to resolve the problem of spurious numerical oscillation and nonlinear instability. A framework to apply nonlinear limiting to a local mean is introduced. The resulting scheme can be proven total variation (1D) or maximum norm (multi D) stable and produces nice numerical results in the test cases. The result is summarized in the preprint entitled 'Nonlinearly Stable Compact Schemes for Shock Calculations', which was submitted to SIAM Journal on Numerical Analysis. Research was continued on issues related to two and three dimensional essentially non-oscillatory (ENO) schemes. The main research topics include: parallel implementation of ENO schemes on Connection Machines; boundary conditions; shock interaction with hydrogen bubbles, a preparation for the full combustion simulation; and direct numerical simulation of compressible sheared turbulence.

1/f Noise Inside a Faraday Cage

NASA Astrophysics Data System (ADS)

Handel, Peter H.; George, Thomas F.

2009-04-01

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

Predicting radiotherapy outcomes using statistical learning techniques

NASA Astrophysics Data System (ADS)

El Naqa, Issam; Bradley, Jeffrey D.; Lindsay, Patricia E.; Hope, Andrew J.; Deasy, Joseph O.

2009-09-01

Radiotherapy outcomes are determined by complex interactions between treatment, anatomical and patient-related variables. A common obstacle to building maximally predictive outcome models for clinical practice is the failure to capture potential complexity of heterogeneous variable interactions and applicability beyond institutional data. We describe a statistical learning methodology that can automatically screen for nonlinear relations among prognostic variables and generalize to unseen data before. In this work, several types of linear and nonlinear kernels to generate interaction terms and approximate the treatment-response function are evaluated. Examples of institutional datasets of esophagitis, pneumonitis and xerostomia endpoints were used. Furthermore, an independent RTOG dataset was used for 'generalizabilty' validation. We formulated the discrimination between risk groups as a supervised learning problem. The distribution of patient groups was initially analyzed using principle components analysis (PCA) to uncover potential nonlinear behavior. The performance of the different methods was evaluated using bivariate correlations and actuarial analysis. Over-fitting was controlled via cross-validation resampling. Our results suggest that a modified support vector machine (SVM) kernel method provided superior performance on leave-one-out testing compared to logistic regression and neural networks in cases where the data exhibited nonlinear behavior on PCA. For instance, in prediction of esophagitis and pneumonitis endpoints, which exhibited nonlinear behavior on PCA, the method provided 21% and 60% improvements, respectively. Furthermore, evaluation on the independent pneumonitis RTOG dataset demonstrated good generalizabilty beyond institutional data in contrast with other models. This indicates that the prediction of treatment response can be improved by utilizing nonlinear kernel methods for discovering important nonlinear interactions among model variables. These models have the capacity to predict on unseen data. Part of this work was first presented at the Seventh International Conference on Machine Learning and Applications, San Diego, CA, USA, 11-13 December 2008.

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.

Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

NASA Astrophysics Data System (ADS)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.

Studies of nonlinear interactions between counter-propagating Alfv'en waves in the LAPD

NASA Astrophysics Data System (ADS)

Auerbach, D. W.; Perez, J. C.; Carter, T. A.; Boldyrev, S.

2007-11-01

From a weak turbulence point of view, nonlinear interactions between shear Alfv'en waves are fundamental to the energy cascade in low-frequency magnetic turbulence. We report here on an experimental study of counter-propagating Alfv'en wave interactions in the Large Plasma Device (LAPD) at UCLA. Colliding, orthogonally polarized kinetic Alfv'en waves are generated by two antennae, separated by 5m along the guide magnetic field. Magnetic field and langmuir probes record plasma behavior between the antennae. When each antenna is operated separately, linearly polarized Alfv'en waves propagate in opposite directions along the guide field. When two antennae simultaneously excite counter propagating waves, we observe multiple side bands in the frequency domain, whose amplitude scales quadratically with wave amplitude. In the spatial domain we observe non-linear superposition in the 2D structure of the waves and spectral broadening in the perpendicular wave-number spectrum. This indicates the presence of nonlinear interaction of the counter propagating Alfv'en waves, and opens the possiblity to investigate Alfv'enic plasma turbulence in controlled and reproducible laboratory experiments.

The influence of surface roughness on the contact stiffness and the contact filter effect in nonlinear wheel-track interaction

NASA Astrophysics Data System (ADS)

Lundberg, Oskar E.; Nordborg, Anders; Lopez Arteaga, Ines

2016-03-01

A state-dependent contact model including nonlinear contact stiffness and nonlinear contact filtering is used to calculate contact forces and rail vibrations with a time-domain wheel-track interaction model. In the proposed method, the full three-dimensional contact geometry is reduced to a point contact in order to lower the computational cost and to reduce the amount of required input roughness-data. Green's functions including the linear dynamics of the wheel and the track are coupled with a point contact model, leading to a numerically efficient model for the wheel-track interaction. Nonlinear effects due to the shape and roughness of the wheel and the rail surfaces are included in the point contact model by pre-calculation of functions for the contact stiffness and contact filters. Numerical results are compared to field measurements of rail vibrations for passenger trains running at 200 kph on a ballast track. Moreover, the influence of vehicle pre-load and different degrees of roughness excitation on the resulting wheel-track interaction is studied by means of numerical predictions.

Agent-based modeling of endotoxin-induced acute inflammatory response in human blood leukocytes.

PubMed

Dong, Xu; Foteinou, Panagiota T; Calvano, Steven E; Lowry, Stephen F; Androulakis, Ioannis P

2010-02-18

Inflammation is a highly complex biological response evoked by many stimuli. A persistent challenge in modeling this dynamic process has been the (nonlinear) nature of the response that precludes the single-variable assumption. Systems-based approaches offer a promising possibility for understanding inflammation in its homeostatic context. In order to study the underlying complexity of the acute inflammatory response, an agent-based framework is developed that models the emerging host response as the outcome of orchestrated interactions associated with intricate signaling cascades and intercellular immune system interactions. An agent-based modeling (ABM) framework is proposed to study the nonlinear dynamics of acute human inflammation. The model is implemented using NetLogo software. Interacting agents involve either inflammation-specific molecules or cells essential for the propagation of the inflammatory reaction across the system. Spatial orientation of molecule interactions involved in signaling cascades coupled with the cellular heterogeneity are further taken into account. The proposed in silico model is evaluated through its ability to successfully reproduce a self-limited inflammatory response as well as a series of scenarios indicative of the nonlinear dynamics of the response. Such scenarios involve either a persistent (non)infectious response or innate immune tolerance and potentiation effects followed by perturbations in intracellular signaling molecules and cascades. The ABM framework developed in this study provides insight on the stochastic interactions of the mediators involved in the propagation of endotoxin signaling at the cellular response level. The simulation results are in accordance with our prior research effort associated with the development of deterministic human inflammation models that include transcriptional dynamics, signaling, and physiological components. The hypothetical scenarios explored in this study would potentially improve our understanding of how manipulating the behavior of the molecular species could manifest into emergent behavior of the overall system.

Interactions between finite amplitude small and medium-scale waves in the MLT region.

NASA Astrophysics Data System (ADS)

Heale, C. J.; Snively, J. B.

2016-12-01

Small-scale gravity waves can propagate high into the thermosphere and deposit significant momentum and energy into the background flow [e.g., Yamada et al., 2001, Fritts et al., 2014]. However, their propagation, dissipation, and spectral evolution can be significantly altered by other waves and dynamics and the nature of these complex interactions are not yet well understood. While many ray-tracing and time-dependent modeling studies have been performed to investigate interactions between waves of varying scales [e.g., Eckermann and Marks .1996, Sartelet. 2003, Liu et al. 2008, Vanderhoff et al., 2008, Senf and Achatz., 2011, Heale et al., 2015], the majority of these have considered waves of larger (tidal) scales, or have simplified one of the waves to be an imposed "background" and discount (or limit) the nonlinear feedback mechanisms between the two waves. In reality, both waves will influence each other, especially at finite amplitudes when nonlinear effects become important or dominant. We present a study of fully nonlinear interactions between small-scale 10s km, 10 min period) and medium-scale wave packets at finite amplitudes, which include feedback between the two waves and the ambient atmosphere. Time-dependence of the larger-scale wave has been identified as an important factor in reducing reflection [Heale et al., 2015] and critical level effects [Sartelet, 2003, Senf and Achatz, 2011], we choose medium-scale waves of different periods, and thus vertical scales, to investigate how this influences the propagation, filtering, and momentum and energy deposition of the small-scale waves, and in turn how these impacts affect the medium-scale waves. We also consider the observable features of these interactions in the mesosphere and lower thermosphere.

Theoretical Studies of Alfven Waves and Energetic Particle Physics in Fusion Plasmas

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

Chen, Liu

This report summarizes major theoretical findings in the linear as well as nonlinear physics of Alfvén waves and energetic particles in magnetically confined fusion plasmas. On the linear physics, a variational formulation, based on the separation of singular and regular spatial scales, for drift-Alfvén instabilities excited by energetic particles is established. This variational formulation is then applied to derive the general fishbone-like dispersion relations corresponding to the various Alfvén eigenmodes and energetic-particle modes. It is further employed to explore in depth the low-frequency Alfvén eigenmodes and demonstrate the non-perturbative nature of the energetic particles. On the nonlinear physics, new novelmore » findings are obtained on both the nonlinear wave-wave interactions and nonlinear wave-energetic particle interactions. It is demonstrated that both the energetic particles and the fine radial mode structures could qualitatively affect the nonlinear evolution of Alfvén eigenmodes. Meanwhile, a theoretical approach based on the Dyson equation is developed to treat self-consistently the nonlinear interactions between Alfvén waves and energetic particles, and is then applied to explain simulation results of energetic-particle modes. Relevant list of journal publications on the above findings is also included.« less

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.

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

A Nonlinear Interactions Approximation Model for Large-Eddy Simulation

NASA Astrophysics Data System (ADS)

Haliloglu, Mehmet U.; Akhavan, Rayhaneh

2003-11-01

A new approach to LES modelling is proposed based on direct approximation of the nonlinear terms \\overlineu_iuj in the filtered Navier-Stokes equations, instead of the subgrid-scale stress, τ_ij. The proposed model, which we call the Nonlinear Interactions Approximation (NIA) model, uses graded filters and deconvolution to parameterize the local interactions across the LES cutoff, and a Smagorinsky eddy viscosity term to parameterize the distant interactions. A dynamic procedure is used to determine the unknown eddy viscosity coefficient, rendering the model free of adjustable parameters. The proposed NIA model has been applied to LES of turbulent channel flows at Re_τ ≈ 210 and Re_τ ≈ 570. The results show good agreement with DNS not only for the mean and resolved second-order turbulence statistics but also for the full (resolved plus subgrid) Reynolds stress and turbulence intensities.

Compression of Intense Laser Pulses in Plasma

NASA Astrophysics Data System (ADS)

Fisch, Nathaniel J.; Malkin, Vladimir M.; Shvets, Gennady

2001-10-01

A counterpropagating short pulse can absorb the energy of a long laser pulse in plasma, resulting in pulse compression. For processing very high power and very high total energy, plasma is an ideal medium. Thus, in plasma one can contemplate the compression of micron light pulses to exawatts per square cm or fluences to kilojoules per square cm, prior to the vacuum focus. Two nonlinear plasma effects have recently been proposed to accomplish compression at very high power in counterpropagating geometry: One is compression by means of Compton or so-called superradiant scattering, where the nonlinear interaction of the plasma electrons with the lasers dominates the plasma restoring motion due to charge imbalance [G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, Phys. Rev. Lett. v. 81, 4879 (1998)]. The second is fast compression by means of stimulated backward Raman scattering (SBRS), where the amplification process outruns deleterious processes associated with the ultraintense pulse [V. M. Malkin, G. Shvets, N. J. Fisch, Phys. Rev. Lett., v. 82, 4448 (1999)]. In each of these regimes, in a realistic plasma, there are technological challenges that must be met and competing effects that must be kept smaller than the desired interaction.

An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids

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

Banks, J.W., E-mail: banksj3@rpi.edu; Henshaw, W.D., E-mail: henshw@rpi.edu; Kapila, A.K., E-mail: kapila@rpi.edu

We describe an added-mass partitioned (AMP) algorithm for solving fluid–structure interaction (FSI) problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements. The computational approach is a mixed Eulerian–Lagrangian scheme that makes use of deforming composite grids (DCG) to treat large changes in the geometry in an accurate, flexible, and robust manner. The current work extends the AMP algorithm developed in Banks et al. [1] for linearly elasticity to the case of nonlinear solids. To ensure stability for the case of light solids, the new AMP algorithm embeds an approximate solution of a nonlinear fluid–solidmore » Riemann (FSR) problem into the interface treatment. The solution to the FSR problem is derived and shown to be of a similar form to that derived for linear solids: the state on the interface being fundamentally an impedance-weighted average of the fluid and solid states. Numerical simulations demonstrate that the AMP algorithm is stable even for light solids when added-mass effects are large. The accuracy and stability of the AMP scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi-analytical solution that is obtained for a rotating solid disk immersed in a fluid. The scheme is applied to the simulation of a planar shock impacting a light elliptical-shaped solid, and comparisons are made between solutions of the FSI problem for a neo-Hookean solid, a linearly elastic solid, and a rigid solid. The ability of the approach to handle large deformations is demonstrated for a problem of a high-speed flow past a light, thin, and flexible solid beam.« less

A statistical state dynamics approach to wall turbulence.

PubMed

Farrell, B F; Gayme, D F; Ioannou, P J

2017-03-13

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'band-limiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into 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).

A statistical state dynamics approach to wall turbulence

PubMed Central

Gayme, D. F.; Ioannou, P. J.

2017-01-01

This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation–perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or ‘band-limiting’ can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD approach provides new analytical and computational tools that allow new insights into 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:28167577

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

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

NASA Astrophysics Data System (ADS)

Texier, Christophe; Mitscherling, Johannes

2018-02-01

We study the nonlinear conductance G ˜∂2I /∂ V2|V =0 in coherent quasi-one-dimensional weakly disordered metallic wires. Our analysis is based on the scattering approach and includes the effect of Coulomb interaction. The nonlinear conductance correlations can be related to integrals of two fundamental correlation functions: the correlator of functional derivatives of the conductance and the correlator of injectivities (the injectivity is the contribution to the local density of states of eigenstates incoming from one contact). These correlators are obtained explicitly by using diagrammatic techniques for weakly disordered metals. In a coherent wire of length L , we obtain rms (G )≃0.006 ETh-1 (and =0 ), where ETh=ℏ D /L2 is the Thouless energy of the wire and D the diffusion constant; the small dimensionless factor results from screening, i.e., cannot be obtained within a simple theory for noninteracting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal; the antisymmetric part of the nonlinear conductance (at high magnetic field) being much smaller than the symmetric one, rms (Ga)≃0.001 (gETh) -1 , where g ≫1 is the dimensionless (linear) conductance of the wire. In a weakly coherent wire (i.e., Lφ≪L , where Lφ is the phase coherence length), the nonlinear conductance is of the same order as the result G0 of a free electron calculation (although screening again strongly reduces the dimensionless prefactor); we get G ˜G0˜(Lφ/L ) 7 /2ETh-1 , while the antisymmetric part (at high magnetic field) now behaves as Ga˜(Lφ/L ) 11 /2(gETh) -1≪G . The effect of thermal fluctuations is studied: when the thermal length LT=√{ℏ D /kBT } is the smallest length scale, LT≪Lφ≪L , the free electron result G0˜(LT/L ) 3(Lφ/L ) 1 /2ETh-1 is negligible and the dominant contribution is provided by screening, G ˜(LT/L ) (Lφ/L ) 7 /2ETh-1 ; in this regime, the antisymmetric part is Ga˜(LT/L ) 2(Lφ/L ) 7 /2(gETh) -1 . All the precise dimensionless prefactors are obtained. Crossovers from zero to strong magnetic field regimes are also analyzed.

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.

Six-component semi-discrete integrable nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksiy O.

2018-01-01

We suggest the six-component integrable nonlinear system on a quasi-one-dimensional lattice. Due to its symmetrical form, the general system permits a number of reductions; one of which treated as the semi-discrete integrable nonlinear Schrödinger system on a lattice with three structural elements in the unit cell is considered in considerable details. Besides six truly independent basic field variables, the system is characterized by four concomitant fields whose background values produce three additional types of inter-site resonant interactions between the basic fields. As a result, the system dynamics becomes associated with the highly nonstandard form of Poisson structure. The elementary Poisson brackets between all field variables are calculated and presented explicitly. The richness of system dynamics is demonstrated on the multi-component soliton solution written in terms of properly parameterized soliton characteristics.

TIME-GCM study of the ionospheric equatorial vertical drift changes during the 2006 stratospheric sudden warming

NASA Astrophysics Data System (ADS)

Maute, A.; Hagan, M. E.; Richmond, A. D.; Roble, R. G.

2014-02-01

This modeling study quantifies the daytime low-latitude vertical E×B drift changes in the longitudinal wave number 1 (wn1) to wn4 during the major extended January 2006 stratospheric sudden warming (SSW) period as simulated by the National Center for Atmospheric Research thermosphere-ionosphere-mesosphere electrodynamics general circulation model (TIME-GCM), and attributes the drift changes to specific tides and planetary waves (PWs). The largest drift amplitude change (approximately 5 m/s) is seen in wn1 with a strong temporal correlation to the SSW. The wn1 drift is primarily caused by the semidiurnal westward propagating tide with zonal wave number 1 (SW1), and secondarily by a stationary planetary wave with zonal wave number 1 (PW1). SW1 is generated by the nonlinear interaction of PW1 and the migrating semidiurnal tide (SW2) at high latitude around 90-100 km. The simulations suggest that the E region PW1 around 100-130 km at the different latitudes has different origins: at high latitudes, the PW1 is related to the original stratospheric PW1; at midlatitudes, the model indicates PW1 is due to the nonlinear interaction of SW1 and SW2 around 95-105 km; and at low latitudes, the PW1 might be caused by the nonlinear interaction between DE2 and DE3. The time evolution of the simulated wn4 in the vertical E×B drift amplitude shows no temporal correlation with the SSW. The wn4 in the low-latitude vertical drift is attributed to the diurnal eastward propagating tide with zonal wave number 3 (DE3), and the contributions from SE2, TE1, and PW4 are negligible.

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

NASA Astrophysics Data System (ADS)

Khatri, Devvrath

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a finite element model (FEM) using the commercially available software Abaqus, which takes into account many of these characteristic features. The finite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specific application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.

Inferring genetic interactions via a nonlinear model and an optimization algorithm.

PubMed

Chen, Chung-Ming; Lee, Chih; Chuang, Cheng-Long; Wang, Chia-Chang; Shieh, Grace S

2010-02-26

Biochemical pathways are gradually becoming recognized as central to complex human diseases and recently genetic/transcriptional interactions have been shown to be able to predict partial pathways. With the abundant information made available by microarray gene expression data (MGED), nonlinear modeling of these interactions is now feasible. Two of the latest advances in nonlinear modeling used sigmoid models to depict transcriptional interaction of a transcription factor (TF) for a target gene, but do not model cooperative or competitive interactions of several TFs for a target. An S-shape model and an optimization algorithm (GASA) were developed to infer genetic interactions/transcriptional regulation of several genes simultaneously using MGED. GASA consists of a genetic algorithm (GA) and a simulated annealing (SA) algorithm, which is enhanced by a steepest gradient descent algorithm to avoid being trapped in local minimum. Using simulated data with various degrees of noise, we studied how GASA with two model selection criteria and two search spaces performed. Furthermore, GASA was shown to outperform network component analysis, the time series network inference algorithm (TSNI), GA with regular GA (GAGA) and GA with regular SA. Two applications are demonstrated. First, GASA is applied to infer a subnetwork of human T-cell apoptosis. Several of the predicted interactions are supported by the literature. Second, GASA was applied to infer the transcriptional factors of 34 cell cycle regulated targets in S. cerevisiae, and GASA performed better than one of the latest advances in nonlinear modeling, GAGA and TSNI. Moreover, GASA is able to predict multiple transcription factors for certain targets, and these results coincide with experiments confirmed data in YEASTRACT. GASA is shown to infer both genetic interactions and transcriptional regulatory interactions well. In particular, GASA seems able to characterize the nonlinear mechanism of transcriptional regulatory interactions (TIs) in yeast, and may be applied to infer TIs in other organisms. The predicted genetic interactions of a subnetwork of human T-cell apoptosis coincide with existing partial pathways, suggesting the potential of GASA on inferring biochemical pathways.

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

Petri net modeling of high-order genetic systems using grammatical evolution.

PubMed

Moore, Jason H; Hahn, Lance W

2003-11-01

Understanding how DNA sequence variations impact human health through a hierarchy of biochemical and physiological systems is expected to improve the diagnosis, prevention, and treatment of common, complex human diseases. We have previously developed a hierarchical dynamic systems approach based on Petri nets for generating biochemical network models that are consistent with genetic models of disease susceptibility. This modeling approach uses an evolutionary computation approach called grammatical evolution as a search strategy for optimal Petri net models. We have previously demonstrated that this approach routinely identifies biochemical network models that are consistent with a variety of genetic models in which disease susceptibility is determined by nonlinear interactions between two DNA sequence variations. In the present study, we evaluate whether the Petri net approach is capable of identifying biochemical networks that are consistent with disease susceptibility due to higher order nonlinear interactions between three DNA sequence variations. The results indicate that our model-building approach is capable of routinely identifying good, but not perfect, Petri net models. Ideas for improving the algorithm for this high-dimensional problem are presented.

Interaction of Kelvin waves and nonlocality of energy transfer in superfluids

NASA Astrophysics Data System (ADS)

Laurie, Jason; L'Vov, Victor S.; Nazarenko, Sergey; Rudenko, Oleksii

2010-03-01

We argue that the physics of interacting Kelvin Waves (KWs) is highly nontrivial and cannot be understood on the basis of pure dimensional reasoning. A consistent theory of KW turbulence in superfluids should be based upon explicit knowledge of their interactions. To achieve this, we present a detailed calculation and comprehensive analysis of the interaction coefficients for KW turbuelence, thereby, resolving previous mistakes stemming from unaccounted contributions. As a first application of this analysis, we derive a local nonlinear (partial differential) equation. This equation is much simpler for analysis and numerical simulations of KWs than the Biot-Savart equation, and in contrast to the completely integrable local induction approximation (in which the energy exchange between KWs is absent), describes the nonlinear dynamics of KWs. Second, we show that the previously suggested Kozik-Svistunov energy spectrum for KWs, which has often been used in the analysis of experimental and numerical data in superfluid turbulence, is irrelevant, because it is based upon an erroneous assumption of the locality of the energy transfer through scales. Moreover, we demonstrate the weak nonlocality of the inverse cascade spectrum with a constant particle-number flux and find resulting logarithmic corrections to this spectrum.

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.

A Census of Plasma Waves and Structures Associated With an Injection Front in the Inner Magnetosphere

NASA Astrophysics Data System (ADS)

Malaspina, David M.; Ukhorskiy, Aleksandr; Chu, Xiangning; Wygant, John

2018-04-01

Now that observations have conclusively established that the inner magnetosphere is abundantly populated with kinetic electric field structures and nonlinear waves, attention has turned to quantifying the ability of these structures and waves to scatter and accelerate inner magnetospheric plasma populations. A necessary step in that quantification is determining the distribution of observed structure and wave properties (e.g., occurrence rates, amplitudes, and spatial scales). Kinetic structures and nonlinear waves have broadband signatures in frequency space, and consequently, high-resolution time domain electric and magnetic field data are required to uniquely identify such structures and waves as well as determine their properties. However, most high-resolution fields data are collected with a strong bias toward high-amplitude signals in a preselected frequency range, strongly biasing observations of structure and wave properties. In this study, an ˜45 min unbroken interval of 16,384 samples/s field burst data, encompassing an electron injection event, is examined. This data set enables an unbiased census of the kinetic structures and nonlinear waves driven by this electron injection, as well as determination of their "typical" properties. It is found that the properties determined using this unbiased burst data are considerably different than those inferred from amplitude-biased burst data, with significant implications for wave-particle interactions due to kinetic structures and nonlinear waves in the inner magnetosphere.

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.

The Properties of Lion Roars and Electron Dynamics in Mirror Mode Waves Observed by the Magnetospheric MultiScale Mission

NASA Astrophysics Data System (ADS)

Breuillard, H.; Le Contel, O.; Chust, T.; Berthomier, M.; Retino, A.; Turner, D. L.; Nakamura, R.; Baumjohann, W.; Cozzani, G.; Catapano, F.; Alexandrova, A.; Mirioni, L.; Graham, D. B.; Argall, M. R.; Fischer, D.; Wilder, F. D.; Gershman, D. J.; Varsani, A.; Lindqvist, P.-A.; Khotyaintsev, Yu. V.; Marklund, G.; Ergun, R. E.; Goodrich, K. A.; Ahmadi, N.; Burch, J. L.; Torbert, R. B.; Needell, G.; Chutter, M.; Rau, D.; Dors, I.; Russell, C. T.; Magnes, W.; Strangeway, R. J.; Bromund, K. R.; Wei, H.; Plaschke, F.; Anderson, B. J.; Le, G.; Moore, T. E.; Giles, B. L.; Paterson, W. R.; Pollock, C. J.; Dorelli, J. C.; Avanov, L. A.; Saito, Y.; Lavraud, B.; Fuselier, S. A.; Mauk, B. H.; Cohen, I. J.; Fennell, J. F.

2018-01-01

Mirror mode waves are ubiquitous in the Earth's magnetosheath, in particular behind the quasi-perpendicular shock. Embedded in these nonlinear structures, intense lion roars are often observed. Lion roars are characterized by whistler wave packets at a frequency ˜100 Hz, which are thought to be generated in the magnetic field minima. In this study, we make use of the high time resolution instruments on board the Magnetospheric MultiScale mission to investigate these waves and the associated electron dynamics in the quasi-perpendicular magnetosheath on 22 January 2016. We show that despite a core electron parallel anisotropy, lion roars can be generated locally in the range 0.05-0.2fce by the perpendicular anisotropy of electrons in a particular energy range. We also show that intense lion roars can be observed up to higher frequencies due to the sharp nonlinear peaks of the signal, which appear as sharp spikes in the dynamic spectra. As a result, a high sampling rate is needed to estimate correctly their amplitude, and the latter might have been underestimated in previous studies using lower time resolution instruments. We also present for the first-time 3-D high time resolution electron velocity distribution functions in mirror modes. We demonstrate that the dynamics of electrons trapped in the mirror mode structures are consistent with the Kivelson and Southwood (1996) model. However, these electrons can also interact with the embedded lion roars: first signatures of electron quasi-linear pitch angle diffusion and possible signatures of nonlinear interaction with high-amplitude wave packets are presented. These processes can lead to electron untrapping from mirror modes.

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.

Using Recursive Regression to Explore Nonlinear Relationships and Interactions: A Tutorial Applied to a Multicultural Education Study

ERIC Educational Resources Information Center

Strang, Kenneth David

2009-01-01

This paper discusses how a seldom-used statistical procedure, recursive regression (RR), can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and…

Advances in nonlinear optical materials and devices

NASA Technical Reports Server (NTRS)

Byer, Robert L.

1991-01-01

The recent progress in the application of nonlinear techniques to extend the frequency of laser sources has come from the joint progress in laser sources and in nonlinear materials. A brief summary of the progress in diode pumped solid state lasers is followed by an overview of progress in nonlinear frequency extension by harmonic generation and parametric processes. Improved nonlinear materials including bulk crystals, quasiphasematched interactions, guided wave devices, and quantum well intersubband studies are discussed with the idea of identifying areas of future progress in nonlinear materials and devices.

MHD shocks in coronal mass ejections

NASA Technical Reports Server (NTRS)

Steinolfson, R. S.

1991-01-01

The primary objective of this research program is the study of the magnetohydrodynamic (MHD) shocks and nonlinear simple waves produced as a result of the interaction of ejected lower coronal plasma with the ambient corona. The types of shocks and nonlinear simple waves produced for representative coronal conditions and disturbance velocities were determined. The wave system and the interactions between the ejecta and ambient corona were studied using both analytic theory and numerical solutions of the time-dependent, nonlinear MHD equations. Observations from the SMM coronagraph/polarimeter provided both guidance and motivation and are used extensively in evaluating the results. As a natural consequence of the comparisons with the data, the simulations assisted in better understanding the physical interactions in coronal mass ejections (CME's).

Three-dimensional femtosecond laser processing for lab-on-a-chip applications

NASA Astrophysics Data System (ADS)

Sima, Felix; Sugioka, Koji; Vázquez, Rebeca Martínez; Osellame, Roberto; Kelemen, Lóránd; Ormos, Pal

2018-02-01

The extremely high peak intensity associated with ultrashort pulse width of femtosecond laser allows us to induce nonlinear interaction such as multiphoton absorption and tunneling ionization with materials that are transparent to the laser wavelength. More importantly, focusing the femtosecond laser beam inside the transparent materials confines the nonlinear interaction only within the focal volume, enabling three-dimensional (3D) micro- and nanofabrication. This 3D capability offers three different schemes, which involve undeformative, subtractive, and additive processing. The undeformative processing preforms internal refractive index modification to construct optical microcomponents including optical waveguides. Subtractive processing can realize the direct fabrication of 3D microfluidics, micromechanics, microelectronics, and photonic microcomponents in glass. Additive processing represented by two-photon polymerization enables the fabrication of 3D polymer micro- and nanostructures for photonic and microfluidic devices. These different schemes can be integrated to realize more functional microdevices including lab-on-a-chip devices, which are miniaturized laboratories that can perform reaction, detection, analysis, separation, and synthesis of biochemical materials with high efficiency, high speed, high sensitivity, low reagent consumption, and low waste production. This review paper describes the principles and applications of femtosecond laser 3D micro- and nanofabrication for lab-on-a-chip applications. A hybrid technique that promises to enhance functionality of lab-on-a-chip devices is also introduced.

Activities report in quantum optics

NASA Astrophysics Data System (ADS)

1985-03-01

Soft X-ray radiation from laser plasmas, intense Planck radiation, X-ray spectroscopy with transmission gratings, simulation of laser-produced shock waves, self-similar expansion in vacuum, radiation hydrodynamics, electronic structure of highly compressed matter, and heavy-ion beams for inertial confinement were investigated, and a high power iodine laser was developed. Laser-spectroscopy experiments, as well as a gravitational wave experiments were conducted. The fundamentals of light-matter interaction and nonlinear dynamics were studied. Many-photon ionization of molecules; spectroscopy of shock pairs; interaction of excited molecules with surfaces; IR laser applications; organic photochemistry with UV lasers; theoretical chemistry; and a ClF laser were investigated. Thin layers, and a high-pressure CO2 laser were studied.

Head-on collision of the second mode internal solitary waves

NASA Astrophysics Data System (ADS)

Terletska, Kateryna; Maderich, Vladimir; Jung, Kyung Tae

2017-04-01

Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internal waves on the oceanic shelf. Large amplitude internal solitary waves (ISW) of second mode containing trapped cores associated with closed streamlines can also transport plankton and nutrients. An interaction of ISWs with trapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-on collision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3D numerical model based on the Navier-Stokes equations for a continuously stratified fluid. Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneous deep layers can be identified: (i) the weakly nonlinear waves; (ii) the stable strongly nonlinear waves with trapped cores; and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Four interaction regimes for symmetric collision were separated from simulation results using this classification: (A) an almost elastic interaction of the weakly nonlinear waves; (B) a non-elastic interaction of waves with trapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h; (C) an almost elastic interaction of stable strongly nonlinear waves with trapped cores; (D) non-elastic interaction of the unstable strongly nonlinear waves. The unexpected result of simulation was that relative loss of energy due to the collision was maximal for regime B. New regime appeared when ISW of different amplitudes belonged to class (ii) collide. In result of interaction the exchange of mass between ISW occurred: the trapped core of smaller wave was entrained by core of larger ISW without mixing forming a new ISW of larger amplitude whereas in smaller ISW core of smaller wave totally substituted by fluid from larger wave. Overall, the wave characteristics induced by head-on collision agree well with the results of several available laboratory experiments. References [1] V. Maderich, K. T. Jung, K. Terletska, I. Brovchenko, T. Talipova, "Incomplete similarity of internal solitary waves with trapped core," Fluid Dynamics Research 47, 035511 (2015).

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.

Cases Study of Nonlinear Interaction Between Near-Inertial Waves Induced by Typhoon and Diurnal Tides Near the Xisha Islands

NASA Astrophysics Data System (ADS)

Liu, Junliang; He, Yinghui; Li, Juan; Cai, Shuqun; Wang, Dongxiao; Huang, Yandan

2018-04-01

Nonlinear interaction between near-inertial waves (NIWs) and diurnal tides (DTs) after nine typhoons near the Xisha Islands of the northwestern South China Sea (SCS) were investigated using three-year in situ mooring observation data. It was found that a harmonic wave (f + D1, hereafter referred to as fD1 wave), with a frequency equal to the sum of frequencies of NIWs and DTs (hereafter referred to as f and D1, respectively), was generated via nonlinear interaction between typhoon-induced NIWs and DTs after each typhoon. The fD1 wave mainly concentrates in the subsurface layer, and is mainly induced by the first component of the vertical nonlinear momentum term, the product of the vertical velocity of DT and vertical shear of near-inertial current (hereafter referred to as Component 1), in which the vertical shear of the near-inertial current greatly affects the strength of the fD1 current. The larger the Component 1, the stronger the fD1 currents. The background preexisting mesoscale anticyclonic eddy near the mooring site may also enhance the vertical velocity of DT and thus Component 1, which subsequently facilitates the nonlinear interaction-induced energy transfer to the fD1 wave and enhances the fD1 currents after the passage of a typhoon.

Experimental Proof for the Role of Nonlinear Photoionization in Plasmonic Phototherapy.

PubMed

Minai, Limor; Zeidan, Adel; Yeheskely-Hayon, Daniella; Yudovich, Shimon; Kviatkovsky, Inna; Yelin, Dvir

2016-07-13

Targeting individual cells within a heterogeneous tissue is a key challenge in cancer therapy, encouraging new approaches for cancer treatment that complement the shortcomings of conventional therapies. The highly localized interactions triggered by focused laser beams promise great potential for targeting single cells or small cell clusters; however, most laser-tissue interactions often involve macroscopic processes that may harm healthy nearby tissue and reduce specificity. Specific targeting of living cells using femtosecond pulses and nanoparticles has been demonstrated promising for various potential therapeutic applications including drug delivery via optoporation, drug release, and selective cell death. Here, using an intense resonant femtosecond pulse and cell-specific gold nanorods, we show that at certain irradiation parameters cell death is triggered by nonlinear plasmonic photoionization and not by thermally driven processes. The experimental results are supported by a physical model for the pulse-particle-medium interactions. A good correlation is found between the calculated total number and energy of the generated free electrons and the observed cell death, suggesting that femtosecond photoionization plays the dominant role in cell death.

Many-body effects in nonlinear optical responses of 2D layered semiconductors

DOE PAGES

Aivazian, Grant; Yu, Hongyi; Wu, Sanfeng; ...

2017-01-05

We performed ultrafast degenerate pump-probe spectroscopy on monolayer WSe2 near its exciton resonance. The observed differential reflectance signals exhibit signatures of strong many-body interactions including the exciton-exciton interaction and free carrier induced band gap renormalization. The exciton-exciton interaction results in a resonance blue shift which lasts for the exciton lifetime (several ps), while the band gap renormalization manifests as a resonance red shift with several tens ps lifetime. Our model based on the many-body interactions for the nonlinear optical susceptibility ts well the experimental observations. The power dependence of the spectra shows that with the increase of pump power, themore » exciton population increases linearly and then saturates, while the free carrier density increases superlinearly, implying that exciton Auger recombination could be the origin of these free carriers. Our model demonstrates a simple but efficient method for quantitatively analyzing the spectra, and indicates the important role of Coulomb interactions in nonlinear optical responses of such 2D materials.« less

Many-body effects in nonlinear optical responses of 2D layered semiconductors

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

Aivazian, Grant; Yu, Hongyi; Wu, Sanfeng

We performed ultrafast degenerate pump-probe spectroscopy on monolayer WSe2 near its exciton resonance. The observed differential reflectance signals exhibit signatures of strong many-body interactions including the exciton-exciton interaction and free carrier induced band gap renormalization. The exciton-exciton interaction results in a resonance blue shift which lasts for the exciton lifetime (several ps), while the band gap renormalization manifests as a resonance red shift with several tens ps lifetime. Our model based on the many-body interactions for the nonlinear optical susceptibility ts well the experimental observations. The power dependence of the spectra shows that with the increase of pump power, themore » exciton population increases linearly and then saturates, while the free carrier density increases superlinearly, implying that exciton Auger recombination could be the origin of these free carriers. Our model demonstrates a simple but efficient method for quantitatively analyzing the spectra, and indicates the important role of Coulomb interactions in nonlinear optical responses of such 2D materials.« less

Demystifying the Complexities of Gravity Wave Dynamics in the Middle Atmosphere: a Roadmap to Improved Weather Forecasts through High-Fidelity Modeling

NASA Astrophysics Data System (ADS)

Mixa, T.; Fritts, D. C.; Bossert, K.; Laughman, B.; Wang, L.; Lund, T.; Kantha, L. H.

2017-12-01

Gravity waves play a profound role in the mixing of the atmosphere, transporting vast amounts of momentum and energy among different altitudes as they propagate vertically. Above 60km in the middle atmosphere, high wave amplitudes enable a series of complex, nonlinear interactions with the background environment that produce highly-localized wind and temperature variations which alter the layering structure of the atmosphere. These small-scale interactions account for a significant portion of energy transport in the middle atmosphere, but they are difficult to characterize, occurring at spatial scales that are both challenging to observe with ground instruments and prohibitively small to include in weather forecasting models. Using high fidelity numerical simulations, these nuanced wave interactions are analyzed to better our understanding of these dynamics and improve the accuracy of long-term weather forecasting.

Statistical State Dynamics Based Study of the Role of Nonlinearity in the Maintenance of Turbulence in Couette Flow

NASA Astrophysics Data System (ADS)

Farrell, Brian; Ioannou, Petros; Nikolaidis, Marios-Andreas

2017-11-01

While linear non-normality underlies the mechanism of energy transfer from the externally driven flow to the perturbation field, nonlinearity is also known to play an essential role in sustaining turbulence. We report a study based on the statistical state dynamics of Couette flow turbulence with the goal of better understanding the role of nonlinearity in sustaining turbulence. The statistical state dynamics implementations used are ensemble closures at second order in a cumulant expansion of the Navier-Stokes equations in which the averaging operator is the streamwise mean. Two fundamentally non-normal mechanisms potentially contributing to maintaining the second cumulant are identified. These are essentially parametric perturbation growth arising from interaction of the perturbations with the fluctuating mean flow and transient growth of perturbations arising from nonlinear interaction between components of the perturbation field. By the method of selectively including these mechanisms parametric growth is found to maintain the perturbation field in the turbulent state while the more commonly invoked mechanism associated with transient growth of perturbations arising from scattering by nonlinear interaction is found to suppress perturbation variance. Funded by ERC Coturb Madrid Summer Program and NSF AGS-1246929.

Mastodon

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

Coleman, Justin Leigh; Veeraraghavan, Swetha; Bolisetti, Chandrakanth

MASTODON has the capability to model stochastic nonlinear soil-structure interaction (NLSSI) in a dynamic probabilistic risk assessment framework. The NLSSI simulations include structural dynamics, time integration, dynamic porous media flow, nonlinear hysteretic soil constitutive models, geometric nonlinearities (gapping, sliding, and uplift). MASTODON is also the MOOSE based master application for dynamic PRA of external hazards.

Ultra-fast switching of light by absorption saturation in vacuum ultra-violet region.

PubMed

Yoneda, Hitoki; Inubushi, Yuichi; Tanaka, Toshihiro; Yamaguchi, Yuta; Sato, Fumiya; Morimoto, Shunsuke; Kumagai, Taisuke; Nagasono, Mitsuru; Higashiya, Atsushi; Yabashi, Makina; Ishikawa, Tetsuya; Ohashi, Haruhiko; Kimura, Hiroaki; Kitamura, Hikaru; Kodama, Ryosuke

2009-12-21

Advances in free electron lasers producing high energy photons [Nat. Photonics 2(9), 555-559 (2008)] are expected to open up a new science of nonlinear optics of high energy photons. Specifically, lasers of photon energy higher than the plasma frequency of a metal can show new interaction features because they can penetrate deeply into metals without strong reflection. Here we show the observation of ultra-fast switching of vacuum ultra-violet (VUV) light caused by saturable absorption of a solid metal target. A strong gating is observed at energy fluences above 6J/cm2 at wavelength of 51 nm with tin metal thin layers. The ratio of the transmission at high intensity to low intensity is typically greater than 100:1. This means we can design new nonlinear photonic devices such as auto-correlator and pulse slicer for the VUV region.

Theoretical analysis and Vsim simulation of a low-voltage high-efficiency 250 GHz gyrotron

NASA Astrophysics Data System (ADS)

An, Chenxiang; Zhang, Dian; Zhang, Jun; Zhong, Huihuang

2018-02-01

Low-voltage, high-frequency gyrotrons with hundreds of watts of power are useful in radar, magnetic resonance spectroscopy and plasma diagnostic applications. In this paper, a 10 kV, 478 W, 250 GHz gyrotron with an efficiency of nearly 40% and a pitch ratio of 1.5 was designed through linear and nonlinear numerical analyses and Vsim particle-in-cell (PIC) simulation. Vsim is a highly efficient parallel PIC code, but it has seldom been used to carry out electron beam wave interaction simulations of gyro-devices. The setting up of the parameters required for the Vsim simulations of the gyrotron is presented. The results of Vsim simulations agree well with that of nonlinear numerical calculation. The commercial software Vsim7.2 completed the 3D gyrotron simulation in 80 h using a 20 core, 2.2 GHz personal computer with 256 GBytes of memory.

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

Development of a Nonlinear Acoustic Phased Array and its Interaction with Thin Plates

NASA Astrophysics Data System (ADS)

Anzel, Paul; Donahue, Carly; Daraio, Chiara

2015-03-01

Numerous technologies are based on the principle of focusing acoustic energy. We propose a new device to focus sound waves which exploits highly nonlinear dynamics. The advantages of this device are the capability of generating very highly powerful acoustic pulses and potential operation in high-temperature environments where traditional piezoelectrics may fail. This device is composed of rows of ball bearings placed in contact with a medium of interest and with an actuator on the top. Elastic spherical particles have a contact force that grows with their relative displacement to the three-halves power (Hertzian contact). When several spheres are placed in a row, the particles support the propagation of ``solitary waves''--strong, compact stress-wave pulses whose tendency to disperse is counteracted by the nonlinearity of the sphere's contact force. We present results regarding the experimental operation of the device and its comparison to theory and numerical simulations. We will show how well this system is capable of focusing energy at various locations in the medium, and the limits imposed by pre-compression. Finally, the effects of timing error on energy focusing will be demonstrated. This research has been supported by a NASA Space Technology Research Fellowship.

Route to thermalization in the α-Fermi–Pasta–Ulam system

PubMed Central

Onorato, Miguel; Vozella, Lara; Lvov, Yuri V.

2015-01-01

We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed. PMID:25805822

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

Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based onmore » spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.« less

Advanced Nonlinear Latent Variable Modeling: Distribution Analytic LMS and QML Estimators of Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Kelava, Augustin; Werner, Christina S.; Schermelleh-Engel, Karin; Moosbrugger, Helfried; Zapf, Dieter; Ma, Yue; Cham, Heining; Aiken, Leona S.; West, Stephen G.

2011-01-01

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x[superscript 2] [subscript 1], x[subscript 1]x[subscript 4]) to serve as indicators of each nonlinear latent construct. These approaches require the use of…

A Bayesian Model for the Estimation of Latent Interaction and Quadratic Effects When Latent Variables Are Non-Normally Distributed

ERIC Educational Resources Information Center

Kelava, Augustin; Nagengast, Benjamin

2012-01-01

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent…

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.

Development of a model to select plants with optimum metal phytoextraction potential.

PubMed

Guala, Sebastián D; Vega, Flora A; Covelo, Emma F

2011-07-01

The aim of the present study is to propose a nonlinear model which provides an indicator for the maximum phytoextraction of metals to help in the decision-making process. Research into different species and strategies plays an important role in the application of phytoextraction techniques to the remediation of contaminated soil. Also, the convenience of species according to their biomass and pollutant accumulation capacities has gained important space in discussions regarding remediation strategies, whether to choose species with low accumulation capacities and high biomass or high accumulation capacities with low biomass. The effects of heavy metals in soil on plant growth are studied by means of a nonlinear interaction model which relates the dynamics of the uptake of heavy metals by plants to heavy metal deposed in soil. The model, presented theoretically, provides an indicator for the maximum phytoextraction of metals which depends on adjustable parameters of both the plant and the environmental conditions. Finally, in order to clarify its applicability, a series of experimental results found in the literature are presented to show how the model performs consistently with real data. The inhibition of plant growth due to heavy metal concentration can be predicted by a simple kinetic model. The model proposed in this study makes it possible to characterize the nonlinear behaviour of the soil-plant interaction with heavy metal pollution in order to establish maximum uptake values for heavy metals in the harvestable part of plants.

Low-loss saturable absorbers based on tapered fibers embedded in carbon nanotube/polymer composites

NASA Astrophysics Data System (ADS)

Martinez, Amos; Al Araimi, Mohammed; Dmitriev, Artemiy; Lutsyk, Petro; Li, Shen; Mou, Chengbo; Rozhin, Alexey; Sumetsky, Misha; Turitsyn, Sergei

2017-12-01

The emergence of low-dimensional materials has opened new opportunities in the fabrication of compact nonlinear photonic devices. Single-walled carbon nanotubes were among the first of those materials to attract the attention of the photonics community owing to their high third order susceptibility, broadband operation, and ultrafast response. Saturable absorption, in particular, has become a widespread application for nanotubes in the mode-locking of a fiber laser where they are used as nonlinear passive amplitude modulators to initiate pulsed operation. Numerous approaches have been proposed for the integration of nanotubes in fiber systems; these can be divided into those that rely on direct interaction (where the nanotubes are sandwiched between fiber connectors) and those that rely on lateral interaction with the evanescence field of the propagating wave. Tapered fibers, in particular, offer excellent flexibility to adjust the nonlinearity of nanotube-based devices but suffer from high losses (typically exceeding 50%) and poor saturable to non-saturable absorption ratios (typically above 1:5). In this paper, we propose a method to fabricate carbon nanotube saturable absorbers with controllable saturation power, low-losses (as low as 15%), and large saturable to non-saturable loss ratios approaching 1:1. This is achieved by optimizing the procedure of embedding tapered fibers in low-refractive index polymers. In addition, this study sheds light in the operation of these devices, highlighting a trade-off between losses and saturation power and providing guidelines for the design of saturable absorbers according to their application.

Human systems dynamics: Toward a computational model

NASA Astrophysics Data System (ADS)

Eoyang, Glenda H.

2012-09-01

A robust and reliable computational model of complex human systems dynamics could support advancements in theory and practice for social systems at all levels, from intrapersonal experience to global politics and economics. Models of human interactions have evolved from traditional, Newtonian systems assumptions, which served a variety of practical and theoretical needs of the past. Another class of models has been inspired and informed by models and methods from nonlinear dynamics, chaos, and complexity science. None of the existing models, however, is able to represent the open, high dimension, and nonlinear self-organizing dynamics of social systems. An effective model will represent interactions at multiple levels to generate emergent patterns of social and political life of individuals and groups. Existing models and modeling methods are considered and assessed against characteristic pattern-forming processes in observed and experienced phenomena of human systems. A conceptual model, CDE Model, based on the conditions for self-organizing in human systems, is explored as an alternative to existing models and methods. While the new model overcomes the limitations of previous models, it also provides an explanatory base and foundation for prospective analysis to inform real-time meaning making and action taking in response to complex conditions in the real world. An invitation is extended to readers to engage in developing a computational model that incorporates the assumptions, meta-variables, and relationships of this open, high dimension, and nonlinear conceptual model of the complex dynamics of human systems.

Predicting the Highly Nonlinear Mechanical Properties of Polymeric Materials

NASA Astrophysics Data System (ADS)

Porter, David

2009-06-01

Over the past few years, we have developed models that calculate the highly nonlinear mechanical properties of polymers as a function of temperature, strain and strain rate from their molecular and morphological structure. A review of these models is presented here, with emphasis on combining the fundamental aspects of molecular physics that dictate these properties and the pragmatic need to make realistic predictions for our customers; the designer of new materials and the engineers who use these materials. The models calculate the highly nonlinear mechanical properties of polymers as a function of temperature, strain and strain rate from their molecular structure. The model is based upon the premise that mechanical properties are a direct consequence of energy stored and energy dissipated during deformation of a material. This premise is transformed into a consistent set of structure-property relations for the equation of state, EoS, and the engineering constitutive relations in a polymer by quantifying energy storage and loss at the molecular level of interactions between characteristic groups of atoms in a polymer. These relations are derived from a simple volumetric mean field Lennard-Jones potential function for the potential energy of intermolecular interactions in a polymer. First, properties such as temperature-volume relations and glass transition temperature are calculated directly from the potential function. Then, the `shock' EoS is derived simply by differentiating the potential function with respect to volume, assuming that the molecules cannot relax in the time scales of the deformation. The energy components are then used to predict the dynamic mechanical spectrum of a polymer in terms of temperature and rate. This can be transformed directly into the highly nonlinear stress-strain relations through yield. The constitutive relations are formulated as a set of analytical equations that predict properties directly in terms of a small set of structural parameters that can be calculated directly and independently from the chemical composition and morphology of a polymer. A number of examples are given to illustrate the model and also to show that the method can be applied, with appropriate modifications, to other materials.

Analytical filtration model for nonlinear viscoplastic oil in the theory of oil production stimulation and heating of oil reservoir in a dual-well system

NASA Astrophysics Data System (ADS)

Ivanovich Astafev, Vladimir; Igorevich Gubanov, Sergey; Alexandrovna Olkhovskaya, Valeria; Mikhailovna Sylantyeva, Anastasia; Mikhailovich Zinovyev, Alexey

2018-02-01

Production of high-viscosity oil and design of field development systems for such oil is one of the most promising directions in the development of world oil industry. The ability of high-viscosity oil to show in filtration process properties typical for non-Newtonian systems is proven by experimental studies. Nonlinear relationship between the pressure gradient and the rate of oil flow is due to interaction of high-molecular substances, in particular, asphaltenes and tars that form a plastic structure in it. The authors of this article have used the analytical model of stationary influx of nonlinear viscoplastic oil to the well bottom in order to provide rationale for the intensifying impact on a reservoir. They also have analyzed the method of periodic heating of productive reservoir by means of dual-wells. The high-temperature source is placed at the bottom of the vertical well, very close to the reservoir; at the same time the side well, located outside the zone of expected rock damage, is used for production. Suggested method of systemic treatment of reservoirs with dual wells can be useful for small fields of high-viscosity oil. The effect is based on the opportunity to control the structural and mechanical properties of high-viscosity oil and to increase depletion of reserves.

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.

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.

A Simple Theory of Capillary-Gravity Wave Turbulence

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1995-01-01

Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.

Sliding Mode Thermal Control System for Space Station Furnace Facility

NASA Technical Reports Server (NTRS)

Jackson Mark E.; Shtessel, Yuri B.

1998-01-01

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

On the interpretation of energy and energy fluxes of nonlinear internal waves: An example from Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.; Butman, B.

2006-01-01

A self-consistent formalism to estimate baroclinic energy densities and fluxes resulting from the propagation of internal waves of arbitrary amplitude is derived using the concept of available potential energy. The method can be applied to numerical, laboratory or field data. The total energy flux is shown to be the sum of the linear energy flux ??? u??? p??? dz (primes denote baroclinic quantities), plus contributions from the non-hydrostatic pressure anomaly and the self-advection of kinetic and available potential energy. Using highly resolved observations in Massachusetts Bay, it is shown that due to the presence of nonlinear internal waves periodically propagating in the area, ??? u??? p??? dz accounts for only half of the total flux. The same data show that equipartition of available potential and kinetic energy can be violated, especially when the nonlinear waves begin to interact with the bottom. ?? 2006 Cambridge University Press.

Nonlinear adhesion dynamics of confined lipid membranes

NASA Astrophysics Data System (ADS)

To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier

Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.

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

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Non-linear wave interaction in a plasma column

NASA Technical Reports Server (NTRS)

Larsen, J.-M.; Crawford, F. W.

1979-01-01

Non-linear three-wave interaction is analysed for propagation along a cylindrical plasma column surrounded by an infinite dielectric, in the absence of a static magnetic field. An averaged-Lagrangian method is used, and the results are specialized to parametric interaction and mode conversion, assuming an undepleted pump wave. The theory for these two types of interactions is extended to include imperfect synchronism, and the effects of loss. Computations are presented indicating that parametric growth rates of the order of a fraction of a decibel per centimeter should be obtainable for plausible laboratory plasma column parameters.

Response of jammed packings to thermal fluctuations

NASA Astrophysics Data System (ADS)

Wu, Qikai; Bertrand, Thibault; Shattuck, Mark D.; O'Hern, Corey S.

2017-12-01

We focus on the response of mechanically stable (MS) packings of frictionless, bidisperse disks to thermal fluctuations, with the aim of quantifying how nonlinearities affect system properties at finite temperature. In contrast, numerous prior studies characterized the structural and mechanical properties of MS packings of frictionless spherical particles at zero temperature. Packings of disks with purely repulsive contact interactions possess two main types of nonlinearities, one from the form of the interaction potential (e.g., either linear or Hertzian spring interactions) and one from the breaking (or forming) of interparticle contacts. To identify the temperature regime at which the contact-breaking nonlinearities begin to contribute, we first calculated the minimum temperatures Tc b required to break a single contact in the MS packing for both single- and multiple-eigenmode perturbations of the T =0 MS packing. We find that the temperature required to break a single contact for equal velocity-amplitude perturbations involving all eigenmodes approaches the minimum value obtained for a perturbation in the direction connecting disk pairs with the smallest overlap. We then studied deviations in the constant volume specific heat C¯V and deviations of the average disk positions Δ r from their T =0 values in the temperature regime TC ¯V100 for linear spring interactions is independent of system size. This result emphasizes that contact-breaking nonlinearities are dominant over form nonlinearities in the low-temperature range Tc b

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

NASA Astrophysics Data System (ADS)

Fiorina, B.; Lele, S. K.

2007-03-01

A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594-601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of 'wiggles' is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.

Reduced order modeling of fluid/structure interaction.

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

Barone, Matthew Franklin; Kalashnikova, Irina; Segalman, Daniel Joseph

2009-11-01

This report describes work performed from October 2007 through September 2009 under the Sandia Laboratory Directed Research and Development project titled 'Reduced Order Modeling of Fluid/Structure Interaction.' This project addresses fundamental aspects of techniques for construction of predictive Reduced Order Models (ROMs). A ROM is defined as a model, derived from a sequence of high-fidelity simulations, that preserves the essential physics and predictive capability of the original simulations but at a much lower computational cost. Techniques are developed for construction of provably stable linear Galerkin projection ROMs for compressible fluid flow, including a method for enforcing boundary conditions that preservesmore » numerical stability. A convergence proof and error estimates are given for this class of ROM, and the method is demonstrated on a series of model problems. A reduced order method, based on the method of quadratic components, for solving the von Karman nonlinear plate equations is developed and tested. This method is applied to the problem of nonlinear limit cycle oscillations encountered when the plate interacts with an adjacent supersonic flow. A stability-preserving method for coupling the linear fluid ROM with the structural dynamics model for the elastic plate is constructed and tested. Methods for constructing efficient ROMs for nonlinear fluid equations are developed and tested on a one-dimensional convection-diffusion-reaction equation. These methods are combined with a symmetrization approach to construct a ROM technique for application to the compressible Navier-Stokes equations.« less

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.

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Generation of terahertz radiation upon filtration of a supercontinuum produced during the propagation of a femtosecond laser pulse in a GaAs crystal

NASA Astrophysics Data System (ADS)

Vardanyan, Aleksandr O.; Oganesyan, David L.

2008-11-01

The results of a theoretical study of the formation of a supercontinuum produced due to the interaction of femtosecond laser pulses with an isotropic nonlinear medium are presented. The system of nonlinear Maxwell's equations was numerically integrated in time by the finite-difference method. The interaction of mutually orthogonal linearly-polarised 1.98-μm, 30-fs, 30-nJ pulses propagating along the normal to the 110 plane in a 1-mm-long GaAs crystal was considered. In the nonlinear part of the polarisation medium, the inertialless second-order nonlinear susceptibility was taken into account. The formation process of a terahertz pulse obtained due to the supercontinuum filtration was studied.

Complex and Nonlinear Pedagogy and the Implications for Physical Education

ERIC Educational Resources Information Center

Chow, Jia Yi; Atencio, Matthew

2014-01-01

There is increasing support to describe and examine the teaching of game skills in physical education from a complex and nonlinear perspective. The emergence of game behaviours as a consequence of the dynamic interactions of the learner, the game environment and the task constraints within the game context highlights the nonlinear and complex…

Exact multisoliton solutions of general nonlinear Schrödinger equation with derivative.

PubMed

Li, Qi; Duan, Qiu-yuan; Zhang, Jian-bing

2014-01-01

Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.

A Learning Progression Should Address Regression: Insights from Developing Non-Linear Reasoning in Ecology

ERIC Educational Resources Information Center

Hovardas, Tasos

2016-01-01

Although ecological systems at varying scales involve non-linear interactions, learners insist thinking in a linear fashion when they deal with ecological phenomena. The overall objective of the present contribution was to propose a hypothetical learning progression for developing non-linear reasoning in prey-predator systems and to provide…

Theory of plasmonic effects in nonlinear optics: the case of graphene

NASA Astrophysics Data System (ADS)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

NASA Technical Reports Server (NTRS)

Enns, Dale F.; Bugajski, Daniel J.; Carter, John; Antoniewicz, Bob

1994-01-01

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

Cross scale interactions, nonlinearities, and forecasting catastrophic events

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, Roger A.; Bestelmeyer, Brandon T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, Kris M.

2004-01-01

Catastrophic events share characteristic nonlinear behaviors that are often generated by cross-scale interactions and feedbacks among system elements. These events result in surprises that cannot easily be predicted based on information obtained at a single scale. Progress on catastrophic events has focused on one of the following two areas: nonlinear dynamics through time without an explicit consideration of spatial connectivity [Holling, C. S. (1992) Ecol. Monogr. 62, 447–502] or spatial connectivity and the spread of contagious processes without a consideration of cross-scale interactions and feedbacks [Zeng, N., Neeling, J. D., Lau, L. M. & Tucker, C. J. (1999) Science 286, 1537–1540]. These approaches rarely have ventured beyond traditional disciplinary boundaries. We provide an interdisciplinary, conceptual, and general mathematical framework for understanding and forecasting nonlinear dynamics through time and across space. We illustrate the generality and usefulness of our approach by using new data and recasting published data from ecology (wildfires and desertification), epidemiology (infectious diseases), and engineering (structural failures). We show that decisions that minimize the likelihood of catastrophic events must be based on cross-scale interactions, and such decisions will often be counterintuitive. Given the continuing challenges associated with global change, approaches that cross disciplinary boundaries to include interactions and feedbacks at multiple scales are needed to increase our ability to predict catastrophic events and develop strategies for minimizing their occurrence and impacts. Our framework is an important step in developing predictive tools and designing experiments to examine cross-scale interactions.

Non-linear blend coding in the moth antennal lobe emerges from random glomerular networks

PubMed Central

Capurro, Alberto; Baroni, Fabiano; Olsson, Shannon B.; Kuebler, Linda S.; Karout, Salah; Hansson, Bill S.; Pearce, Timothy C.

2012-01-01

Neural responses to odor blends often exhibit non-linear interactions to blend components. The first olfactory processing center in insects, the antennal lobe (AL), exhibits a complex network connectivity. We attempt to determine if non-linear blend interactions can arise purely as a function of the AL network connectivity itself, without necessitating additional factors such as competitive ligand binding at the periphery or intrinsic cellular properties. To assess this, we compared blend interactions among responses from single neurons recorded intracellularly in the AL of the moth Manduca sexta with those generated using a population-based computational model constructed from the morphologically based connectivity pattern of projection neurons (PNs) and local interneurons (LNs) with randomized connection probabilities from which we excluded detailed intrinsic neuronal properties. The model accurately predicted most of the proportions of blend interaction types observed in the physiological data. Our simulations also indicate that input from LNs is important in establishing both the type of blend interaction and the nature of the neuronal response (excitation or inhibition) exhibited by AL neurons. For LNs, the only input that significantly impacted the blend interaction type was received from other LNs, while for PNs the input from olfactory sensory neurons and other PNs contributed agonistically with the LN input to shape the AL output. Our results demonstrate that non-linear blend interactions can be a natural consequence of AL connectivity, and highlight the importance of lateral inhibition as a key feature of blend coding to be addressed in future experimental and computational studies. PMID:22529799

Nonlinear propagation of light in Dirac matter.

PubMed

Eliasson, Bengt; Shukla, P K

2011-09-01

The nonlinear interaction between intense laser light and a quantum plasma is modeled by a collective Dirac equation coupled with the Maxwell equations. The model is used to study the nonlinear propagation of relativistically intense laser light in a quantum plasma including the electron spin-1/2 effect. The relativistic effects due to the high-intensity laser light lead, in general, to a downshift of the laser frequency, similar to a classical plasma where the relativistic mass increase leads to self-induced transparency of laser light and other associated effects. The electron spin-1/2 effects lead to a frequency upshift or downshift of the electromagnetic (EM) wave, depending on the spin state of the plasma and the polarization of the EM wave. For laboratory solid density plasmas, the spin-1/2 effects on the propagation of light are small, but they may be significant in superdense plasma in the core of white dwarf stars. We also discuss extensions of the model to include kinetic effects of a distribution of the electrons on the nonlinear propagation of EM waves in a quantum plasma.

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.

A weakly nonlinear theory for wave-vortex interactions in curved channel flow

NASA Technical Reports Server (NTRS)

Singer, Bart A.; Erlebacher, Gordon; Zang, Thomas A.

1992-01-01

A weakly nonlinear theory is developed to study the interaction of Tollmien-Schlichting (TS) waves and Dean vortices in curved channel flow. The predictions obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. Some discrepancies in the results of a previous theory with direct numerical simulations are resolved.

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.

Nonlinear optical interactions in silicon waveguides

NASA Astrophysics Data System (ADS)

Kuyken, B.; Leo, F.; Clemmen, S.; Dave, U.; Van Laer, R.; Ideguchi, T.; Zhao, H.; Liu, X.; Safioui, J.; Coen, S.; Gorza, S. P.; Selvaraja, S. K.; Massar, S.; Osgood, R. M.; Verheyen, P.; Van Campenhout, J.; Baets, R.; Green, W. M. J.; Roelkens, G.

2017-03-01

The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

Nonlinear Curve-Fitting Program

NASA Technical Reports Server (NTRS)

Everhart, Joel L.; Badavi, Forooz F.

1989-01-01

Nonlinear optimization algorithm helps in finding best-fit curve. Nonlinear Curve Fitting Program, NLINEAR, interactive curve-fitting routine based on description of quadratic expansion of X(sup 2) statistic. Utilizes nonlinear optimization algorithm calculating best statistically weighted values of parameters of fitting function and X(sup 2) minimized. Provides user with such statistical information as goodness of fit and estimated values of parameters producing highest degree of correlation between experimental data and mathematical model. Written in FORTRAN 77.

Study of solar wind spectra by nonlinear waves interaction

NASA Astrophysics Data System (ADS)

Dwivedi, Navin; Sharma, Rampal; Narita, Yasuhito

2014-05-01

The nature of small-scale turbulent fluctuations in the solar wind (SW) turbulence is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations predict the evidence of the dominance of kinetic Alfvén waves (KAW) at sub-ion scales with frequency below than ion cyclotron frequency, while other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode is more relevant. In the present work, nonlinear interaction of kinetic Alfvén wave with whistler wave is considered as one of the possible cause responsible for the solar wind turbulence. A set of coupled dimensionless equations are derived for the intermediate beta plasmas and the nonlinear interaction between these two wave modes has been studied. As a consequence of ponderomotive nonlinearity, the pump KAW becomes filamented when its power exceeds the threshold for the filamentation instability. Whistler is considered to be weak and thus doesn't have enough intensity to initiate its own localization. It gets localized while propagating through the density channel created by KAW localization. In addition, spectral scales of power spectra of KAW and whistler are also calculated. The steeper spectra are found with scaling greater than -5/3. This type of nonlinear interaction between different wave modes and steeper spectra is one of the reasons for the solar wind turbulence and particles acceleration. This work is partially supported by DST (India) and FP7/STORM (313038)

Laser-Matter Interaction in Dielectrics: Insight from Picosecond-Pulsed Second-Harmonic Generation in Periodically Poled LiTaO3

NASA Astrophysics Data System (ADS)

Louchev, Oleg A.; Wada, Satoshi; Panchenko, Vladislav Ya.

2017-08-01

We develop a modified two-temperature (2T) model of laser-matter interaction in dielectrics based on experimental insight from picosecond-pulsed high-frequency temperature-controlled second-harmonic (515 nm) generation in periodically poled stoichiometric LiTaO3 crystal and required for computational treatment of short-pulsed nonlinear optics and materials processing applications. We show that the incorporation of an extended set of recombination-kinetics-related energy-release and heat-exchange processes following short-pulsed photoionization by two-photon absorption of the second harmonic allows accurate simulation of the electron-lattice relaxation dynamics and electron-lattice temperature evolution in LiTaO3 crystal in nonlinear laser-frequency conversion. Our experimentally confirmed model and detailed simulation study show that two-photon ionization with the recombination mechanism via ion-electron-lattice interaction followed by a direct transfer of the recombination energy to the lattice is the main laser-matter energy-transfer pathway responsible for the majority of the crystal lattice heating (approximately 90%) continuing for approximately 50 ps after laser-pulse termination and competing with effect of electron-phonon energy transfer from the free electrons. This time delay is due to a recombination bottleneck which hinders faster relaxation to thermal equilibrium in photoionized dielectric crystal. Generally, our study suggests that in dielectrics photoionized by short-pulsed radiation with intensity range used in nonlinear laser-frequency conversion, the electron-lattice relaxation period is defined by the recombination-stage bottleneck of a few tens of picoseconds and not by the time of the electron-phonon energy transfer. This modification of the 2T model can be applied to a broad range of processes involving laser-matter interactions in dielectrics and semiconductors for charge density reaching the range of 1021- 1022 cm-3 .

Nonlinear interaction of the Tsugaru Warm Current and tide in the Tsugaru Strait

NASA Astrophysics Data System (ADS)

Wada, Ryota; Waseda, Takuji; Nanjo, Hirotada

2012-06-01

The Tsugaru Strait, which connects the Sea of Japan with the Pacific Ocean, is characterized by the eastward Tsugaru Warm Current (TWC) and oscillating tidal currents of similar magnitude. A 15-day current observation was conducted in one of the two narrow channels in the strait, at the northwest tip of the Shimokita Peninsula. The observation revealed that the spectral energy of the semidiurnal current exceeds that of the diurnal current, contrary to the conventional view. The Tsugaru Strait regional model was developed to study the mechanism of this spectral energy reversal (140-141.5° E, 40.4-42.6° N, 500 m grid resolution). At the eastern and western open boundaries, the model was driven by the constant Tsugaru warm current and tidal elevation, which was adjusted by comparing the model with tidal gauge observations within the channel. The relative magnitude of the spectral energies differed from that of the observation when the model was driven by tide only. However, the spectral energy levels were reversed when the model was driven by both tide and current. The nonlinear interaction of periodic tidal currents and the steady TWC was explained by the vorticity equation, which describes the production and advection of residual currents from tidal currents. According to the model results, flow separation and advection of vorticity by the TWC was the most prominent factor in this phenomenon. Because of the strong nonlinearities, flow separation around the headland occurred during the tidal period with dominant current magnitude and furnished the main difference between the diurnal and semidiurnal interactions. These phenomena were enhanced by the complex topography, and demonstrate the importance of scale interaction, especially when developing high-resolution regional models.

Wave-vortex interactions in the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Guo, Yuan; Bühler, Oliver

2014-02-01

This is a theoretical study of wave-vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave-vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave-vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.

Petawatt laser absorption bounded

PubMed Central

Levy, Matthew C.; Wilks, Scott C.; Tabak, Max; Libby, Stephen B.; Baring, Matthew G.

2014-01-01

The interaction of petawatt (1015 W) lasers with solid matter forms the basis for advanced scientific applications such as table-top particle accelerators, ultrafast imaging systems and laser fusion. Key metrics for these applications relate to absorption, yet conditions in this regime are so nonlinear that it is often impossible to know the fraction of absorbed light f, and even the range of f is unknown. Here using a relativistic Rankine-Hugoniot-like analysis, we show for the first time that f exhibits a theoretical maximum and minimum. These bounds constrain nonlinear absorption mechanisms across the petawatt regime, forbidding high absorption values at low laser power and low absorption values at high laser power. For applications needing to circumvent the absorption bounds, these results will accelerate a shift from solid targets, towards structured and multilayer targets, and lead the development of new materials. PMID:24938656

The interaction of intense, ultra-short microwave beams with the plasma generated by gas ionization

NASA Astrophysics Data System (ADS)

Shafir, G.; Cao, Y.; Bliokh, Y.; Leopold, J. G.; Levko, D.; Rostov, V.; Gad, R.; Fisher, A.; Bernshtam, V.; Krasik, Ya. E.

2018-03-01

Results of the non-linear interaction of an extremely short (0.6 ns) high power (˜500 MW) X-band focused microwave beam with the plasma generated by gas ionization are presented. Within certain gas pressure ranges, specific to the gas type, the plasma density is considerably lower around the microwave beam axis than at its periphery, thus forming guiding channel through which the beam self-focuses. Outside these pressure ranges, either diffuse or streamer-like plasma is observed. We also observe high energy electrons (˜15 keV), accelerated by the very high-power microwaves. A simplified analytical model of this complicated dynamical system and particle-in-cell numerical simulations confirm the experimental results.

Design of optimal nonlinear network controllers for Alzheimer's disease.

PubMed

Sanchez-Rodriguez, Lazaro M; Iturria-Medina, Yasser; Baines, Erica A; Mallo, Sabela C; Dousty, Mehdy; Sotero, Roberto C

2018-05-01

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer's disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients' biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer's Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks-namely, networks having low average shortest path length, high global efficiency-are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

Visual analysis of mass cytometry data by hierarchical stochastic neighbour embedding reveals rare cell types.

PubMed

van Unen, Vincent; Höllt, Thomas; Pezzotti, Nicola; Li, Na; Reinders, Marcel J T; Eisemann, Elmar; Koning, Frits; Vilanova, Anna; Lelieveldt, Boudewijn P F

2017-11-23

Mass cytometry allows high-resolution dissection of the cellular composition of the immune system. However, the high-dimensionality, large size, and non-linear structure of the data poses considerable challenges for the data analysis. In particular, dimensionality reduction-based techniques like t-SNE offer single-cell resolution but are limited in the number of cells that can be analyzed. Here we introduce Hierarchical Stochastic Neighbor Embedding (HSNE) for the analysis of mass cytometry data sets. HSNE constructs a hierarchy of non-linear similarities that can be interactively explored with a stepwise increase in detail up to the single-cell level. We apply HSNE to a study on gastrointestinal disorders and three other available mass cytometry data sets. We find that HSNE efficiently replicates previous observations and identifies rare cell populations that were previously missed due to downsampling. Thus, HSNE removes the scalability limit of conventional t-SNE analysis, a feature that makes it highly suitable for the analysis of massive high-dimensional data sets.

Engineering aspect of the microwave ionosphere nonlinear interaction experiment (MINIX) with a sounding rocket

NASA Astrophysics Data System (ADS)

Nagatomo, Makoto; Kaya, Nobuyuki; Matsumoto, Hiroshi

The Microwave Ionosphere Nonlinear Interaction Experiment (MINIX) is a sounding rocket experiment to study possible effects of strong microwave fields in case it is used for energy transmission from the Solar Power Satellite (SPS) upon the Earth's atmosphere. Its secondary objective is to develop high power microwave technology for space use. Two rocket-borne magnetrons were used to emit 2.45 GHz microwave in order to make a simulated condition of power transmission from an SPS to a ground station. Sounding of the environment radiated by microwave was conducted by the diagnostic package onboard the daughter unit which was separated slowly from the mother unit. The main design drivers of this experiment were to build such high power equipments in a standard type of sounding rocket, to keep the cost within the budget and to perform a series of experiments without complete loss of the mission. The key technology for this experiment is a rocket-borne magnetron and high voltage converter. Location of position of the daughter unit relative to the mother unit was a difficult requirement for a spin-stabilized rocket. These problems were solved by application of such a low cost commercial products as a magnetron for microwave oven and a video tape recorder and camera.

Non-linear vehicle-bridge-wind interaction model for running safety assessment of high-speed trains over a high-pier viaduct

NASA Astrophysics Data System (ADS)

Olmos, José M.; Astiz, Miguel Á.

2018-04-01

In order to properly study the high-speed traffic safety on a high-pier viaduct subject to episodes of lateral turbulent winds, an efficient dynamic interaction train-bridge-wind model has been developed and experimentally validated. This model considers the full wheel and rail profiles, the friction between these two bodies in contact, and the piers P-Delta effect. The model has been used to determine the critical train and wind velocities from which the trains cannot travel safely over the O'Eixo Bridge. The dynamic simulations carried out and the results obtained in the time domain show that traffic safety rates exceed the allowed limits for turbulent winds with mean velocities at the deck higher than 25 m/s.

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.

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).

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.

Creep-fatigue interaction at high temperature; Proceedings of the Symposium, 112th ASME Winter Annual Meeting, Atlanta, GA, Dec. 1-6, 1991

NASA Astrophysics Data System (ADS)

Haritos, George K.; Ochoa, O. O.

Various papers on creep-fatigue interaction at high temperature are presented. Individual topics addressed include: analysis of elevated temperature fatigue crack growth mechanisms in Alloy 718, physically based microcrack propagation laws for creep-fatigue-environment interaction, in situ SEM observation of short fatigue crack growth in Waspaloy at 700 C under cyclic and dwell conditions, evolution of creep-fatigue life prediction models, TMF design considerations in turbine airfoils of advanced turbine engines. Also discussed are: high temperature fatigue life prediction computer code based on the total strain version of strainrange partitioning, atomic theory of thermodynamics of internal variables, geometrically nonlinear analysis of interlaminar stresses in unsymmetrically laminated plates subjected to uniform thermal loading, experimental investigation of creep crack tip deformation using moire interferometry. (For individual items see A93-31336 to A93-31344)

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

Masking effects of low-frequency sinusoidal gratings on the detection of contrast modulation in high-frequency carriers

NASA Astrophysics Data System (ADS)

Henning, G. Bruce

2004-04-01

A modification and extension of Kortum and Geisler's model [Vision Res. 35, 1595 (1995)] of early visual nonlinearities that incorporates an expansive nonlinearity (consistent with neurophysiological findings [Vision Res. 35, 2725 (1995)], a normalization based on a local average retinal illumination, similar to Mach's proposal [F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden-Day, San Francisco, Calif., 1965)], and a subsequent compression suggested by Henning et al. [J. Opt. Soc. Am A 17, 1147 (2000)] captures a range of hitherto unexplained interactions between a sinusoidal grating of low spatial frequency and a contrast-modulated grating 2 octaves higher in spatial frequency.

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.

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

NASA Astrophysics Data System (ADS)

Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

2016-02-01

We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

Wavepacket dynamics in a family of nonlinear Fibonacci lattices

NASA Astrophysics Data System (ADS)

Pandey, Mohit; Campbell, David

We examine the dynamics of a quantum particle in a variety of one-dimensional Fibonacci lattices (which are shifted from each other) in the presence of interaction. To describe the nonlinear interactions we employ the discrete nonlinear Schrödinger (DNLS) equation. Using a single-site localized state in the lattice as our initial condition, we evolve the wavepacket numerically using DNLS equation. We compute the root-mean-square width of the wavepacket as it evolves in time and show how the ``global location'' of initial wavepacket affects the dynamics. We compare and contrast our results with earlier studies of related but distinct models.

Nonlinear electromagnetic interactions in energetic materials

DOE PAGES

Wood, Mitchell Anthony; Dalvit, Diego Alejandro; Moore, David Steven

2016-01-12

We study the scattering of electromagnetic waves in anisotropic energetic materials. Nonlinear light-matter interactions in molecular crystals result in frequency-conversion and polarization changes. Applied electromagnetic fields of moderate intensity can induce these nonlinear effects without triggering chemical decomposition, offering a mechanism for the nonionizing identification of explosives. We use molecular-dynamics simulations to compute such two-dimensional THz spectra for planar slabs made of pentaerythritol tetranitrate and ammonium nitrate. Finally, we discuss third-harmonic generation and polarization-conversion processes in such materials. These observed far-field spectral features of the reflected or transmitted light may serve as an alternative tool for standoff explosive detection.

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

NASA Astrophysics Data System (ADS)

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

2016-03-01

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

Energetics of slope flows: linear and weakly nonlinear solutions of the extended Prandtl model

NASA Astrophysics Data System (ADS)

Güttler, Ivan; Marinović, Ivana; Večenaj, Željko; Grisogono, Branko

2016-07-01

The Prandtl model succinctly combines the 1D stationary boundary-layer dynamics and thermodynamics of simple anabatic and katabatic flows over uniformly inclined surfaces. It assumes a balance between the along-the-slope buoyancy component and adiabatic warming/cooling, and the turbulent mixing of momentum and heat. In this study, energetics of the Prandtl model is addressed in terms of the total energy (TE) concept. Furthermore, since the authors recently developed a weakly nonlinear version of the Prandtl model, the TE approach is also exercised on this extended model version, which includes an additional nonlinear term in the thermodynamic equation. Hence, interplay among diffusion, dissipation and temperature-wind interaction of the mean slope flow is further explored. The TE of the nonlinear Prandtl model is assessed in an ensemble of solutions where the Prandtl number, the slope angle and the nonlinearity parameter are perturbed. It is shown that nonlinear effects have the lowest impact on variability in the ensemble of solutions of the weakly nonlinear Prandtl model when compared to the other two governing parameters. The general behavior of the nonlinear solution is similar to the linear solution, except that the maximum of the along-the-slope wind speed in the nonlinear solution reduces for larger slopes. Also, the dominance of PE near the sloped surface, and the elevated maximum of KE in the linear and nonlinear energetics of the extended Prandtl model are found in the PASTEX-94 measurements. The corresponding level where KE>PE most likely marks the bottom of the sublayer subject to shear-driven instabilities. Finally, possible limitations of the weakly nonlinear solutions of the extended Prandtl model are raised. In linear solutions, the local storage of TE term is zero, reflecting the stationarity of solutions by definition. However, in nonlinear solutions, the diffusion, dissipation and interaction terms (where the height of the maximum interaction is proportional to the height of the low-level jet by the factor ≈4/9) do not balance and the local storage of TE attains non-zero values. In order to examine the issue of non-stationarity, the inclusion of velocity-pressure covariance in the momentum equation is suggested for future development of the extended Prandtl model.

Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

NASA Astrophysics Data System (ADS)

Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

2018-01-01

We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

Quantum corrections to the generalized Proca theory via a matter field

NASA Astrophysics Data System (ADS)

Amado, André; Haghani, Zahra; Mohammadi, Azadeh; Shahidi, Shahab

2017-09-01

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.

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.; Novokhatskii, V. V.

1984-04-01

Nonlinear interactions (including wavefront reversal) of light from CW or pulsed 10.6-micron CO2 lasers at the semiconductor-metal phase transition in a VO2 film are investigated experimentally. The results are presented in graphs and characterized in detail. The intensity reflection coefficients of the three-wave interactions are found to be 0.5 percent for a CW reference wave of intensity 900 mW/sq cm and 42 percent for a pulsed reference wave of threshold density 600-800 microjoule/sq cm.

Light-induced valley polarization in interacting and nonlinear Weyl semimetals

NASA Astrophysics Data System (ADS)

Bertrand, Simon; Garate, Ion; Côté, René

2017-08-01

It has been recently predicted that the interplay between Coulomb interactions and Berry curvature can produce interesting optical phenomena in topologically nontrivial two-dimensional insulators. Here, we present a theory of the interband optical absorption for three-dimensional, doped Weyl semimetals. We find that the Berry curvature, Coulomb interactions, and the nonlinearity in the single-particle energy spectrum can together enable a light-induced valley polarization. We support and supplement our numerical results with an analytical toy model calculation, which unveils topologically nontrivial Mahan excitons with nonzero vorticity.

Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.

NASA LeRC/Akron University Graduate Cooperative Fellowship Program and Graduate Student Researchers Program

NASA Technical Reports Server (NTRS)

Fertis, D. G.; Simon, A. L.

1981-01-01

The requisite methodology to solve linear and nonlinear problems associated with the static and dynamic analysis of rotating machinery, their static and dynamic behavior, and the interaction between the rotating and nonrotating parts of an engine is developed. Linear and nonlinear structural engine problems are investigated by developing solution strategies and interactive computational methods whereby the man and computer can communicate directly in making analysis decisions. Representative examples include modifying structural models, changing material, parameters, selecting analysis options and coupling with interactive graphical display for pre- and postprocessing capability.

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

Raman parametric excitation effect upon the third harmonic generation by a metallic nanoparticle lattice

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

Sepehri Javan, N., E-mail: sepehri-javan@uma.ac.ir

2015-08-21

This work is a theoretical study on third harmonic generation in the nonlinear propagation of an intense laser pulse through a periodic three-dimensional lattice of nanoparticles. Using a perturbative method, the nonlinear equations that describe the laser–nanoparticle interaction in the weakly relativistic regime are derived. Additionally, the nonlinear dispersion relation and the amplitude of the third harmonic are obtained. Finally, the effects of the nanoparticle radius and separation length, the distribution of the nanoparticle electron density, and the laser frequency upon the third harmonic efficiency are investigated. In addition to the expected resonance that occurs when the third harmonic resonatesmore » with the plasmon wave, another resonance appears when the nonlinear interaction of the fundamental mode with the third harmonic excites a longitudinal collective plasmon wave via the parametric Raman mechanism.« less

Nonlinear interaction of kinetic Alfven wave and whistler: Turbulent spectra and anisotropic scaling

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

Kumar Dwivedi, Navin; Sharma, R. P.

2013-04-15

In this work, we are presenting the excitation of oblique propagating whistler wave as a consequence of nonlinear interaction between whistler wave and kinetic Alfven wave (KAW) in intermediate beta plasmas. Numerical simulation has been done to study the transient evolution of magnetic field structures of KAW when the nonlinearity arises due to ponderomotive effects by taking the adiabatic response of the background density. Weak oblique propagating whistler signals in these nonlinear plasma density filaments (produced by KAW localization) get amplified. The spectral indices of the power spectrum at different times are calculated with given initial conditions of the simulations.more » Anisotropic scaling laws for KAW and whistlers are presented. The relevance of the present investigation to solar wind turbulence and its acceleration is also pointed out.« less

Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

NASA Technical Reports Server (NTRS)

Balsa, Thomas F.; Gartside, James

1995-01-01

The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Davis, Dominic A. R.; Smith, Frank T.

1993-01-01

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

Kelvin-wave cascade in the vortex filament model

NASA Astrophysics Data System (ADS)

Baggaley, Andrew W.; Laurie, Jason

2014-01-01

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

Note: Nonpolar solute partial molar volume response to attractive interactions with water.

PubMed

Williams, Steven M; Ashbaugh, Henry S

2014-01-07

The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.

Note: Nonpolar solute partial molar volume response to attractive interactions with water

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

Williams, Steven M.; Ashbaugh, Henry S., E-mail: hanka@tulane.edu

2014-01-07

The impact of attractive interactions on the partial molar volumes of methane-like solutes in water is characterized using molecular simulations. Attractions account for a significant 20% volume drop between a repulsive Weeks-Chandler-Andersen and full Lennard-Jones description of methane interactions. The response of the volume to interaction perturbations is characterized by linear fits to our simulations and a rigorous statistical thermodynamic expression for the derivative of the volume to increasing attractions. While a weak non-linear response is observed, an average effective slope accurately captures the volume decrease. This response, however, is anticipated to become more non-linear with increasing solute size.

Speculative behavior and asset price dynamics.

PubMed

Westerhoff, Frank

2003-07-01

This paper deals with speculative trading. Guided by empirical observations, a nonlinear deterministic asset pricing model is developed in which traders repeatedly choose between technical and fundamental analysis to determine their orders. The interaction between the trading rules produces complex dynamics. The model endogenously replicates the stylized facts of excess volatility, high trading volumes, shifts in the level of asset prices, and volatility clustering.

Principles of Nonlinear Optics

DTIC Science & Technology

1989-11-01

modelled by a ring cavity. The nonlinear meterial is between mirrors I and 2. E., E and I r E denote the incident, reflected and transmitted electric...Pasta and S. Ulam, "Studies of Nonlinear Problems I," Los Alamos Rep. LA 1940, 1955. 10. L. F. McGoldrick, "Resonant Interactions among Capillary- gravity ...34 Proc. IEEE, vol. 67, pp. 1442-1443, 1979. 23. P. P. Banerjee, A. Korpel and K. E. Lonngren," Self-refraction of Nonlinear Capillary- gravity Waves

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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.

Nonlinear heating of ions by electron cyclotron frequency waves

NASA Astrophysics Data System (ADS)

Zestanakis, P. A.; Hizanidis, K.; Ram, A. K.; Kominis, Y.

2010-11-01

We study the nonlinear interaction of ions with electron cyclotron (EC) wave packets in a magnetized plasma. Previous studies have shown that such interactions with high frequency electrostatic lower hybrid waves can lead to coherent energization of ions. It requires the frequency bandwidth of the wave packet to be broader than the ion cyclotron frequency [1,2]. For the electromagnetic high frequency EC waves we have developed a more general theory, based on the Lie transform canonical perturbation method [3,4]. We apply the theory to the case of two overlapping EC beams. The wave frequency of each beam is assumed to be frequency modulated with a modulation bandwidth comparable to the ion cyclotron frequency. We present results for both X-mode and O-mode and illustrate the conditions for ion energization. [4pt] [1] D. Benisti, A. K. Ram, and A. Bers, Phys. Plasmas 5, 3224 (1998). [0pt] [2] A. K. Ram, A. Bers, and D. Benisti , J. Geophys. Res. 103, 9431 (1998). [0pt] [3] J.R. Cary and A.N. Kaufman, Phys. Fluids 24, 1238 (1981). [0pt] [4] R.L. Dewar, J. Phys A-Math. Gen 9, 2043 (1976).

Nonlinear QED effects in X-ray emission of pulsars

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

Shakeri, Soroush; Haghighat, Mansour; Xue, She-Sheng, E-mail: Soroush.Shakeri@ph.iut.ac.ir, E-mail: m.haghighat@shirazu.ac.ir, E-mail: xue@icra.it

2017-10-01

In the presence of strong magnetic fields near pulsars, the QED vacuum becomes a birefringent medium due to nonlinear QED interactions. Here, we explore the impact of the effective photon-photon interaction on the polarization evolution of photons propagating through the magnetized QED vacuum of a pulsar. We solve the quantum Boltzmann equation within the framework of the Euler-Heisenberg Lagrangian to find the evolution of the Stokes parameters. We find that linearly polarized X-ray photons propagating outward in the magnetosphere of a rotating neutron star can acquire high values for the circular polarization parameter. Meanwhile, it is shown that the polarizationmore » characteristics of photons besides photon energy depend strongly on parameters of the pulsars such as magnetic field strength, inclination angle and rotational period. Our results are clear predictions of QED vacuum polarization effects in the near vicinity of magnetic stars which can be tested with the upcoming X-ray polarimetric observations.« less

Seasonally forced disease dynamics explored as switching between attractors

NASA Astrophysics Data System (ADS)

Keeling, Matt J.; Rohani, Pejman; Grenfell, Bryan T.

2001-01-01

Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This ‘binary’ nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella.

On the nonlinear aerodynamic and stability characteristics of a generic chine-forebody slender-wing fighter configuration

NASA Technical Reports Server (NTRS)

Erickson, Gary E.; Brandon, Jay M.

1987-01-01

An exploratory investigation was conducted of the nonlinear aerodynamic and stability characteristics of a tailless generic fighter configuration featuring a chine-shaped forebody coupled to a slender cropped delta wing in the NASA Langley Research Center's 12-Foot Low-Speed Wind Tunnel. Forebody and wing vortex flow mechanisms were identified through off-body flow visualizations to explain the trends in the longitudinal and lateral-directional characteristics at extreme attitudes (angles of attack and sideslip). The interactions of the vortical motions with centerline and wing-mounted vertical tail surfaces were studied and the flow phenomena were correlated with the configuration forces and moments. Single degree of freedom, free-to-roll tests were used to study the wing rock susceptibility of the generic fighter model. Modifications to the nose region of the chine forebody were examined and fluid mechanisms were established to account for their ineffectiveness in modulating the highly interactive forebody and wing vortex systems.

Laser-Neuron Interaction with Femtosecond Beat-Modulated 800-1200 nm Photon Beams, as the Treatment of Brain Cancer Tissue. Laser Neurophysics

NASA Astrophysics Data System (ADS)

Stefan, V. Alexander

2011-03-01

I propose a novel mechanism for the brain cancer tissue treatment: nonlinear interaction of ultrashort pulses of beat-photon, (ω1 -- ω2) , or double-photon, (ω1 +ω2) , beams with the cancer tissue. The multiphoton scattering is described via photon diffusion equation. The open-scull cerebral tissue can be irradiated with the beat-modulated photon pulses with the laser irradiances in the range of a few mW/cm2 , and repetition rate of a few 100s Hz generated in the beat-wave driven free electron laser. V. Stefan, B. I. Cohen, and C. Joshi, Nonlinear Mixing of Electromagnetic Waves in PlasmasScience 27 January 1989: V. Alexander Stefan, Genomic Medical Physics: A New Physics in the Making, (S-U-Press, 2008).} This highly accurate cancer tissue ablation removal may prove to be an efficient method for the treatment of brain cancer. Work supported in part by Nikola Tesla Laboratories (Stefan University), La Jolla, CA.

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

Tollmien-Schlichting/vortex interactions in compressible boundary layer flows

NASA Technical Reports Server (NTRS)

Blackaby, Nicholas D.

1993-01-01

The weakly nonlinear interaction of oblique Tollmien-Schlichting waves and longitudinal vortices in compressible, high Reynolds number, boundary-layer flow over a flat plate is considered for all ranges of the Mach number. The interaction equations comprise of equations for the vortex which is indirectly forced by the waves via a boundary condition, whereas a vortex term appears in the amplitude equation for the wave pressure. The downstream solution properties of interaction equations are found to depend on the sign of an interaction coefficient. Compressibility is found to have a significant effect on the interaction properties; principally through its impact on the waves and their governing mechanism, the triple-deck structure. It is found that, in general, the flow quantities will grow slowly with increasing downstream co-ordinate; i.e. in general, solutions do not terminate in abrupt, finite-distance 'break-ups'.

On unravelling mechanism of interplay between cloud and large scale circulation: a grey area in climate science

NASA Astrophysics Data System (ADS)

De, S.; Agarwal, N. K.; Hazra, Anupam; Chaudhari, Hemantkumar S.; Sahai, A. K.

2018-04-01

The interaction between cloud and large scale circulation is much less explored area in climate science. Unfolding the mechanism of coupling between these two parameters is imperative for improved simulation of Indian summer monsoon (ISM) and to reduce imprecision in climate sensitivity of global climate model. This work has made an effort to explore this mechanism with CFSv2 climate model experiments whose cloud has been modified by changing the critical relative humidity (CRH) profile of model during ISM. Study reveals that the variable CRH in CFSv2 has improved the nonlinear interactions between high and low frequency oscillations in wind field (revealed as internal dynamics of monsoon) and modulates realistically the spatial distribution of interactions over Indian landmass during the contrasting monsoon season compared to the existing CRH profile of CFSv2. The lower tropospheric wind error energy in the variable CRH simulation of CFSv2 appears to be minimum due to the reduced nonlinear convergence of error to the planetary scale range from long and synoptic scales (another facet of internal dynamics) compared to as observed from other CRH experiments in normal and deficient monsoons. Hence, the interplay between cloud and large scale circulation through CRH may be manifested as a change in internal dynamics of ISM revealed from scale interactive quasi-linear and nonlinear kinetic energy exchanges in frequency as well as in wavenumber domain during the monsoon period that eventually modify the internal variance of CFSv2 model. Conversely, the reduced wind bias and proper modulation of spatial distribution of scale interaction between the synoptic and low frequency oscillations improve the eastward and northward extent of water vapour flux over Indian landmass that in turn give feedback to the realistic simulation of cloud condensates attributing improved ISM rainfall in CFSv2.

Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming

NASA Astrophysics Data System (ADS)

Hubicki, Christian; Goldman, Daniel; Ames, Aaron

In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

PubMed

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Development of non-linear models predicting daily fine particle concentrations using aerosol optical depth retrievals and ground-based measurements at a municipality in the Brazilian Amazon region

NASA Astrophysics Data System (ADS)

Gonçalves, Karen dos Santos; Winkler, Mirko S.; Benchimol-Barbosa, Paulo Roberto; de Hoogh, Kees; Artaxo, Paulo Eduardo; de Souza Hacon, Sandra; Schindler, Christian; Künzli, Nino

2018-07-01

Epidemiological studies generally use particulate matter measurements with diameter less 2.5 μm (PM2.5) from monitoring networks. Satellite aerosol optical depth (AOD) data has considerable potential in predicting PM2.5 concentrations, and thus provides an alternative method for producing knowledge regarding the level of pollution and its health impact in areas where no ground PM2.5 measurements are available. This is the case in the Brazilian Amazon rainforest region where forest fires are frequent sources of high pollution. In this study, we applied a non-linear model for predicting PM2.5 concentration from AOD retrievals using interaction terms between average temperature, relative humidity, sine, cosine of date in a period of 365,25 days and the square of the lagged relative residual. Regression performance statistics were tested comparing the goodness of fit and R2 based on results from linear regression and non-linear regression for six different models. The regression results for non-linear prediction showed the best performance, explaining on average 82% of the daily PM2.5 concentrations when considering the whole period studied. In the context of Amazonia, it was the first study predicting PM2.5 concentrations using the latest high-resolution AOD products also in combination with the testing of a non-linear model performance. Our results permitted a reliable prediction considering the AOD-PM2.5 relationship and set the basis for further investigations on air pollution impacts in the complex context of Brazilian Amazon Region.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

PubMed

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Breathers in systems with intrinsic and extrinsic nonlinearities

NASA Astrophysics Data System (ADS)

Cruzeiro-Hansson, L.; Eilbeck, J. C.; Marín, J. L.; Russell, F. M.

2000-08-01

We study the interplay between nonlinearity and localization in a model consisting of a quantum quasiparticle interacting with a nonlinear extended lattice. The isolated lattice can support discrete breathers, and the coupling of the quasiparticle to the lattice leads to localized quasiparticle states. Minimum energy states of the full system can have both a breather and a solitonic character. Excited states lead to interesting new phenomena, such as full breather states, which arise from the combination of intrinsic and extrinsic nonlinearity.

Characterizing Observed Limit Cycles in the Cassini Main Engine Guidance Control System

NASA Technical Reports Server (NTRS)

Rizvi, Farheen; Weitl, Raquel M.

2011-01-01

The Cassini spacecraft dynamics-related telemetry during long Main Engine (ME) burns has indicated the presence of stable limit cycles between 0.03-0.04 Hz frequencies. These stable limit cycles cause the spacecraft to possess non-zero oscillating rates for extended periods of time. This indicates that the linear ME guidance control system does not model the complete dynamics of the spacecraft. In this study, we propose that the observed limit cycles in the spacecraft dynamics telemetry appear from a stable interaction between the unmodeled nonlinear elements in the ME guidance control system. Many nonlinearities in the control system emerge from translating the linear engine gimbal actuator (EGA) motion into a spacecraft rotation. One such nonlinearity comes from the gear backlash in the EGA system, which is the focus of this paper. The limit cycle characteristics and behavior can be predicted by modeling this gear backlash nonlinear element via a describing function and studying the interaction of this describing function with the overall dynamics of the spacecraft. The linear ME guidance controller and gear backlash nonlinearity are modeled analytically. The frequency, magnitude, and nature of the limit cycle are obtained from the frequency response of the ME guidance controller and nonlinear element. In addition, the ME guidance controller along with the nonlinearity is simulated. The simulation response contains a limit cycle with similar characterstics as predicted analytically: 0.03-0.04 Hz frequency and stable, sustained oscillations. The analytical and simulated limit cycle responses are compared to the flight telemetry for long burns such as the Saturn Orbit Insertion and Main Engine Orbit Trim Maneuvers. The analytical and simulated limit cycle characteristics compare well with the actual observed limit cycles in the flight telemetry. Both have frequencies between 0.03-0.04 Hz and stable oscillations. This work shows that the stable limit cycles occur due to the interaction between the unmodeled nonlinear elements and linear ME guidance controller.

Nonlinear light-matter interactions in engineered optical media

NASA Astrophysics Data System (ADS)

Litchinitser, Natalia

In this talk, we consider fundamental optical phenomena at the interface of nonlinear and singular optics in artificial media, including theoretical and experimental studies of linear and nonlinear light-matter interactions of vector and singular optical beams in metamaterials. We show that unique optical properties of metamaterials open unlimited prospects to ``engineer'' light itself. Thanks to their ability to manipulate both electric and magnetic field components, metamaterials open new degrees of freedom for tailoring complex polarization states and orbital angular momentum (OAM) of light. We will discuss several approaches to structured light manipulation on the nanoscale using metal-dielectric, all-dielectric and hyperbolic metamaterials. These new functionalities, including polarization and OAM conversion, beam magnification and de-magnification, and sub-wavelength imaging using novel non-resonant hyperlens are likely to enable a new generation of on-chip or all-fiber structured light applications. The emergence of metamaterials also has a strong potential to enable a plethora of novel nonlinear light-matter interactions and even new nonlinear materials. In particular, nonlinear focusing and defocusing effects are of paramount importance for manipulation of the minimum focusing spot size of structured light beams necessary for nanoscale trapping, manipulation, and fundamental spectroscopic studies. Colloidal suspensions offer as a promising platform for engineering polarizibilities and realization of large and tunable nonlinearities. We will present our recent studies of the phenomenon of spatial modulational instability leading to laser beam filamentation in an engineered soft-matter nonlinear medium. Finally, we introduce so-called virtual hyperbolic metamaterials formed by an array of plasma channels in air as a result of self-focusing of an intense laser pulse, and show that such structure can be used to manipulate microwave beams in a free space. This work was supported by the Army Research Office Awards (W911NF-15-1-0146, W911NF-11-1-0297).

Nonlinear Relaxation in Population Dynamics

NASA Astrophysics Data System (ADS)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

Nonlinear Wave-Particle Interaction: Implications for Newborn Planetary and Backstreaming Proton Velocity Distribution Functions

NASA Astrophysics Data System (ADS)

Romanelli, N.; Mazelle, C.; Meziane, K.

2018-02-01

Seen from the solar wind (SW) reference frame, the presence of newborn planetary protons upstream from the Martian and Venusian bow shocks and SW protons reflected from each of them constitutes two sources of nonthermal proton populations. In both cases, the resulting proton velocity distribution function is highly unstable and capable of giving rise to ultralow frequency quasi-monochromatic electromagnetic plasma waves. When these instabilities take place, the resulting nonlinear waves are convected by the SW and interact with nonthermal protons located downstream from the wave generation region (upstream from the bow shock), playing a predominant role in their dynamics. To improve our understanding of these phenomena, we study the interaction between a charged particle and a large-amplitude monochromatic circularly polarized electromagnetic wave propagating parallel to a background magnetic field, from first principles. We determine the number of fix points in velocity space, their stability, and their dependence on different wave-particle parameters. Particularly, we determine the temporal evolution of a charged particle in the pitch angle-gyrophase velocity plane under nominal conditions expected for backstreaming protons in planetary foreshocks and for newborn planetary protons in the upstream regions of Venus and Mars. In addition, the inclusion of wave ellipticity effects provides an explanation for pitch angle distributions of suprathermal protons observed at the Earth's foreshock, reported in previous studies. These analyses constitute a mean to evaluate if nonthermal proton velocity distribution functions observed at these plasma environments present signatures that can be understood in terms of nonlinear wave-particle processes.

Unilateral contact induced blade/casing vibratory interactions in impellers: Analysis for rigid casings

NASA Astrophysics Data System (ADS)

Batailly, Alain; Meingast, Markus; Legrand, Mathias

2015-02-01

This contribution addresses the vibratory analysis of unilateral-contact induced structural interactions between a bladed impeller and its surrounding rigid casing. Such assemblies can be found in helicopter or small aircraft engines for instance and the interactions of interest shall arise due to the always tighter operating clearances between the rotating and stationary components. The investigation is conducted by extending to cyclically symmetric structures an in-house time-marching based tool dedicated to unilateral contact occurrences in turbomachines. The main components of the considered impeller together with the associated assumptions and modelling principles considered in this work are detailed. Typical dynamical features of cyclically symmetric structures, such as the aliasing effect and frequency clustering are explored in this nonlinear framework by means of thorough frequency-domain analyses and harmonic trackings of the numerically predicted impeller displacements. Additional contact maps highlight the existence of critical rotational velocities at which displacements potentially reach high amplitudes due to the synchronization of the bladed assembly vibratory pattern with the shape of the rigid casing. The proposed numerical investigations are also compared to a simpler and (almost) empirical criterion: it is suggested, based on nonlinear numerical simulations with a linear reduced order model of the impeller and a rigid casing, that this criterion may miss important critical velocities emanating from the unfavorable combination of aliasing and contact-induced higher harmonics in the vibratory response of the impeller. Overall, this work suggests a way to enhance guidelines to improve the design of impellers in the context of nonlinear and nonsmooth dynamics.

Counter-propagating wave interaction for contrast-enhanced ultrasound imaging

NASA Astrophysics Data System (ADS)

Renaud, G.; Bosch, J. G.; ten Kate, G. L.; Shamdasani, V.; Entrekin, R.; de Jong, N.; van der Steen, A. F. W.

2012-11-01

Most techniques for contrast-enhanced ultrasound imaging require linear propagation to detect nonlinear scattering of contrast agent microbubbles. Waveform distortion due to nonlinear propagation impairs their ability to distinguish microbubbles from tissue. As a result, tissue can be misclassified as microbubbles, and contrast agent concentration can be overestimated; therefore, these artifacts can significantly impair the quality of medical diagnoses. Contrary to biological tissue, lipid-coated gas microbubbles used as a contrast agent allow the interaction of two acoustic waves propagating in opposite directions (counter-propagation). Based on that principle, we describe a strategy to detect microbubbles that is free from nonlinear propagation artifacts. In vitro images were acquired with an ultrasound scanner in a phantom of tissue-mimicking material with a cavity containing a contrast agent. Unlike the default mode of the scanner using amplitude modulation to detect microbubbles, the pulse sequence exploiting counter-propagating wave interaction creates no pseudoenhancement behind the cavity in the contrast image.

Test particle simulation study of whistler wave packets observed near Comet Giacobini-Zinner

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Tsurutani, B. T.

1989-01-01

Nonlinear interactions of water group ions with large-amplitude whistler wave packets detected at the leading edge of steepened magnetosonic waves observed near Comet Giacobini-Zinner (GZ) are studied using test particle simulations of water-ion interactions with a model wave based on GZ data. Some of the water ions are found to be decelerated in the steepened portion of the magnetosonic wave to the resonance velocity with the whistler wave packets. Through resonance and related nonlinear interaction with the large-amplitude whistler waves, the water ions become trapped by the packet. An energy balance calculation demonstrates that the trapped ions lose their kinetic energy during the trapped motion in the packet. Thus, the nonlinear trapping motion in the wave structure leads to effective energy transfer from the water group ions to the whistler wave packets in the leading edge of the steepened MHD waves.

An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

PubMed

Neilson, Peter D; Neilson, Megan D

2005-09-01

Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

Interactions of localized wave structures and dynamics in the defocusing coupled nonlinear Schrödinger equations.

PubMed

Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong

2017-04-01

We investigate the defocusing coupled nonlinear Schrödinger equations from a 3×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.

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.

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.

Substrate clamping effects on irreversible domain wall dynamics in lead zirconate titanate thin films.

PubMed

Griggio, F; Jesse, S; Kumar, A; Ovchinnikov, O; Kim, H; Jackson, T N; Damjanovic, D; Kalinin, S V; Trolier-McKinstry, S

2012-04-13

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

Information flow to assess cardiorespiratory interactions in patients on weaning trials.

PubMed

Vallverdú, M; Tibaduisa, O; Clariá, F; Hoyer, D; Giraldo, B; Benito, S; Caminal, P

2006-01-01

Nonlinear processes of the autonomic nervous system (ANS) can produce breath-to-breath variability in the pattern of breathing. In order to provide assess to these nonlinear processes, nonlinear statistical dependencies between heart rate variability and respiratory pattern variability are analyzed. In this way, auto-mutual information and cross-mutual information concepts are applied. This information flow analysis is presented as a short-term non linear analysis method to investigate the information flow interactions in patients on weaning trials. 78 patients from mechanical ventilation were studied: Group A of 28 patients that failed to maintain spontaneous breathing and were reconnected; Group B of 50 patients with successful trials. The results show lower complexity with an increase of information flow in group A than in group B. Furthermore, a more (weakly) coupled nonlinear oscillator behavior is observed in the series of group A than in B.

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

Modulated microwave microscopy and probes used therewith

DOEpatents

Lai, Keji; Kelly, Michael; Shen, Zhi-Xun

2012-09-11

A microwave microscope including a probe tip electrode vertically positionable over a sample and projecting downwardly from the end of a cantilever. A transmission line connecting the tip electrode to the electronic control system extends along the cantilever and is separated from a ground plane at the bottom of the cantilever by a dielectric layer. The probe tip may be vertically tapped near or at the sample surface at a low frequency and the microwave signal reflected from the tip/sample interaction is demodulated at the low frequency. Alternatively, a low-frequency electrical signal is also a non-linear electrical element associated with the probe tip to non-linearly interact with the applied microwave signal and the reflected non-linear microwave signal is detected at the low frequency. The non-linear element may be semiconductor junction formed near the apex of the probe tip or be an FET formed at the base of a semiconducting tip.

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.

Hopfield-Kerr model and analogue black hole radiation in dielectrics

NASA Astrophysics Data System (ADS)

Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.; Doronzo, M.

2017-11-01

In the context of the interaction between the electromagnetic field and a dielectric dispersive lossless medium, we present a nonlinear version of the relativistically covariant Hopfield model, which is suitable for the description of a dielectric Kerr perturbation propagating in a dielectric medium. The nonlinearity is introduced in the Lagrangian through a self-interacting term proportional to the fourth power of the polarization field. We find an exact solution for the nonlinear equations describing a propagating perturbation in the dielectric medium. Furthermore, the presence of an analogue Hawking effect, as well as the thermal properties of the model, are discussed, confirming and improving the results achieved in the scalar case.

Vibron Solitons and Soliton-Induced Infrared Spectra of Crystalline Acetanilide

NASA Astrophysics Data System (ADS)

Takeno, S.

1986-01-01

Red-shifted infrared spectra at low temperatures of amide I (C=O stretching) vibrations of crystalline acetanilide measured by Careri et al. are shown to be due to vibron solitons, which are nonlinearity-induced localized modes of vibrons arising from their nonlinear interactions with optic-type phonons. A nonlinear eigenvalue equation giving the eigenfrequency of stationary solitons is solved approximately by introducing lattice Green's functions, and the obtained result is in good agreement with the experimental result. Inclusion of interactions with acoustic phonons yields the Debye-Waller factor in the zero-phonon line spectrum of vibron solitons, in a manner analogous to the case of impurity-induced localized harmonic phonon modes in alkali halides.

User's manual for interactive LINEAR: A FORTRAN program to derive linear aircraft models

NASA Technical Reports Server (NTRS)

Antoniewicz, Robert F.; Duke, Eugene L.; Patterson, Brian P.

1988-01-01

An interactive FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models is documented in this report. The program LINEAR numerically determines a linear system model using nonlinear equations of motion and a user-supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model.

Nonlinear dynamics of toroidal Alfvén eigenmodes in presence of tearing modes

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Sorption of selected organic compounds from water to a peat soil and its humic-acid and humin fractions: Potential sources of the sorption nonlinearity

USGS Publications Warehouse

Chiou, C.T.; Kile, D.E.; Rutherford, D.W.; Sheng, G.; Boyd, S.A.

2000-01-01

The sorption isotherms of ethylene dibromide (EDB), diuron (DUN), and 3,5-dichlorophenol (DCP) from water on the humic acid and humin fractions of a peat soil and on the humic-acid of a muck soil have been measured. The data were compared with those of the solutes with the whole peat from which the humic-acid (HA) and humin (HM) fractions were derived and on which the sorption of the solutes exhibited varying extents of nonlinear capacities at low relative concentrations (C(e)/S(w)). The HA fraction as prepared by the density-fractionated method is relatively pure and presumably free of high- surface-area carbonaceous material (HSACM) that is considered to be responsible for the observed nonlinear sorption for nonpolar solutes (e.g., EDB) on the peat; conversely, the base-insoluble HM fraction as prepared is presumed to be enriched with HSACM, as manifested by the greatly higher BET- (N2) surface area than that of the whole peat. The sorption of EDB on HA exhibits no visible nonlinear effect, whereas the sorption on HM shows an enhanced nonlinearity over that on the whole peat. The sorption of polar DUN and DCP on HA and HM display nonlinear effects comparable with those on the whole peat; the effects are much more significant than those with nonpolar EDB. These results conform to the hypothesis that adsorption onto a small amount of strongly adsorbing HSACM is largely responsible for the nonlinear sorption of nonpolar solutes on soils and that additional specific interactions with the active groups of soil organic matter are responsible for the generally higher nonlinear sorption of the polar solutes.

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Mcrae, D. S.

1992-01-01

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

Multiplying and detecting propagating microwave photons using inelastic Cooper-pair tunneling

NASA Astrophysics Data System (ADS)

Leppäkangas, Juha; Marthaler, Michael; Hazra, Dibyendu; Jebari, Salha; Albert, Romain; Blanchet, Florian; Johansson, Göran; Hofheinz, Max

2018-01-01

The interaction between propagating microwave fields and Cooper-pair tunneling across a DC-voltage-biased Josephson junction can be highly nonlinear. We show theoretically that this nonlinearity can be used to convert an incoming single microwave photon into an outgoing n -photon Fock state in a different mode. In this process, the electrostatic energy released in a Cooper-pair tunneling event is transferred to the outgoing Fock state, providing energy gain. The created multiphoton Fock state is frequency entangled and highly bunched. The conversion can be made reflectionless (impedance matched) so that all incoming photons are converted to n -photon states. With realistic parameters, multiplication ratios n >2 can be reached. By two consecutive multiplications, the outgoing Fock-state number can get sufficiently large to accurately discriminate it from vacuum with linear postamplification and power measurement. Therefore, this amplification scheme can be used as a single-photon detector without dead time.

Highly sensitive nonlinear luminescent ceramics for volumetric and multilayer data carriers

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

Martynovich, E F; Dresvyanskiy, V P; Voitovich, A P

2015-10-31

The interaction of optical ceramics based on wide-bandgap crystals with near-IR femtosecond laser radiation is studied experimentally. The formation of luminescent centres in LiF and MgF{sub 2} ceramics under the action of single laser pulses is considered. Two interaction regimes are used. In the regime of low-aperture focusing of laser radiation (800 nm, 30 fs, 0.3 mJ), multiple selffocusing and filamentation in the samples are observed. The luminescent centres are formed in thin channels induced by light filaments. The average effective self-focusing length is ∼100 μm; the formation of luminescent centres begins at this length and ceases at a wavelengthmore » of about 380 mm. The luminescent trace (spur) induced by a single laser filament was ∼30 μm long and 1.3 μm in diameter. The second regime of light interaction with the sample was based on high-aperture focusing with a simultaneous decrease in the laser pulse energy. This led to the formation of single pits with a diameter smaller than the optical diffraction limit. The luminescent centres induced by the laser radiation were aggregated colour centres. The mechanism of their creation included the highly-nonlinear generation of electron – hole pairs in the filamentation region, their recombination with the formation of anion excitons and the decay of excitons into Fresnel defects by the Lushchik – Vitol – Hersh – Pooley mechanism, as well as their recharging, migration and aggregation. (laser applications and other topics in quantum electronics)« less

Complex nonlinear autonomic nervous system modulation link cardiac autonomic neuropathy and peripheral vascular disease.

PubMed

Khalaf, Kinda; Jelinek, Herbert F; Robinson, Caroline; Cornforth, David J; Tarvainen, Mika P; Al-Aubaidy, Hayder

2015-01-01

Physiological interactions are abundant within, and between, body systems. These interactions may evolve into discrete states during pathophysiological processes resulting from common mechanisms. An association between arterial stenosis, identified by low ankle-brachial pressure index (ABPI) and cardiovascular disease (CVD) as been reported. Whether an association between vascular calcification-characterized by high ABPI and a different pathophysiology-is similarly associated with CVD, has not been established. The current study aims to investigate the association between ABPI, and cardiac rhythm, as an indicator of cardiovascular health and functionality, utilizing heart rate variability (HRV). Two hundred and thirty six patients underwent ABPI assessment. Standard time and frequency domain, and non-linear HRV measures were determined from 5-min electrocardiogram. ABPI data were divided into normal (n = 101), low (n = 67) and high (n = 66) and compared to HRV measures.(DFAα1 and SampEn were significantly different between the low ABPI, high ABPI and control groups (p < 0.05). A possible coupling between arterial stenosis and vascular calcification with decreased and increased HRV respectively was observed. Our results suggest a model for interpreting the relationship between vascular pathophysiology and cardiac rhythm. The cardiovascular system may be viewed as a complex system comprising a number of interacting subsystems. These cardiac and vascular subsystems/networks may be coupled and undergo transitions in response to internal or external perturbations. From a clinical perspective, the significantly increased sample entropy compared to the normal ABPI group and the decreased and increased complex correlation properties measured by DFA for the low and high ABPI groups respectively, may be useful indicators that a more holistic treatment approach in line with this more complex clinical picture is required.

On the design of experiments for the study of extreme field limits in the ultra-relativistic interaction of electromagnetic waves with plasmas

NASA Astrophysics Data System (ADS)

Bulanov, Sergei V.; Esirkepov, Timur Z.; Hayashi, Yukio; Kando, Masaki; Kiriyama, Hiromitsu; Koga, James K.; Kondo, Kiminori; Kotaki, Hideyuki; Pirozhkov, Alexander S.; Bulanov, Stepan S.; Zhidkov, Alexei G.; Chen, Pisin; Neely, David; Kato, Yoshiaki; Narozhny, Nikolay B.; Korn, Georg

2011-06-01

The critical electric field of quantum electrodynamics, called also the Schwinger field, is so strong that it produces electron-positron pairs from vacuum, converting the energy of light into matter. Since the dawn of quantum electrodynamics, there has been a dream on how to reach it on Earth. With the rise of laser technology this field has become feasible through the construction of extremely high power lasers or/and with the sophisticated use of nonlinear processes in relativistic plasmas. This is one of the most attractive motivations for extremely high power laser development, i.e. producing matter from vacuum by pure light in fundamental process of quantum electrodynamics in the nonperturbative regime. Recently it has been realized that a laser with intensity well below the Schwinger limit can create an avalanche of electron-positron pairs similar to a discharge before attaining the Schwinger field. It has also been realized that the Schwinger limit can be reached using an appropriate configuration of laser beams. In experiments on the collision of laser light and high intensity electromagnetic pulses generated by relativistic flying mirrors, with electron bunches produced by a conventional accelerator and with laser wake field accelerated electrons the studying of extreme field limits in the nonlinear interaction of electromagnetic waves is proposed. The regimes of dominant radiation reaction, which completely changes the electromagnetic wave-matter interaction, will be revealed. This will result in a new powerful source of high brightness gamma-rays. A possibility of the demonstration of the electronpositron pair creation in vacuum via multi-photon processes can be realized. This will allow modeling under terrestrial laboratory conditions neutron star magnetospheres, cosmological gamma ray bursts and the Leptonic Era of the Universe.

System theoretic models for high density VLSI structures

NASA Astrophysics Data System (ADS)

Dickinson, Bradley W.; Hopkins, William E., Jr.

This research project involved the development of mathematical models for analysis, synthesis, and simulation of large systems of interacting devices. The work was motivated by problems that may become important in high density VLSI chips with characteristic feature sizes less than 1 micron: it is anticipated that interactions of neighboring devices will play an important role in the determination of circuit properties. It is hoped that the combination of high device densities and such local interactions can somehow be exploited to increase circuit speed and to reduce power consumption. To address these issues from the point of view of system theory, research was pursued in the areas of nonlinear and stochastic systems and into neural network models. Statistical models were developed to characterize various features of the dynamic behavior of interacting systems. Random process models for studying the resulting asynchronous modes of operation were investigated. The local interactions themselves may be modeled as stochastic effects. The resulting behavior was investigated through the use of various scaling limits, and by a combination of other analytical and simulation techniques. Techniques arising in a variety of disciplines where models of interaction were formulated and explored were considered and adapted for use.

Integrable pair-transition-coupled nonlinear Schrödinger equations.

PubMed

Ling, Liming; Zhao, Li-Chen

2015-08-01

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

Propagation and Interactions of Ultrahigh Power Light: Relativistic Nonlinear Optics

DTIC Science & Technology

2014-09-30

energy electron beams [16,17]. In the simplest implementation, a 2-mm supersonic nozzle is used to produce a high density gas flow (ne=10 19 cm-3...was a high-density jet of neutral helium produced by a 3 or 4 mm-diameter supersonic Laval nozzle . The neutral density profile (characterized...250 MeV and total charge of 0.1 nC (>50 MeV) Figure 7: (a) Gas target profiles, measured using tomography, at a height of 2 mm above the nozzle

X-ray two-photon absorption with high fluence XFEL pulses

DOE PAGES

Hoszowska, Joanna; Szlachetko, J.; Dousse, J. -Cl.; ...

2015-09-07

Here, we report on nonlinear interaction of solid Fe with intense femtosecond hard x-ray free-electron laser (XFEL) pulses. The experiment was performed at the CXI end-station of the Linac Coherent Light Source (LCLS) by means of high- resolution x-ray emission spectroscopy. The focused x-ray beam provided extreme fluence of ~10 5 photons/Å 2. Two-photon absorption leading to K-shell hollow atom formation and to single K-shell ionization of solid Fe was investigated.

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.

New model for high-power electromagnetic field instability in transparent media

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

Gruzdev, V.E.; Libenson, M.N.

A model of high-power field instability is developed to describe local abrupt increasing of electromagnetic field intensity in transparent dielectric. Small local enhancement of the field amplitude is initiated by low-absorbing spherical inclusion which size is less than radiation wavelength. Exceeding threshold of optical bistability results in abrupt increasing of field amplitude in the defect that also leads to local increasing of field amplitude in the host material in the vicinity of the inclusion. Bearing in mind nonlinear dependence of refractive index of the host material on light intensity we develop a model to describe spreading of initial defect upmore » to size appropriate for the first resonant field mode to be formed. Increasing of refraction index due to nonlinear light-matter interaction and existence of high-Q eigenmodes of dielectric sphere can both cause positive feedback`s and result in field instability in the medium. Estimates are obtained of the threshold value of incident-field amplitude.« less

Onset of chaos in helical vortex breakdown at low Reynolds number

NASA Astrophysics Data System (ADS)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

Linear and nonlinear frequency- and time-domain spectroscopy with multiple frequency combs.

PubMed

Bennett, Kochise; Rouxel, Jeremy R; Mukamel, Shaul

2017-09-07

Two techniques that employ equally spaced trains of optical pulses to map an optical high frequency into a low frequency modulation of the signal that can be detected in real time are compared. The development of phase-stable optical frequency combs has opened up new avenues to metrology and spectroscopy. The ability to generate a series of frequency spikes with precisely controlled separation permits a fast, highly accurate sampling of the material response. Recently, pairs of frequency combs with slightly different repetition rates have been utilized to down-convert material susceptibilities from the optical to microwave regime where they can be recorded in real time. We show how this one-dimensional dual comb technique can be extended to multiple dimensions by using several combs. We demonstrate how nonlinear susceptibilities can be quickly acquired using this technique. In a second class of techniques, sequences of ultrafast mode locked laser pulses are used to recover pathways of interactions contributing to nonlinear susceptibilities by using a photo-acoustic modulation varying along the sequences. We show that these techniques can be viewed as a time-domain analog of the multiple frequency comb scheme.

Quantum X waves with orbital angular momentum in nonlinear dispersive media

NASA Astrophysics Data System (ADS)

Ornigotti, Marco; Conti, Claudio; Szameit, Alexander

2018-06-01

We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.

Nonlinear flutter analysis of composite panels

NASA Astrophysics Data System (ADS)

An, Xiaomin; Wang, Yan

2018-05-01

Nonlinear panel flutter is an interesting subject of fluid-structure interaction. In this paper, nonlinear flutter characteristics of curved composite panels are studied in very low supersonic flow. The composite panel with geometric nonlinearity is modeled by a nonlinear finite element method; and the responses are computed by the nonlinear Newmark algorithm. An unsteady aerodynamic solver, which contains a flux splitting scheme and dual time marching technology, is employed in calculating the unsteady pressure of the motion of the panel. Based on a half-step staggered coupled solution, the aeroelastic responses of two composite panels with different radius of R = 5 and R = 2.5 are computed and compared with each other at different dynamic pressure for Ma = 1.05. The nonlinear flutter characteristics comprising limited cycle oscillations and chaos are analyzed and discussed.

One-dimensional optical wave turbulence: Experiment and theory

NASA Astrophysics Data System (ADS)

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

2012-05-01

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

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.

Quantum droplets of light in the presence of synthetic magnetic fields

NASA Astrophysics Data System (ADS)

Wilson, Kali; Westerberg, Niclas; Valiente, Manuel; Duncan, Callum; Wright, Ewan; Ohberg, Patrik; Faccio, Daniele

2017-04-01

Recently, quantum droplets have been demonstrated in dipolar Bose-Einstein condensates, where the long range (nonlocal) attractive interaction is counterbalanced by a local repulsive interaction. In this work, we investigate the formation of quantum droplets in a two-dimensional nonlocal fluid of light. Fluids of light allow us to control the geometry of the system, and thus introduce vorticity which in turn creates an artificial magnetic field for the quantum droplet. In a quantum fluid of light, the photons comprising the fluid are treated as a gas of interacting Bose-particles, where the nonlocal interaction comes from the nonlinearity inherent in the material, in our case an attractive third-order thermo-optical nonlinearity. In contrast to matter-wave droplets, photon fluid droplets are not stabilised by local particle-particle scattering, but from the quantum pressure itself, i.e., a balance between diffraction and the nonlocal nonlinearity. We will present a numerical and analytical investigation of the ground state of these droplets and of their subsequent dynamics under the influence of a self-induced artificial magnetic field, and discuss experimental work with the possibility to include artificial gauge interactions between droplets.

Cross-conditional entropy and coherence analysis of pharmaco-EEG changes induced by alprazolam.

PubMed

Alonso, J F; Mañanas, M A; Romero, S; Rojas-Martínez, M; Riba, J

2012-06-01

Quantitative analysis of electroencephalographic signals (EEG) and their interpretation constitute a helpful tool in the assessment of the bioavailability of psychoactive drugs in the brain. Furthermore, psychotropic drug groups have typical signatures which relate biochemical mechanisms with specific EEG changes. To analyze the pharmacological effect of a dose of alprazolam on the connectivity of the brain during wakefulness by means of linear and nonlinear approaches. EEG signals were recorded after alprazolam administration in a placebo-controlled crossover clinical trial. Nonlinear couplings assessed by means of corrected cross-conditional entropy were compared to linear couplings measured with the classical magnitude squared coherence. Linear variables evidenced a statistically significant drug-induced decrease, whereas nonlinear variables showed significant increases. All changes were highly correlated to drug plasma concentrations. The spatial distribution of the observed connectivity changes clearly differed from a previous study: changes before and after the maximum drug effect were mainly observed over the anterior half of the scalp. Additionally, a new variable with very low computational cost was defined to evaluate nonlinear coupling. This is particularly interesting when all pairs of EEG channels are assessed as in this study. Results showed that alprazolam induced changes in terms of uncoupling between regions of the scalp, with opposite trends depending on the variables: decrease in linear ones and increase in nonlinear features. Maps provided consistent information about the way brain changed in terms of connectivity being definitely necessary to evaluate separately linear and nonlinear interactions.

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.

Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities

NASA Astrophysics Data System (ADS)

Ghaffari, Reza; Sauer, Roger A.

2018-06-01

The nonlinear frequencies of pre-stressed graphene-based structures, such as flat graphene sheets and carbon nanotubes, are calculated. These structures are modeled with a nonlinear hyperelastic shell model. The model is calibrated with quantum mechanics data and is valid for high strains. Analytical solutions of the natural frequencies of various plates are obtained for the Canham bending model by assuming infinitesimal strains. These solutions are used for the verification of the numerical results. The performance of the model is illustrated by means of several examples. Modal analysis is performed for square plates under pure dilatation or uniaxial stretch, circular plates under pure dilatation or under the effects of an adhesive substrate, and carbon nanotubes under uniaxial compression or stretch. The adhesive substrate is modeled with van der Waals interaction (based on the Lennard-Jones potential) and a coarse grained contact model. It is shown that the analytical natural frequencies underestimate the real ones, and this should be considered in the design of devices based on graphene structures.

Validation of a High-Order Prefactored Compact Scheme on Nonlinear Flows with Complex Geometries

NASA Technical Reports Server (NTRS)

Hixon, Ray; Mankbadi, Reda R.; Povinelli, L. A. (Technical Monitor)

2000-01-01

Three benchmark problems are solved using a sixth-order prefactored compact scheme employing an explicit 10th-order filter with optimized fourth-order Runge-Kutta time stepping. The problems solved are the following: (1) propagation of sound waves through a transonic nozzle; (2) shock-sound interaction; and (3) single airfoil gust response. In the first two problems, the spatial accuracy of the scheme is tested on a stretched grid, and the effectiveness of boundary conditions is shown. The solution stability and accuracy near a shock discontinuity is shown as well. Also, 1-D nonlinear characteristic boundary conditions will be evaluated. In the third problem, a nonlinear Euler solver will be used that solves the equations in generalized curvilinear coordinates using the chain rule transformation. This work, continuing earlier work on flat-plate cascades and Joukowski airfoils, will focus mainly on the effect of the grid and boundary conditions on the accuracy of the solution. The grids were generated using a commercially available grid generator, GridPro/az3000.